Daily Papers

Recent advances in Neural Fields have enabled powerful, discretization-invariant methods for learning neural operators that approximate solutions of Partial Differential Equations (PDEs) on general geometries. Building on these developments, we introduce enf2enf, an encoder--decoder methodology for predicting steady-state Partial Differential Equations with non-parameterized geometric variability, based on recently proposed Equivariant Neural Field architectures. In enf2enf, input geometries are encoded into latent point cloud embeddings that inherently preserve geometric grounding and capture local phenomena. The resulting representations are then combined with global parameters and directly decoded into continuous output fields, thus efficiently modeling the coupling between geometry and physics. By leveraging the inductive biases of locality and translation invariance, our approach is able to capture fine-scale physical features as well as complex shape variations, thereby enhancing generalization and physical compliance. Extensive experiments on a high-fidelity aerodynamic dataset, a hyper-elastic material benchmark, and multi-element airfoil geometries, demonstrate that the proposed model achieves superior or competitive performance compared to state-of-the-art graph based, operator learning, and neural field methods. Notably, our method supports real time inference and zero-shot super-resolution, enabling efficient training on low-resolution meshes while maintaining high accuracy on full-scale discretizations.

Semi-Supervised Visual Grounding (SSVG) is a new challenge for its sparse labeled data with the need for multimodel understanding. A previous study, RefTeacher, makes the first attempt to tackle this task by adopting the teacher-student framework to provide pseudo confidence supervision and attention-based supervision. However, this approach is incompatible with current state-of-the-art visual grounding models, which follow the Transformer-based pipeline. These pipelines directly regress results without region proposals or foreground binary classification, rendering them unsuitable for fitting in RefTeacher due to the absence of confidence scores. Furthermore, the geometric difference in teacher and student inputs, stemming from different data augmentations, induces natural misalignment in attention-based constraints. To establish a compatible SSVG framework, our paper proposes the ACTive REtraining approach for Semi-Supervised Visual Grounding, abbreviated as ACTRESS. Initially, the model is enhanced by incorporating an additional quantized detection head to expose its detection confidence. Building upon this, ACTRESS consists of an active sampling strategy and a selective retraining strategy. The active sampling strategy iteratively selects high-quality pseudo labels by evaluating three crucial aspects: Faithfulness, Robustness, and Confidence, optimizing the utilization of unlabeled data. The selective retraining strategy retrains the model with periodic re-initialization of specific parameters, facilitating the model's escape from local minima. Extensive experiments demonstrates our superior performance on widely-used benchmark datasets.

Scene generation with 3D assets presents a complex challenge, requiring both high-level semantic understanding and low-level geometric reasoning. While Multimodal Large Language Models (MLLMs) excel at semantic tasks, their application to 3D scene generation is hindered by their limited grounding on 3D geometry. In this paper, we investigate how to best work with MLLMs in an object placement task. Towards this goal, we introduce a novel framework, FirePlace, that applies existing MLLMs in (1) 3D geometric reasoning and the extraction of relevant geometric details from the 3D scene, (2) constructing and solving geometric constraints on the extracted low-level geometry, and (3) pruning for final placements that conform to common sense. By combining geometric reasoning with real-world understanding of MLLMs, our method can propose object placements that satisfy both geometric constraints as well as high-level semantic common-sense considerations. Our experiments show that these capabilities allow our method to place objects more effectively in complex scenes with intricate geometry, surpassing the quality of prior work.

In this paper, we propose an efficient multi-level convolution architecture for 3D visual grounding. Conventional methods are difficult to meet the requirements of real-time inference due to the two-stage or point-based architecture. Inspired by the success of multi-level fully sparse convolutional architecture in 3D object detection, we aim to build a new 3D visual grounding framework following this technical route. However, as in 3D visual grounding task the 3D scene representation should be deeply interacted with text features, sparse convolution-based architecture is inefficient for this interaction due to the large amount of voxel features. To this end, we propose text-guided pruning (TGP) and completion-based addition (CBA) to deeply fuse 3D scene representation and text features in an efficient way by gradual region pruning and target completion. Specifically, TGP iteratively sparsifies the 3D scene representation and thus efficiently interacts the voxel features with text features by cross-attention. To mitigate the affect of pruning on delicate geometric information, CBA adaptively fixes the over-pruned region by voxel completion with negligible computational overhead. Compared with previous single-stage methods, our method achieves top inference speed and surpasses previous fastest method by 100\% FPS. Our method also achieves state-of-the-art accuracy even compared with two-stage methods, with +1.13 lead of [email protected] on ScanRefer, and +2.6 and +3.2 leads on NR3D and SR3D respectively. The code is available at https://github.com/GWxuan/TSP3D{https://github.com/GWxuan/TSP3D}.

Multimodal Large Language Models (MLLMs) exhibit impressive capabilities across a variety of tasks, especially when equipped with carefully designed visual prompts. However, existing studies primarily focus on logical reasoning and visual understanding, while the capability of MLLMs to operate effectively in 3D vision remains an ongoing area of exploration. In this paper, we introduce a novel visual prompting method, called 3DAxisPrompt, to elicit the 3D understanding capabilities of MLLMs in real-world scenes. More specifically, our method leverages the 3D coordinate axis and masks generated from the Segment Anything Model (SAM) to provide explicit geometric priors to MLLMs and then extend their impressive 2D grounding and reasoning ability to real-world 3D scenarios. Besides, we first provide a thorough investigation of the potential visual prompting formats and conclude our findings to reveal the potential and limits of 3D understanding capabilities in GPT-4o, as a representative of MLLMs. Finally, we build evaluation environments with four datasets, i.e., ScanRefer, ScanNet, FMB, and nuScene datasets, covering various 3D tasks. Based on this, we conduct extensive quantitative and qualitative experiments, which demonstrate the effectiveness of the proposed method. Overall, our study reveals that MLLMs, with the help of 3DAxisPrompt, can effectively perceive an object's 3D position in real-world scenarios. Nevertheless, a single prompt engineering approach does not consistently achieve the best outcomes for all 3D tasks. This study highlights the feasibility of leveraging MLLMs for 3D vision grounding/reasoning with prompt engineering techniques.

The CLEVR dataset has been used extensively in language grounded visual reasoning in Machine Learning (ML) and Natural Language Processing (NLP) domains. We present a graph parser library for CLEVR, that provides functionalities for object-centric attributes and relationships extraction, and construction of structural graph representations for dual modalities. Structural order-invariant representations enable geometric learning and can aid in downstream tasks like language grounding to vision, robotics, compositionality, interpretability, and computational grammar construction. We provide three extensible main components - parser, embedder, and visualizer that can be tailored to suit specific learning setups. We also provide out-of-the-box functionality for seamless integration with popular deep graph neural network (GNN) libraries. Additionally, we discuss downstream usage and applications of the library, and how it accelerates research for the NLP research community.

Recent popularity of Large Language Models (LLMs) has opened countless possibilities in automating numerous AI tasks by connecting LLMs to various domain-specific models or APIs, where LLMs serve as dispatchers while domain-specific models or APIs are action executors. Despite the vast numbers of domain-specific models/APIs, they still struggle to comprehensively cover super diverse automation demands in the interaction between human and User Interfaces (UIs). In this work, we build a multimodal model to ground natural language instructions in given UI screenshots as a generic UI task automation executor. This metadata-free grounding model, consisting of a visual encoder and a language decoder, is first pretrained on well studied document understanding tasks and then learns to decode spatial information from UI screenshots in a promptable way. To facilitate the exploitation of image-to-text pretrained knowledge, we follow the pixel-to-sequence paradigm to predict geometric coordinates in a sequence of tokens using a language decoder. We further propose an innovative Reinforcement Learning (RL) based algorithm to supervise the tokens in such sequence jointly with visually semantic metrics, which effectively strengthens the spatial decoding capability of the pixel-to-sequence paradigm. Extensive experiments demonstrate our proposed reinforced UI instruction grounding model outperforms the state-of-the-art methods by a clear margin and shows the potential as a generic UI task automation API.

3D visual grounding is the task of localizing the object in a 3D scene which is referred by a description in natural language. With a wide range of applications ranging from autonomous indoor robotics to AR/VR, the task has recently risen in popularity. A common formulation to tackle 3D visual grounding is grounding-by-detection, where localization is done via bounding boxes. However, for real-life applications that require physical interactions, a bounding box insufficiently describes the geometry of an object. We therefore tackle the problem of dense 3D visual grounding, i.e. referral-based 3D instance segmentation. We propose a dense 3D grounding network ConcreteNet, featuring three novel stand-alone modules which aim to improve grounding performance for challenging repetitive instances, i.e. instances with distractors of the same semantic class. First, we introduce a bottom-up attentive fusion module that aims to disambiguate inter-instance relational cues, next we construct a contrastive training scheme to induce separation in the latent space, and finally we resolve view-dependent utterances via a learned global camera token. ConcreteNet ranks 1st on the challenging ScanRefer online benchmark by a considerable +9.43% accuracy at 50% IoU and has won the ICCV 3rd Workshop on Language for 3D Scenes "3D Object Localization" challenge.

Affordance grounding refers to the task of finding the area of an object with which one can interact. It is a fundamental but challenging task, as a successful solution requires the comprehensive understanding of a scene in multiple aspects including detection, localization, and recognition of objects with their parts, of geo-spatial configuration/layout of the scene, of 3D shapes and physics, as well as of the functionality and potential interaction of the objects and humans. Much of the knowledge is hidden and beyond the image content with the supervised labels from a limited training set. In this paper, we make an attempt to improve the generalization capability of the current affordance grounding by taking the advantage of the rich world, abstract, and human-object-interaction knowledge from pretrained large-scale vision language models. Under the AGD20K benchmark, our proposed model demonstrates a significant performance gain over the competing methods for in-the-wild object affordance grounding. We further demonstrate it can ground affordance for objects from random Internet images, even if both objects and actions are unseen during training. Project site: https://jasonqsy.github.io/AffordanceLLM/

Although great progress has been made in 3D visual grounding, current models still rely on explicit textual descriptions for grounding and lack the ability to reason human intentions from implicit instructions. We propose a new task called 3D reasoning grounding and introduce a new benchmark ScanReason which provides over 10K question-answer-location pairs from five reasoning types that require the synerization of reasoning and grounding. We further design our approach, ReGround3D, composed of the visual-centric reasoning module empowered by Multi-modal Large Language Model (MLLM) and the 3D grounding module to obtain accurate object locations by looking back to the enhanced geometry and fine-grained details from the 3D scenes. A chain-of-grounding mechanism is proposed to further boost the performance with interleaved reasoning and grounding steps during inference. Extensive experiments on the proposed benchmark validate the effectiveness of our proposed approach.

Grounding natural language in physical 3D environments is essential for the advancement of embodied artificial intelligence. Current datasets and models for 3D visual grounding predominantly focus on identifying and localizing objects from static, object-centric descriptions. These approaches do not adequately address the dynamic and sequential nature of task-oriented grounding necessary for practical applications. In this work, we propose a new task: Task-oriented Sequential Grounding in 3D scenes, wherein an agent must follow detailed step-by-step instructions to complete daily activities by locating a sequence of target objects in indoor scenes. To facilitate this task, we introduce SG3D, a large-scale dataset containing 22,346 tasks with 112,236 steps across 4,895 real-world 3D scenes. The dataset is constructed using a combination of RGB-D scans from various 3D scene datasets and an automated task generation pipeline, followed by human verification for quality assurance. We adapted three state-of-the-art 3D visual grounding models to the sequential grounding task and evaluated their performance on SG3D. Our results reveal that while these models perform well on traditional benchmarks, they face significant challenges with task-oriented sequential grounding, underscoring the need for further research in this area.

Geometry problem solving is a well-recognized testbed for evaluating the high-level multi-modal reasoning capability of deep models. In most existing works, two main geometry problems: calculation and proving, are usually treated as two specific tasks, hindering a deep model to unify its reasoning capability on multiple math tasks. However, in essence, these two tasks have similar problem representations and overlapped math knowledge which can improve the understanding and reasoning ability of a deep model on both two tasks. Therefore, we construct a large-scale Unified Geometry problem benchmark, UniGeo, which contains 4,998 calculation problems and 9,543 proving problems. Each proving problem is annotated with a multi-step proof with reasons and mathematical expressions. The proof can be easily reformulated as a proving sequence that shares the same formats with the annotated program sequence for calculation problems. Naturally, we also present a unified multi-task Geometric Transformer framework, Geoformer, to tackle calculation and proving problems simultaneously in the form of sequence generation, which finally shows the reasoning ability can be improved on both two tasks by unifying formulation. Furthermore, we propose a Mathematical Expression Pretraining (MEP) method that aims to predict the mathematical expressions in the problem solution, thus improving the Geoformer model. Experiments on the UniGeo demonstrate that our proposed Geoformer obtains state-of-the-art performance by outperforming task-specific model NGS with over 5.6% and 3.2% accuracies on calculation and proving problems, respectively.

Automatic math problem solving has recently attracted increasing attention as a long-standing AI benchmark. In this paper, we focus on solving geometric problems, which requires a comprehensive understanding of textual descriptions, visual diagrams, and theorem knowledge. However, the existing methods were highly dependent on handcraft rules and were merely evaluated on small-scale datasets. Therefore, we propose a Geometric Question Answering dataset GeoQA, containing 4,998 geometric problems with corresponding annotated programs, which illustrate the solving process of the given problems. Compared with another publicly available dataset GeoS, GeoQA is 25 times larger, in which the program annotations can provide a practical testbed for future research on explicit and explainable numerical reasoning. Moreover, we introduce a Neural Geometric Solver (NGS) to address geometric problems by comprehensively parsing multimodal information and generating interpretable programs. We further add multiple self-supervised auxiliary tasks on NGS to enhance cross-modal semantic representation. Extensive experiments on GeoQA validate the effectiveness of our proposed NGS and auxiliary tasks. However, the results are still significantly lower than human performance, which leaves large room for future research. Our benchmark and code are released at https://github.com/chen-judge/GeoQA .

3D Visual Grounding (3DVG) aims to locate objects in 3D scenes based on textual descriptions, which is essential for applications like augmented reality and robotics. Traditional 3DVG approaches rely on annotated 3D datasets and predefined object categories, limiting scalability and adaptability. To overcome these limitations, we introduce SeeGround, a zero-shot 3DVG framework leveraging 2D Vision-Language Models (VLMs) trained on large-scale 2D data. We propose to represent 3D scenes as a hybrid of query-aligned rendered images and spatially enriched text descriptions, bridging the gap between 3D data and 2D-VLMs input formats. We propose two modules: the Perspective Adaptation Module, which dynamically selects viewpoints for query-relevant image rendering, and the Fusion Alignment Module, which integrates 2D images with 3D spatial descriptions to enhance object localization. Extensive experiments on ScanRefer and Nr3D demonstrate that our approach outperforms existing zero-shot methods by large margins. Notably, we exceed weakly supervised methods and rival some fully supervised ones, outperforming previous SOTA by 7.7% on ScanRefer and 7.1% on Nr3D, showcasing its effectiveness.

Unified visual grounding pursues a simple and generic technical route to leverage multi-task data with less task-specific design. The most advanced methods typically present boxes and masks as vertex sequences to model referring detection and segmentation as an autoregressive sequential vertex generation paradigm. However, generating high-dimensional vertex sequences sequentially is error-prone because the upstream of the sequence remains static and cannot be refined based on downstream vertex information, even if there is a significant location gap. Besides, with limited vertexes, the inferior fitting of objects with complex contours restricts the performance upper bound. To deal with this dilemma, we propose a parallel vertex generation paradigm for superior high-dimension scalability with a diffusion model by simply modifying the noise dimension. An intuitive materialization of our paradigm is Parallel Vertex Diffusion (PVD) to directly set vertex coordinates as the generation target and use a diffusion model to train and infer. We claim that it has two flaws: (1) unnormalized coordinate caused a high variance of loss value; (2) the original training objective of PVD only considers point consistency but ignores geometry consistency. To solve the first flaw, Center Anchor Mechanism (CAM) is designed to convert coordinates as normalized offset values to stabilize the training loss value. For the second flaw, Angle summation loss (ASL) is designed to constrain the geometry difference of prediction and ground truth vertexes for geometry-level consistency. Empirical results show that our PVD achieves state-of-the-art in both referring detection and segmentation, and our paradigm is more scalable and efficient than sequential vertex generation with high-dimension data.

3D Visual Grounding (3DVG) aims at localizing 3D object based on textual descriptions. Conventional supervised methods for 3DVG often necessitate extensive annotations and a predefined vocabulary, which can be restrictive. To address this issue, we propose a novel visual programming approach for zero-shot open-vocabulary 3DVG, leveraging the capabilities of large language models (LLMs). Our approach begins with a unique dialog-based method, engaging with LLMs to establish a foundational understanding of zero-shot 3DVG. Building on this, we design a visual program that consists of three types of modules, i.e., view-independent, view-dependent, and functional modules. These modules, specifically tailored for 3D scenarios, work collaboratively to perform complex reasoning and inference. Furthermore, we develop an innovative language-object correlation module to extend the scope of existing 3D object detectors into open-vocabulary scenarios. Extensive experiments demonstrate that our zero-shot approach can outperform some supervised baselines, marking a significant stride towards effective 3DVG.

Remote sensing (RS) visual grounding aims to use natural language expression to locate specific objects (in the form of the bounding box or segmentation mask) in RS images, enhancing human interaction with intelligent RS interpretation systems. Early research in this area was primarily based on horizontal bounding boxes (HBBs), but as more diverse RS datasets have become available, tasks involving oriented bounding boxes (OBBs) and segmentation masks have emerged. In practical applications, different targets require different grounding types: HBB can localize an object's position, OBB provides its orientation, and mask depicts its shape. However, existing specialized methods are typically tailored to a single type of RS visual grounding task and are hard to generalize across tasks. In contrast, large vision-language models (VLMs) exhibit powerful multi-task learning capabilities but struggle to handle dense prediction tasks like segmentation. This paper proposes GeoGround, a novel framework that unifies support for HBB, OBB, and mask RS visual grounding tasks, allowing flexible output selection. Rather than customizing the architecture of VLM, our work aims to elegantly support pixel-level visual grounding output through the Text-Mask technique. We define prompt-assisted and geometry-guided learning to enhance consistency across different signals. To support model training, we present refGeo, a large-scale RS visual instruction-following dataset containing 161k image-text pairs. Experimental results show that GeoGround demonstrates strong performance across four RS visual grounding tasks, matching or surpassing the performance of specialized methods on multiple benchmarks. Code available at https://github.com/zytx121/GeoGround

Grounding 3D object affordance seeks to locate objects' ''action possibilities'' regions in the 3D space, which serves as a link between perception and operation for embodied agents. Existing studies primarily focus on connecting visual affordances with geometry structures, e.g. relying on annotations to declare interactive regions of interest on the object and establishing a mapping between the regions and affordances. However, the essence of learning object affordance is to understand how to use it, and the manner that detaches interactions is limited in generalization. Normally, humans possess the ability to perceive object affordances in the physical world through demonstration images or videos. Motivated by this, we introduce a novel task setting: grounding 3D object affordance from 2D interactions in images, which faces the challenge of anticipating affordance through interactions of different sources. To address this problem, we devise a novel Interaction-driven 3D Affordance Grounding Network (IAG), which aligns the region feature of objects from different sources and models the interactive contexts for 3D object affordance grounding. Besides, we collect a Point-Image Affordance Dataset (PIAD) to support the proposed task. Comprehensive experiments on PIAD demonstrate the reliability of the proposed task and the superiority of our method. The project is available at https://github.com/yyvhang/IAGNet.

3D visual grounding is the ability to localize objects in 3D scenes conditioned by utterances. Most existing methods devote the referring head to localize the referred object directly, causing failure in complex scenarios. In addition, it does not illustrate how and why the network reaches the final decision. In this paper, we address this question Can we design an interpretable 3D visual grounding framework that has the potential to mimic the human perception system?. To this end, we formulate the 3D visual grounding problem as a sequence-to-sequence task by first predicting a chain of anchors and then the final target. Interpretability not only improves the overall performance but also helps us identify failure cases. Following the chain of thoughts approach enables us to decompose the referring task into interpretable intermediate steps, boosting the performance and making our framework extremely data-efficient. Moreover, our proposed framework can be easily integrated into any existing architecture. We validate our approach through comprehensive experiments on the Nr3D, Sr3D, and Scanrefer benchmarks and show consistent performance gains compared to existing methods without requiring manually annotated data. Furthermore, our proposed framework, dubbed CoT3DRef, is significantly data-efficient, whereas on the Sr3D dataset, when trained only on 10% of the data, we match the SOTA performance that trained on the entire data.

Problems involving geometric data arise in a variety of fields, including computer vision, robotics, chemistry, and physics. Such data can take numerous forms, such as points, direction vectors, planes, or transformations, but to date there is no single architecture that can be applied to such a wide variety of geometric types while respecting their symmetries. In this paper we introduce the Geometric Algebra Transformer (GATr), a general-purpose architecture for geometric data. GATr represents inputs, outputs, and hidden states in the projective geometric algebra, which offers an efficient 16-dimensional vector space representation of common geometric objects as well as operators acting on them. GATr is equivariant with respect to E(3), the symmetry group of 3D Euclidean space. As a transformer, GATr is scalable, expressive, and versatile. In experiments with n-body modeling and robotic planning, GATr shows strong improvements over non-geometric baselines.

We propose GroundUp, the first sketch-based ideation tool for 3D city massing of urban areas. We focus on early-stage urban design, where sketching is a common tool and the design starts from balancing building volumes (masses) and open spaces. With Human-Centered AI in mind, we aim to help architects quickly revise their ideas by easily switching between 2D sketches and 3D models, allowing for smoother iteration and sharing of ideas. Inspired by feedback from architects and existing workflows, our system takes as a first input a user sketch of multiple buildings in a top-down view. The user then draws a perspective sketch of the envisioned site. Our method is designed to exploit the complementarity of information in the two sketches and allows users to quickly preview and adjust the inferred 3D shapes. Our model has two main components. First, we propose a novel sketch-to-depth prediction network for perspective sketches that exploits top-down sketch shapes. Second, we use depth cues derived from the perspective sketch as a condition to our diffusion model, which ultimately completes the geometry in a top-down view. Thus, our final 3D geometry is represented as a heightfield, allowing users to construct the city `from the ground up'.

3D visual grounding (3DVG), which aims to correlate a natural language description with the target object within a 3D scene, is a significant yet challenging task. Despite recent advancements in this domain, existing approaches commonly encounter a shortage: a limited amount and diversity of text3D pairs available for training. Moreover, they fall short in effectively leveraging different contextual clues (e.g., rich spatial relations within the 3D visual space) for grounding. To address these limitations, we propose AugRefer, a novel approach for advancing 3D visual grounding. AugRefer introduces cross-modal augmentation designed to extensively generate diverse text-3D pairs by placing objects into 3D scenes and creating accurate and semantically rich descriptions using foundation models. Notably, the resulting pairs can be utilized by any existing 3DVG methods for enriching their training data. Additionally, AugRefer presents a language-spatial adaptive decoder that effectively adapts the potential referring objects based on the language description and various 3D spatial relations. Extensive experiments on three benchmark datasets clearly validate the effectiveness of AugRefer.

3D visual grounding (3DVG) is challenging because of the requirement of understanding on visual information, language and spatial relationships. While supervised approaches have achieved superior performance, they are constrained by the scarcity and high cost of 3D vision-language datasets. On the other hand, LLM/VLM based agents are proposed for 3DVG, eliminating the need for training data. However, these methods incur prohibitive time and token costs during inference. To address the challenges, we introduce a novel training-free symbolic framework for 3D visual grounding, namely Evolvable Symbolic Visual Grounder, that offers significantly reduced inference costs compared to previous agent-based methods while maintaining comparable performance. EaSe uses LLM generated codes to compute on spatial relationships. EaSe also implements an automatic pipeline to evaluate and optimize the quality of these codes and integrate VLMs to assist in the grounding process. Experimental results demonstrate that EaSe achieves 52.9% accuracy on Nr3D dataset and 49.2% [email protected] on ScanRefer, which is top-tier among training-free methods. Moreover, it substantially reduces the inference time and cost, offering a balanced trade-off between performance and efficiency. Codes are available at https://github.com/OpenRobotLab/EaSe.

From a single image, visual cues can help deduce intrinsic and extrinsic camera parameters like the focal length and the gravity direction. This single-image calibration can benefit various downstream applications like image editing and 3D mapping. Current approaches to this problem are based on either classical geometry with lines and vanishing points or on deep neural networks trained end-to-end. The learned approaches are more robust but struggle to generalize to new environments and are less accurate than their classical counterparts. We hypothesize that they lack the constraints that 3D geometry provides. In this work, we introduce GeoCalib, a deep neural network that leverages universal rules of 3D geometry through an optimization process. GeoCalib is trained end-to-end to estimate camera parameters and learns to find useful visual cues from the data. Experiments on various benchmarks show that GeoCalib is more robust and more accurate than existing classical and learned approaches. Its internal optimization estimates uncertainties, which help flag failure cases and benefit downstream applications like visual localization. The code and trained models are publicly available at https://github.com/cvg/GeoCalib.

Geometric methods for solving open-world off-road navigation tasks, by learning occupancy and metric maps, provide good generalization but can be brittle in outdoor environments that violate their assumptions (e.g., tall grass). Learning-based methods can directly learn collision-free behavior from raw observations, but are difficult to integrate with standard geometry-based pipelines. This creates an unfortunate conflict -- either use learning and lose out on well-understood geometric navigational components, or do not use it, in favor of extensively hand-tuned geometry-based cost maps. In this work, we reject this dichotomy by designing the learning and non-learning-based components in a way such that they can be effectively combined in a self-supervised manner. Both components contribute to a planning criterion: the learned component contributes predicted traversability as rewards, while the geometric component contributes obstacle cost information. We instantiate and comparatively evaluate our system in both in-distribution and out-of-distribution environments, showing that this approach inherits complementary gains from the learned and geometric components and significantly outperforms either of them. Videos of our results are hosted at https://sites.google.com/view/hybrid-imitative-planning

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges, such as handling thin structures and non-watertight geometries, which limit their flexibility and accuracy. In contrast, we propose a novel geometric data representation that models geometry as distributions-a powerful representation that makes no assumptions about surface genus, connectivity, or boundary conditions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions, capturing fine-grained geometric details. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity. Additionally, we explore applications using our representation, such as textured mesh representation, neural surface compression, dynamic object modeling, and rendering, highlighting its potential to advance 3D geometric learning.

Multimodal large language models (MLLMs) have made rapid progress in recent years, yet continue to struggle with low-level visual perception (LLVP) -- particularly the ability to accurately describe the geometric details of an image. This capability is crucial for applications in areas such as robotics, medical image analysis, and manufacturing. In this paper, we first introduce Geoperception, a benchmark designed to evaluate an MLLM's ability to accurately transcribe 2D geometric information from an image. Using this benchmark, we demonstrate the limitations of leading MLLMs, and then conduct a comprehensive empirical study to explore strategies for improving their performance on geometric tasks. Our findings highlight the benefits of certain model architectures, training techniques, and data strategies, including the use of high-fidelity synthetic data and multi-stage training with a data curriculum. Notably, we find that a data curriculum enables models to learn challenging geometry understanding tasks which they fail to learn from scratch. Leveraging these insights, we develop Euclid, a family of models specifically optimized for strong low-level geometric perception. Although purely trained on synthetic multimodal data, Euclid shows strong generalization ability to novel geometry shapes. For instance, Euclid outperforms the best closed-source model, Gemini-1.5-Pro, by up to 58.56% on certain Geoperception benchmark tasks and 10.65% on average across all tasks.

3D visual grounding is a critical skill for household robots, enabling them to navigate, manipulate objects, and answer questions based on their environment. While existing approaches often rely on extensive labeled data or exhibit limitations in handling complex language queries, we propose LLM-Grounder, a novel zero-shot, open-vocabulary, Large Language Model (LLM)-based 3D visual grounding pipeline. LLM-Grounder utilizes an LLM to decompose complex natural language queries into semantic constituents and employs a visual grounding tool, such as OpenScene or LERF, to identify objects in a 3D scene. The LLM then evaluates the spatial and commonsense relations among the proposed objects to make a final grounding decision. Our method does not require any labeled training data and can generalize to novel 3D scenes and arbitrary text queries. We evaluate LLM-Grounder on the ScanRefer benchmark and demonstrate state-of-the-art zero-shot grounding accuracy. Our findings indicate that LLMs significantly improve the grounding capability, especially for complex language queries, making LLM-Grounder an effective approach for 3D vision-language tasks in robotics. Videos and interactive demos can be found on the project website https://chat-with-nerf.github.io/ .

3D visual grounding involves finding a target object in a 3D scene that corresponds to a given sentence query. Although many approaches have been proposed and achieved impressive performance, they all require dense object-sentence pair annotations in 3D point clouds, which are both time-consuming and expensive. To address the problem that fine-grained annotated data is difficult to obtain, we propose to leverage weakly supervised annotations to learn the 3D visual grounding model, i.e., only coarse scene-sentence correspondences are used to learn object-sentence links. To accomplish this, we design a novel semantic matching model that analyzes the semantic similarity between object proposals and sentences in a coarse-to-fine manner. Specifically, we first extract object proposals and coarsely select the top-K candidates based on feature and class similarity matrices. Next, we reconstruct the masked keywords of the sentence using each candidate one by one, and the reconstructed accuracy finely reflects the semantic similarity of each candidate to the query. Additionally, we distill the coarse-to-fine semantic matching knowledge into a typical two-stage 3D visual grounding model, which reduces inference costs and improves performance by taking full advantage of the well-studied structure of the existing architectures. We conduct extensive experiments on ScanRefer, Nr3D, and Sr3D, which demonstrate the effectiveness of our proposed method.

This paper aims to develop an accurate 3D geometry representation of satellite images using satellite-ground image pairs. Our focus is on the challenging problem of 3D-aware ground-views synthesis from a satellite image. We draw inspiration from the density field representation used in volumetric neural rendering and propose a new approach, called Sat2Density. Our method utilizes the properties of ground-view panoramas for the sky and non-sky regions to learn faithful density fields of 3D scenes in a geometric perspective. Unlike other methods that require extra depth information during training, our Sat2Density can automatically learn accurate and faithful 3D geometry via density representation without depth supervision. This advancement significantly improves the ground-view panorama synthesis task. Additionally, our study provides a new geometric perspective to understand the relationship between satellite and ground-view images in 3D space.

Proving geometric theorems constitutes a hallmark of visual reasoning combining both intuitive and logical skills. Therefore, automated theorem proving of Olympiad-level geometry problems is considered a notable milestone in human-level automated reasoning. The introduction of AlphaGeometry, a neuro-symbolic model trained with 100 million synthetic samples, marked a major breakthrough. It solved 25 of 30 International Mathematical Olympiad (IMO) problems whereas the reported baseline based on Wu's method solved only ten. In this note, we revisit the IMO-AG-30 Challenge introduced with AlphaGeometry, and find that Wu's method is surprisingly strong. Wu's method alone can solve 15 problems, and some of them are not solved by any of the other methods. This leads to two key findings: (i) Combining Wu's method with the classic synthetic methods of deductive databases and angle, ratio, and distance chasing solves 21 out of 30 methods by just using a CPU-only laptop with a time limit of 5 minutes per problem. Essentially, this classic method solves just 4 problems less than AlphaGeometry and establishes the first fully symbolic baseline strong enough to rival the performance of an IMO silver medalist. (ii) Wu's method even solves 2 of the 5 problems that AlphaGeometry failed to solve. Thus, by combining AlphaGeometry with Wu's method we set a new state-of-the-art for automated theorem proving on IMO-AG-30, solving 27 out of 30 problems, the first AI method which outperforms an IMO gold medalist.

The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data that is inherently nonEuclidean. This data can exhibit intricate geometric, topological and algebraic structure: from the geometry of the curvature of space-time, to topologically complex interactions between neurons in the brain, to the algebraic transformations describing symmetries of physical systems. Extracting knowledge from such non-Euclidean data necessitates a broader mathematical perspective. Echoing the 19th-century revolutions that gave rise to non-Euclidean geometry, an emerging line of research is redefining modern machine learning with non-Euclidean structures. Its goal: generalizing classical methods to unconventional data types with geometry, topology, and algebra. In this review, we provide an accessible gateway to this fast-growing field and propose a graphical taxonomy that integrates recent advances into an intuitive unified framework. We subsequently extract insights into current challenges and highlight exciting opportunities for future development in this field.

Recent advancements in 3D object reconstruction from single images have primarily focused on improving the accuracy of object shapes. Yet, these techniques often fail to accurately capture the inter-relation between the object, ground, and camera. As a result, the reconstructed objects often appear floating or tilted when placed on flat surfaces. This limitation significantly affects 3D-aware image editing applications like shadow rendering and object pose manipulation. To address this issue, we introduce ORG (Object Reconstruction with Ground), a novel task aimed at reconstructing 3D object geometry in conjunction with the ground surface. Our method uses two compact pixel-level representations to depict the relationship between camera, object, and ground. Experiments show that the proposed ORG model can effectively reconstruct object-ground geometry on unseen data, significantly enhancing the quality of shadow generation and pose manipulation compared to conventional single-image 3D reconstruction techniques.

3D vision-language grounding, which focuses on aligning language with the 3D physical environment, stands as a cornerstone in the development of embodied agents. In comparison to recent advancements in the 2D domain, grounding language in 3D scenes faces several significant challenges: (i) the inherent complexity of 3D scenes due to the diverse object configurations, their rich attributes, and intricate relationships; (ii) the scarcity of paired 3D vision-language data to support grounded learning; and (iii) the absence of a unified learning framework to distill knowledge from grounded 3D data. In this work, we aim to address these three major challenges in 3D vision-language by examining the potential of systematically upscaling 3D vision-language learning in indoor environments. We introduce the first million-scale 3D vision-language dataset, SceneVerse, encompassing about 68K 3D indoor scenes and comprising 2.5M vision-language pairs derived from both human annotations and our scalable scene-graph-based generation approach. We demonstrate that this scaling allows for a unified pre-training framework, Grounded Pre-training for Scenes (GPS), for 3D vision-language learning. Through extensive experiments, we showcase the effectiveness of GPS by achieving state-of-the-art performance on all existing 3D visual grounding benchmarks. The vast potential of SceneVerse and GPS is unveiled through zero-shot transfer experiments in the challenging 3D vision-language tasks. Project website: https://scene-verse.github.io .

Learning to manipulate dynamic and deformable objects from a single demonstration video holds great promise in terms of scalability. Previous approaches have predominantly focused on either replaying object relationships or actor trajectories. The former often struggles to generalize across diverse tasks, while the latter suffers from data inefficiency. Moreover, both methodologies encounter challenges in capturing invisible physical attributes, such as forces. In this paper, we propose to interpret video demonstrations through Parameterized Symbolic Abstraction Graphs (PSAG), where nodes represent objects and edges denote relationships between objects. We further ground geometric constraints through simulation to estimate non-geometric, visually imperceptible attributes. The augmented PSAG is then applied in real robot experiments. Our approach has been validated across a range of tasks, such as Cutting Avocado, Cutting Vegetable, Pouring Liquid, Rolling Dough, and Slicing Pizza. We demonstrate successful generalization to novel objects with distinct visual and physical properties.

Despite their proficiency in general tasks, Multi-modal Large Language Models (MLLMs) struggle with automatic Geometry Problem Solving (GPS), which demands understanding diagrams, interpreting symbols, and performing complex reasoning. This limitation arises from their pre-training on natural images and texts, along with the lack of automated verification in the problem-solving process. Besides, current geometric specialists are limited by their task-specific designs, making them less effective for broader geometric problems. To this end, we present GeoX, a multi-modal large model focusing on geometric understanding and reasoning tasks. Given the significant differences between geometric diagram-symbol and natural image-text, we introduce unimodal pre-training to develop a diagram encoder and symbol decoder, enhancing the understanding of geometric images and corpora. Furthermore, we introduce geometry-language alignment, an effective pre-training paradigm that bridges the modality gap between unimodal geometric experts. We propose a Generator-And-Sampler Transformer (GS-Former) to generate discriminative queries and eliminate uninformative representations from unevenly distributed geometric signals. Finally, GeoX benefits from visual instruction tuning, empowering it to take geometric images and questions as input and generate verifiable solutions. Experiments show that GeoX outperforms both generalists and geometric specialists on publicly recognized benchmarks, such as GeoQA, UniGeo, Geometry3K, and PGPS9k.

We introduce the task of localizing a flexible number of objects in real-world 3D scenes using natural language descriptions. Existing 3D visual grounding tasks focus on localizing a unique object given a text description. However, such a strict setting is unnatural as localizing potentially multiple objects is a common need in real-world scenarios and robotic tasks (e.g., visual navigation and object rearrangement). To address this setting we propose Multi3DRefer, generalizing the ScanRefer dataset and task. Our dataset contains 61926 descriptions of 11609 objects, where zero, single or multiple target objects are referenced by each description. We also introduce a new evaluation metric and benchmark methods from prior work to enable further investigation of multi-modal 3D scene understanding. Furthermore, we develop a better baseline leveraging 2D features from CLIP by rendering object proposals online with contrastive learning, which outperforms the state of the art on the ScanRefer benchmark.

The topic of stitching images with globally natural structures holds paramount significance. Current methodologies exhibit the ability to preserve local geometric structures, yet fall short in maintaining relationships between these geometric structures. In this paper, we endeavor to safeguard the overall, OBJect-level structures within images based on Global Similarity Prior, while concurrently mitigating distortion and ghosting artifacts with OBJ-GSP. Our approach leverages the Segment Anything Model to extract geometric structures with semantic information, enhancing the algorithm's ability to preserve objects in a manner that aligns more intuitively with human perception. We seek to identify spatial constraints that govern the relationships between various geometric boundaries. Recognizing that multiple geometric boundaries collectively define complete objects, we employ triangular meshes to safeguard not only individual geometric structures but also the overall shapes of objects within the images. Empirical evaluations across multiple image stitching datasets demonstrate that our method establishes a new state-of-the-art benchmark in image stitching. Our implementation and dataset is publicly available at https://github.com/RussRobin/OBJ-GSP .

3D visual grounding is an emerging research area dedicated to making connections between the 3D physical world and natural language, which is crucial for achieving embodied intelligence. In this paper, we propose DASANet, a Dual Attribute-Spatial relation Alignment Network that separately models and aligns object attributes and spatial relation features between language and 3D vision modalities. We decompose both the language and 3D point cloud input into two separate parts and design a dual-branch attention module to separately model the decomposed inputs while preserving global context in attribute-spatial feature fusion by cross attentions. Our DASANet achieves the highest grounding accuracy 65.1% on the Nr3D dataset, 1.3% higher than the best competitor. Besides, the visualization of the two branches proves that our method is efficient and highly interpretable.

Visual grounding, a crucial vision-language task involving the understanding of the visual context based on the query expression, necessitates the model to capture the interactions between objects, as well as various spatial and attribute information. However, the annotation data of visual grounding task is limited due to its time-consuming and labor-intensive annotation process, resulting in the trained models being constrained from generalizing its capability to a broader domain. To address this challenge, we propose GroundVLP, a simple yet effective zero-shot method that harnesses visual grounding ability from the existing models trained from image-text pairs and pure object detection data, both of which are more conveniently obtainable and offer a broader domain compared to visual grounding annotation data. GroundVLP proposes a fusion mechanism that combines the heatmap from GradCAM and the object proposals of open-vocabulary detectors. We demonstrate that the proposed method significantly outperforms other zero-shot methods on RefCOCO/+/g datasets, surpassing prior zero-shot state-of-the-art by approximately 28\% on the test split of RefCOCO and RefCOCO+. Furthermore, GroundVLP performs comparably to or even better than some non-VLP-based supervised models on the Flickr30k entities dataset. Our code is available at https://github.com/om-ai-lab/GroundVLP.

Data heterogeneity in federated learning, characterized by a significant misalignment between local and global distributions, leads to divergent local optimization directions and hinders global model training. Existing studies mainly focus on optimizing local updates or global aggregation, but these indirect approaches demonstrate instability when handling highly heterogeneous data distributions, especially in scenarios where label skew and domain skew coexist. To address this, we propose a geometry-guided data generation method that centers on simulating the global embedding distribution locally. We first introduce the concept of the geometric shape of an embedding distribution and then address the challenge of obtaining global geometric shapes under privacy constraints. Subsequently, we propose GGEUR, which leverages global geometric shapes to guide the generation of new samples, enabling a closer approximation to the ideal global distribution. In single-domain scenarios, we augment samples based on global geometric shapes to enhance model generalization; in multi-domain scenarios, we further employ class prototypes to simulate the global distribution across domains. Extensive experimental results demonstrate that our method significantly enhances the performance of existing approaches in handling highly heterogeneous data, including scenarios with label skew, domain skew, and their coexistence. Code published at: https://github.com/WeiDai-David/2025CVPR_GGEUR

Geometric Deep Learning has recently made striking progress with the advent of continuous deep implicit fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid, resulting in a learnable parameterization that is unlimited in resolution. Unfortunately, these methods are often unsuitable for applications that require an explicit mesh-based surface representation because converting an implicit field to such a representation relies on the Marching Cubes algorithm, which cannot be differentiated with respect to the underlying implicit field. In this work, we remove this limitation and introduce a differentiable way to produce explicit surface mesh representations from Deep Implicit Fields. Our key insight is that by reasoning on how implicit field perturbations impact local surface geometry, one can ultimately differentiate the 3D location of surface samples with respect to the underlying deep implicit field. We exploit this to define DeepMesh - an end-to-end differentiable mesh representation that can vary its topology. We validate our theoretical insight through several applications: Single view 3D Reconstruction via Differentiable Rendering, Physically-Driven Shape Optimization, Full Scene 3D Reconstruction from Scans and End-to-End Training. In all cases our end-to-end differentiable parameterization gives us an edge over state-of-the-art algorithms.

We introduce ORIGEN, the first zero-shot method for 3D orientation grounding in text-to-image generation across multiple objects and diverse categories. While previous work on spatial grounding in image generation has mainly focused on 2D positioning, it lacks control over 3D orientation. To address this, we propose a reward-guided sampling approach using a pretrained discriminative model for 3D orientation estimation and a one-step text-to-image generative flow model. While gradient-ascent-based optimization is a natural choice for reward-based guidance, it struggles to maintain image realism. Instead, we adopt a sampling-based approach using Langevin dynamics, which extends gradient ascent by simply injecting random noise--requiring just a single additional line of code. Additionally, we introduce adaptive time rescaling based on the reward function to accelerate convergence. Our experiments show that ORIGEN outperforms both training-based and test-time guidance methods across quantitative metrics and user studies.

We propose a system for rearranging objects in a scene to achieve a desired object-scene placing relationship, such as a book inserted in an open slot of a bookshelf. The pipeline generalizes to novel geometries, poses, and layouts of both scenes and objects, and is trained from demonstrations to operate directly on 3D point clouds. Our system overcomes challenges associated with the existence of many geometrically-similar rearrangement solutions for a given scene. By leveraging an iterative pose de-noising training procedure, we can fit multi-modal demonstration data and produce multi-modal outputs while remaining precise and accurate. We also show the advantages of conditioning on relevant local geometric features while ignoring irrelevant global structure that harms both generalization and precision. We demonstrate our approach on three distinct rearrangement tasks that require handling multi-modality and generalization over object shape and pose in both simulation and the real world. Project website, code, and videos: https://anthonysimeonov.github.io/rpdiff-multi-modal/

3D scene generation has quickly become a challenging new research direction, fueled by consistent improvements of 2D generative diffusion models. Most prior work in this area generates scenes by iteratively stitching newly generated frames with existing geometry. These works often depend on pre-trained monocular depth estimators to lift the generated images into 3D, fusing them with the existing scene representation. These approaches are then often evaluated via a text metric, measuring the similarity between the generated images and a given text prompt. In this work, we make two fundamental contributions to the field of 3D scene generation. First, we note that lifting images to 3D with a monocular depth estimation model is suboptimal as it ignores the geometry of the existing scene. We thus introduce a novel depth completion model, trained via teacher distillation and self-training to learn the 3D fusion process, resulting in improved geometric coherence of the scene. Second, we introduce a new benchmarking scheme for scene generation methods that is based on ground truth geometry, and thus measures the quality of the structure of the scene.

3D visual grounding aims to find the object within point clouds mentioned by free-form natural language descriptions with rich semantic cues. However, existing methods either extract the sentence-level features coupling all words or focus more on object names, which would lose the word-level information or neglect other attributes. To alleviate these issues, we present EDA that Explicitly Decouples the textual attributes in a sentence and conducts Dense Alignment between such fine-grained language and point cloud objects. Specifically, we first propose a text decoupling module to produce textual features for every semantic component. Then, we design two losses to supervise the dense matching between two modalities: position alignment loss and semantic alignment loss. On top of that, we further introduce a new visual grounding task, locating objects without object names, which can thoroughly evaluate the model's dense alignment capacity. Through experiments, we achieve state-of-the-art performance on two widely-adopted 3D visual grounding datasets, ScanRefer and SR3D/NR3D, and obtain absolute leadership on our newly-proposed task. The source code is available at https://github.com/yanmin-wu/EDA.

Recent advances in large multimodal models (LMMs) have recognized fine-grained grounding as an imperative factor of visual understanding and dialogue. However, the benefits of such representation in LMMs are limited to the natural image domain, and these models perform poorly for remote sensing (RS). The distinct overhead viewpoint, scale variation, and presence of small objects in high-resolution RS imagery present a unique challenge in region-level comprehension. Moreover, the development of the grounding conversation capability of LMMs within RS is hindered by the lack of granular, RS domain-specific grounded data. Addressing these limitations, we propose GeoPixel - the first end-to-end high resolution RS-LMM that supports pixel-level grounding. This capability allows fine-grained visual perception by generating interleaved masks in conversation. GeoPixel supports up to 4K HD resolution in any aspect ratio, ideal for high-precision RS image analysis. To support the grounded conversation generation (GCG) in RS imagery, we curate a visually grounded dataset GeoPixelD through a semi-automated pipeline that utilizes set-of-marks prompting and spatial priors tailored for RS data to methodically control the data generation process. GeoPixel demonstrates superior performance in pixel-level comprehension, surpassing existing LMMs in both single-target and multi-target segmentation tasks. Our methodological ablation studies validate the effectiveness of each component in the overall architecture. Our code and data will be publicly released.

Predicting realistic ground views from satellite imagery in urban scenes is a challenging task due to the significant view gaps between satellite and ground-view images. We propose a novel pipeline to tackle this challenge, by generating geospecifc views that maximally respect the weak geometry and texture from multi-view satellite images. Different from existing approaches that hallucinate images from cues such as partial semantics or geometry from overhead satellite images, our method directly predicts ground-view images at geolocation by using a comprehensive set of information from the satellite image, resulting in ground-level images with a resolution boost at a factor of ten or more. We leverage a novel building refinement method to reduce geometric distortions in satellite data at ground level, which ensures the creation of accurate conditions for view synthesis using diffusion networks. Moreover, we proposed a novel geospecific prior, which prompts distribution learning of diffusion models to respect image samples that are closer to the geolocation of the predicted images. We demonstrate our pipeline is the first to generate close-to-real and geospecific ground views merely based on satellite images.

We present GeoManip, a framework to enable generalist robots to leverage essential conditions derived from object and part relationships, as geometric constraints, for robot manipulation. For example, cutting the carrot requires adhering to a geometric constraint: the blade of the knife should be perpendicular to the carrot's direction. By interpreting these constraints through symbolic language representations and translating them into low-level actions, GeoManip bridges the gap between natural language and robotic execution, enabling greater generalizability across diverse even unseen tasks, objects, and scenarios. Unlike vision-language-action models that require extensive training, operates training-free by utilizing large foundational models: a constraint generation module that predicts stage-specific geometric constraints and a geometry parser that identifies object parts involved in these constraints. A solver then optimizes trajectories to satisfy inferred constraints from task descriptions and the scene. Furthermore, GeoManip learns in-context and provides five appealing human-robot interaction features: on-the-fly policy adaptation, learning from human demonstrations, learning from failure cases, long-horizon action planning, and efficient data collection for imitation learning. Extensive evaluations on both simulations and real-world scenarios demonstrate GeoManip's state-of-the-art performance, with superior out-of-distribution generalization while avoiding costly model training.

Localizing objects in 3D scenes according to the semantics of a given natural language is a fundamental yet important task in the field of multimedia understanding, which benefits various real-world applications such as robotics and autonomous driving. However, the majority of existing 3D object grounding methods are restricted to a single-sentence input describing an individual object, which cannot comprehend and reason more contextualized descriptions of multiple objects in more practical 3D cases. To this end, we introduce a new challenging task, called 3D Dense Object Grounding (3D DOG), to jointly localize multiple objects described in a more complicated paragraph rather than a single sentence. Instead of naively localizing each sentence-guided object independently, we found that dense objects described in the same paragraph are often semantically related and spatially located in a focused region of the 3D scene. To explore such semantic and spatial relationships of densely referred objects for more accurate localization, we propose a novel Stacked Transformer based framework for 3D DOG, named 3DOGSFormer. Specifically, we first devise a contextual query-driven local transformer decoder to generate initial grounding proposals for each target object. Then, we employ a proposal-guided global transformer decoder that exploits the local object features to learn their correlation for further refining initial grounding proposals. Extensive experiments on three challenging benchmarks (Nr3D, Sr3D, and ScanRefer) show that our proposed 3DOGSFormer outperforms state-of-the-art 3D single-object grounding methods and their dense-object variants by significant margins.

We present a novel generative 3D modeling system, coined CraftsMan, which can generate high-fidelity 3D geometries with highly varied shapes, regular mesh topologies, and detailed surfaces, and, notably, allows for refining the geometry in an interactive manner. Despite the significant advancements in 3D generation, existing methods still struggle with lengthy optimization processes, irregular mesh topologies, noisy surfaces, and difficulties in accommodating user edits, consequently impeding their widespread adoption and implementation in 3D modeling software. Our work is inspired by the craftsman, who usually roughs out the holistic figure of the work first and elaborates the surface details subsequently. Specifically, we employ a 3D native diffusion model, which operates on latent space learned from latent set-based 3D representations, to generate coarse geometries with regular mesh topology in seconds. In particular, this process takes as input a text prompt or a reference image and leverages a powerful multi-view (MV) diffusion model to generate multiple views of the coarse geometry, which are fed into our MV-conditioned 3D diffusion model for generating the 3D geometry, significantly improving robustness and generalizability. Following that, a normal-based geometry refiner is used to significantly enhance the surface details. This refinement can be performed automatically, or interactively with user-supplied edits. Extensive experiments demonstrate that our method achieves high efficacy in producing superior-quality 3D assets compared to existing methods. HomePage: https://craftsman3d.github.io/, Code: https://github.com/wyysf-98/CraftsMan

Aerial imagery analysis is critical for many research fields. However, obtaining frequent high-quality aerial images is not always accessible due to its high effort and cost requirements. One solution is to use the Ground-to-Aerial (G2A) technique to synthesize aerial images from easily collectible ground images. However, G2A is rarely studied, because of its challenges, including but not limited to, the drastic view changes, occlusion, and range of visibility. In this paper, we present a novel Geometric Preserving Ground-to-Aerial (G2A) image synthesis (GPG2A) model that can generate realistic aerial images from ground images. GPG2A consists of two stages. The first stage predicts the Bird's Eye View (BEV) segmentation (referred to as the BEV layout map) from the ground image. The second stage synthesizes the aerial image from the predicted BEV layout map and text descriptions of the ground image. To train our model, we present a new multi-modal cross-view dataset, namely VIGORv2 which is built upon VIGOR with newly collected aerial images, maps, and text descriptions. Our extensive experiments illustrate that GPG2A synthesizes better geometry-preserved aerial images than existing models. We also present two applications, data augmentation for cross-view geo-localization and sketch-based region search, to further verify the effectiveness of our GPG2A. The code and data will be publicly available.

We introduce GeoWizard, a new generative foundation model designed for estimating geometric attributes, e.g., depth and normals, from single images. While significant research has already been conducted in this area, the progress has been substantially limited by the low diversity and poor quality of publicly available datasets. As a result, the prior works either are constrained to limited scenarios or suffer from the inability to capture geometric details. In this paper, we demonstrate that generative models, as opposed to traditional discriminative models (e.g., CNNs and Transformers), can effectively address the inherently ill-posed problem. We further show that leveraging diffusion priors can markedly improve generalization, detail preservation, and efficiency in resource usage. Specifically, we extend the original stable diffusion model to jointly predict depth and normal, allowing mutual information exchange and high consistency between the two representations. More importantly, we propose a simple yet effective strategy to segregate the complex data distribution of various scenes into distinct sub-distributions. This strategy enables our model to recognize different scene layouts, capturing 3D geometry with remarkable fidelity. GeoWizard sets new benchmarks for zero-shot depth and normal prediction, significantly enhancing many downstream applications such as 3D reconstruction, 2D content creation, and novel viewpoint synthesis.

Much of the success of deep learning is drawn from building architectures that properly respect underlying symmetry and structure in the data on which they operate - a set of considerations that have been united under the banner of geometric deep learning. Often problems in the physical sciences deal with relatively small sets of points in two- or three-dimensional space wherein translation, rotation, and permutation equivariance are important or even vital for models to be useful in practice. In this work, we present rotation- and permutation-equivariant architectures for deep learning on these small point clouds, composed of a set of products of terms from the geometric algebra and reductions over those products using an attention mechanism. The geometric algebra provides valuable mathematical structure by which to combine vector, scalar, and other types of geometric inputs in a systematic way to account for rotation invariance or covariance, while attention yields a powerful way to impose permutation equivariance. We demonstrate the usefulness of these architectures by training models to solve sample problems relevant to physics, chemistry, and biology.

We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric algebra, which builds on isometries encoded as elements of the Pin(p,q,r) group. We then propose the concept of group action layers, which linearly combine object transformations using pre-specified group actions. Together with a new activation and normalization scheme, these layers serve as adjustable geometric templates that can be refined via gradient descent. Theoretical advantages are strongly reflected in the modeling of three-dimensional rigid body transformations as well as large-scale fluid dynamics simulations, showing significantly improved performance over traditional methods.

Existing Large Multimodal Models (LMMs) struggle with mathematical geometric reasoning due to a lack of high-quality image-text paired data. Current geometric data generation approaches, which apply preset templates to generate geometric data or use Large Language Models (LLMs) to rephrase questions and answers (Q&A), unavoidably limit data accuracy and diversity. To synthesize higher-quality data, we propose a two-stage Reverse Chain-of-Thought (R-CoT) geometry problem generation pipeline. First, we introduce GeoChain to produce high-fidelity geometric images and corresponding descriptions highlighting relations among geometric elements. We then design a Reverse A&Q method that reasons step-by-step based on the descriptions and generates questions in reverse from the reasoning results. Experiments demonstrate that the proposed method brings significant and consistent improvements on multiple LMM baselines, achieving new performance records in the 2B, 7B, and 8B settings. Notably, R-CoT-8B significantly outperforms previous state-of-the-art open-source mathematical models by 16.6% on MathVista and 9.2% on GeoQA, while also surpassing the closed-source model GPT-4o by an average of 13% across both datasets. The code is available at https://github.com/dle666/R-CoT.

The recent video grounding works attempt to introduce vanilla contrastive learning into video grounding. However, we claim that this naive solution is suboptimal. Contrastive learning requires two key properties: (1) alignment of features of similar samples, and (2) uniformity of the induced distribution of the normalized features on the hypersphere. Due to two annoying issues in video grounding: (1) the co-existence of some visual entities in both ground truth and other moments, \ie semantic overlapping; (2) only a few moments in the video are annotated, \ie sparse annotation dilemma, vanilla contrastive learning is unable to model the correlations between temporally distant moments and learned inconsistent video representations. Both characteristics lead to vanilla contrastive learning being unsuitable for video grounding. In this paper, we introduce Geodesic and Game Localization (G2L), a semantically aligned and uniform video grounding framework via geodesic and game theory. We quantify the correlations among moments leveraging the geodesic distance that guides the model to learn the correct cross-modal representations. Furthermore, from the novel perspective of game theory, we propose semantic Shapley interaction based on geodesic distance sampling to learn fine-grained semantic alignment in similar moments. Experiments on three benchmarks demonstrate the effectiveness of our method.

We present a method for estimating neural scenes representations of objects given only a single image. The core of our method is the estimation of a geometric scaffold for the object and its use as a guide for the reconstruction of the underlying radiance field. Our formulation is based on a generative process that first maps a latent code to a voxelized shape, and then renders it to an image, with the object appearance being controlled by a second latent code. During inference, we optimize both the latent codes and the networks to fit a test image of a new object. The explicit disentanglement of shape and appearance allows our model to be fine-tuned given a single image. We can then render new views in a geometrically consistent manner and they represent faithfully the input object. Additionally, our method is able to generalize to images outside of the training domain (more realistic renderings and even real photographs). Finally, the inferred geometric scaffold is itself an accurate estimate of the object's 3D shape. We demonstrate in several experiments the effectiveness of our approach in both synthetic and real images.

Recently, "visual o1" began to enter people's vision, with expectations that this slow-thinking design can solve visual reasoning tasks, especially geometric math problems. However, the reality is that current LVLMs (Large Vision Language Models) can hardly even accurately copy a geometric figure, let alone truly understand the complex inherent logic and spatial relationships within geometric shapes. We believe accurate copying (strong perception) is the first step to visual o1. Accordingly, we introduce the concept of "slow perception" (SP), which guides the model to gradually perceive basic point-line combinations, as our humans, reconstruct complex geometric structures progressively. There are two-fold stages in SP: a) perception decomposition. Perception is not instantaneous. In this stage, complex geometric figures are broken down into basic simple units to unify geometry representation. b) perception flow, which acknowledges that accurately tracing a line is not an easy task. This stage aims to avoid "long visual jumps" in regressing line segments by using a proposed "perceptual ruler" to trace each line stroke-by-stroke. Surprisingly, such a human-like perception manner enjoys an inference time scaling law -- the slower, the better. Researchers strive to speed up the model's perception in the past, but we slow it down again, allowing the model to read the image step-by-step and carefully.

Text-to-3D generation by distilling pretrained large-scale text-to-image diffusion models has shown great promise but still suffers from inconsistent 3D geometric structures (Janus problems) and severe artifacts. The aforementioned problems mainly stem from 2D diffusion models lacking 3D awareness during the lifting. In this work, we present GeoDream, a novel method that incorporates explicit generalized 3D priors with 2D diffusion priors to enhance the capability of obtaining unambiguous 3D consistent geometric structures without sacrificing diversity or fidelity. Specifically, we first utilize a multi-view diffusion model to generate posed images and then construct cost volume from the predicted image, which serves as native 3D geometric priors, ensuring spatial consistency in 3D space. Subsequently, we further propose to harness 3D geometric priors to unlock the great potential of 3D awareness in 2D diffusion priors via a disentangled design. Notably, disentangling 2D and 3D priors allows us to refine 3D geometric priors further. We justify that the refined 3D geometric priors aid in the 3D-aware capability of 2D diffusion priors, which in turn provides superior guidance for the refinement of 3D geometric priors. Our numerical and visual comparisons demonstrate that GeoDream generates more 3D consistent textured meshes with high-resolution realistic renderings (i.e., 1024 times 1024) and adheres more closely to semantic coherence.

Large language models (LLMs) have shown remarkable proficiency in human-level reasoning and generation capabilities, which encourages extensive research on their application in mathematical problem solving. However, current work has been largely focused on text-based mathematical problems, with limited investigation in problems involving geometric information. Addressing this gap, we aim to enable LLMs to solve geometric problems by understanding image input. We first analyze the limitations of current Multimodal Large Language Models (MLLMs) in this area: they struggle to accurately comprehending basic geometric elements and their relationships. To overcome these challenges, we take advantage of the unique characteristics of geometric problems (such as unique geometric logical form, and geometric scalability) and the capacity of the textual LLMs to build an enriched multimodal geometry dataset based on existing data. The augmented dataset, Geo170K, contains more than 170K geometric image-caption and question-answer pairs. Utilizing our constructed Geo170K dataset, we develop G-LLaVA, which demonstrates exceptional performance in solving geometric problems, significantly outperforming GPT-4-V on the MathVista benchmark with only 7B parameters.

The expressive power of Graph Neural Networks (GNNs) has been studied extensively through the Weisfeiler-Leman (WL) graph isomorphism test. However, standard GNNs and the WL framework are inapplicable for geometric graphs embedded in Euclidean space, such as biomolecules, materials, and other physical systems. In this work, we propose a geometric version of the WL test (GWL) for discriminating geometric graphs while respecting the underlying physical symmetries: permutations, rotation, reflection, and translation. We use GWL to characterise the expressive power of geometric GNNs that are invariant or equivariant to physical symmetries in terms of distinguishing geometric graphs. GWL unpacks how key design choices influence geometric GNN expressivity: (1) Invariant layers have limited expressivity as they cannot distinguish one-hop identical geometric graphs; (2) Equivariant layers distinguish a larger class of graphs by propagating geometric information beyond local neighbourhoods; (3) Higher order tensors and scalarisation enable maximally powerful geometric GNNs; and (4) GWL's discrimination-based perspective is equivalent to universal approximation. Synthetic experiments supplementing our results are available at https://github.com/chaitjo/geometric-gnn-dojo

In this paper, we present Gaussian Splatting based text-to-3D generation (GSGEN), a novel approach for generating high-quality 3D objects. Previous methods suffer from inaccurate geometry and limited fidelity due to the absence of 3D prior and proper representation. We leverage 3D Gaussian Splatting, a recent state-of-the-art representation, to address existing shortcomings by exploiting the explicit nature that enables the incorporation of 3D prior. Specifically, our method adopts a progressive optimization strategy, which includes a geometry optimization stage and an appearance refinement stage. In geometry optimization, a coarse representation is established under a 3D geometry prior along with the ordinary 2D SDS loss, ensuring a sensible and 3D-consistent rough shape. Subsequently, the obtained Gaussians undergo an iterative refinement to enrich details. In this stage, we increase the number of Gaussians by compactness-based densification to enhance continuity and improve fidelity. With these designs, our approach can generate 3D content with delicate details and more accurate geometry. Extensive evaluations demonstrate the effectiveness of our method, especially for capturing high-frequency components. Video results are provided at https://gsgen3d.github.io. Our code is available at https://github.com/gsgen3d/gsgen

Existing fully-supervised point cloud segmentation methods suffer in the dynamic testing environment with emerging new classes. Few-shot point cloud segmentation algorithms address this problem by learning to adapt to new classes at the sacrifice of segmentation accuracy for the base classes, which severely impedes its practicality. This largely motivates us to present the first attempt at a more practical paradigm of generalized few-shot point cloud segmentation, which requires the model to generalize to new categories with only a few support point clouds and simultaneously retain the capability to segment base classes. We propose the geometric words to represent geometric components shared between the base and novel classes, and incorporate them into a novel geometric-aware semantic representation to facilitate better generalization to the new classes without forgetting the old ones. Moreover, we introduce geometric prototypes to guide the segmentation with geometric prior knowledge. Extensive experiments on S3DIS and ScanNet consistently illustrate the superior performance of our method over baseline methods. Our code is available at: https://github.com/Pixie8888/GFS-3DSeg_GWs.

Geometric Deep Learning has recently made striking progress with the advent of continuous Deep Implicit Fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid, resulting in a learnable parameterization that is not limited in resolution. Unfortunately, these methods are often not suitable for applications that require an explicit mesh-based surface representation because converting an implicit field to such a representation relies on the Marching Cubes algorithm, which cannot be differentiated with respect to the underlying implicit field. In this work, we remove this limitation and introduce a differentiable way to produce explicit surface mesh representations from Deep Signed Distance Functions. Our key insight is that by reasoning on how implicit field perturbations impact local surface geometry, one can ultimately differentiate the 3D location of surface samples with respect to the underlying deep implicit field. We exploit this to define MeshSDF, an end-to-end differentiable mesh representation which can vary its topology. We use two different applications to validate our theoretical insight: Single-View Reconstruction via Differentiable Rendering and Physically-Driven Shape Optimization. In both cases our differentiable parameterization gives us an edge over state-of-the-art algorithms.

We introduce the task of 3D visual grounding in large-scale dynamic scenes based on natural linguistic descriptions and online captured multi-modal visual data, including 2D images and 3D LiDAR point clouds. We present a novel method, dubbed WildRefer, for this task by fully utilizing the rich appearance information in images, the position and geometric clues in point cloud as well as the semantic knowledge of language descriptions. Besides, we propose two novel datasets, i.e., STRefer and LifeRefer, which focus on large-scale human-centric daily-life scenarios accompanied with abundant 3D object and natural language annotations. Our datasets are significant for the research of 3D visual grounding in the wild and has huge potential to boost the development of autonomous driving and service robots. Extensive experiments and ablation studies demonstrate that our method achieves state-of-the-art performance on the proposed benchmarks. The code is provided in https://github.com/4DVLab/WildRefer.

Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as geometric graphs, i.e., graphs with nodes positioned in the Euclidean space given an arbitrarily chosen global coordinate system, for instance vehicles in a traffic scene. Notwithstanding the arbitrary global coordinate system, the governing dynamics of the respective dynamical systems are invariant to rotations and translations, also known as Galilean invariance. As ignoring these invariances leads to worse generalization, in this work we propose local coordinate frames per node-object to induce roto-translation invariance to the geometric graph of the interacting dynamical system. Further, the local coordinate frames allow for a natural definition of anisotropic filtering in graph neural networks. Experiments in traffic scenes, 3D motion capture, and colliding particles demonstrate that the proposed approach comfortably outperforms the recent state-of-the-art.

In this paper we demonstrate how sub-Riemannian geometry can be used for manifold learning and surface reconstruction by combining local linear approximations of a point cloud to obtain lower dimensional bundles. Local approximations obtained by local PCAs are collected into a rank k tangent subbundle on R^d, k<d, which we call a principal subbundle. This determines a sub-Riemannian metric on R^d. We show that sub-Riemannian geodesics with respect to this metric can successfully be applied to a number of important problems, such as: explicit construction of an approximating submanifold M, construction of a representation of the point-cloud in R^k, and computation of distances between observations, taking the learned geometry into account. The reconstruction is guaranteed to equal the true submanifold in the limit case where tangent spaces are estimated exactly. Via simulations, we show that the framework is robust when applied to noisy data. Furthermore, the framework generalizes to observations on an a priori known Riemannian manifold.

Mathematical geometric problem solving (GPS) often requires effective integration of multimodal information and verifiable logical coherence. Despite the fast development of large language models in general problem solving, it remains unresolved regarding with both methodology and benchmarks, especially given the fact that exiting synthetic GPS benchmarks are often not self-verified and contain noise and self-contradicted information due to the illusion of LLMs. In this paper, we propose a scalable data engine called TrustGeoGen for problem generation, with formal verification to provide a principled benchmark, which we believe lays the foundation for the further development of methods for GPS. The engine synthesizes geometric data through four key innovations: 1) multimodal-aligned generation of diagrams, textual descriptions, and stepwise solutions; 2) formal verification ensuring rule-compliant reasoning paths; 3) a bootstrapping mechanism enabling complexity escalation via recursive state generation and 4) our devised GeoExplore series algorithms simultaneously produce multi-solution variants and self-reflective backtracking traces. By formal logical verification, TrustGeoGen produces GeoTrust-200K dataset with guaranteed modality integrity, along with GeoTrust-test testset. Experiments reveal the state-of-the-art models achieve only 49.17\% accuracy on GeoTrust-test, demonstrating its evaluation stringency. Crucially, models trained on GeoTrust achieve OOD generalization on GeoQA, significantly reducing logical inconsistencies relative to pseudo-label annotated by OpenAI-o1. Our code is available at https://github.com/Alpha-Innovator/TrustGeoGen

A Sheaf Neural Network (SNN) is a type of Graph Neural Network (GNN) that operates on a sheaf, an object that equips a graph with vector spaces over its nodes and edges and linear maps between these spaces. SNNs have been shown to have useful theoretical properties that help tackle issues arising from heterophily and over-smoothing. One complication intrinsic to these models is finding a good sheaf for the task to be solved. Previous works proposed two diametrically opposed approaches: manually constructing the sheaf based on domain knowledge and learning the sheaf end-to-end using gradient-based methods. However, domain knowledge is often insufficient, while learning a sheaf could lead to overfitting and significant computational overhead. In this work, we propose a novel way of computing sheaves drawing inspiration from Riemannian geometry: we leverage the manifold assumption to compute manifold-and-graph-aware orthogonal maps, which optimally align the tangent spaces of neighbouring data points. We show that this approach achieves promising results with less computational overhead when compared to previous SNN models. Overall, this work provides an interesting connection between algebraic topology and differential geometry, and we hope that it will spark future research in this direction.

Emerging 3D geometric foundation models, such as DUSt3R, offer a promising approach for in-the-wild 3D vision tasks. However, due to the high-dimensional nature of the problem space and scarcity of high-quality 3D data, these pre-trained models still struggle to generalize to many challenging circumstances, such as limited view overlap or low lighting. To address this, we propose LoRA3D, an efficient self-calibration pipeline to specialize the pre-trained models to target scenes using their own multi-view predictions. Taking sparse RGB images as input, we leverage robust optimization techniques to refine multi-view predictions and align them into a global coordinate frame. In particular, we incorporate prediction confidence into the geometric optimization process, automatically re-weighting the confidence to better reflect point estimation accuracy. We use the calibrated confidence to generate high-quality pseudo labels for the calibrating views and use low-rank adaptation (LoRA) to fine-tune the models on the pseudo-labeled data. Our method does not require any external priors or manual labels. It completes the self-calibration process on a single standard GPU within just 5 minutes. Each low-rank adapter requires only 18MB of storage. We evaluated our method on more than 160 scenes from the Replica, TUM and Waymo Open datasets, achieving up to 88% performance improvement on 3D reconstruction, multi-view pose estimation and novel-view rendering.

The integration of geometric reconstruction and generative modeling remains a critical challenge in developing AI systems capable of human-like spatial reasoning. This paper proposes Aether, a unified framework that enables geometry-aware reasoning in world models by jointly optimizing three core capabilities: (1) 4D dynamic reconstruction, (2) action-conditioned video prediction, and (3) goal-conditioned visual planning. Through task-interleaved feature learning, Aether achieves synergistic knowledge sharing across reconstruction, prediction, and planning objectives. Building upon video generation models, our framework demonstrates unprecedented synthetic-to-real generalization despite never observing real-world data during training. Furthermore, our approach achieves zero-shot generalization in both action following and reconstruction tasks, thanks to its intrinsic geometric modeling. Remarkably, even without real-world data, its reconstruction performance far exceeds that of domain-specific models. Additionally, Aether leverages a geometry-informed action space to seamlessly translate predictions into actions, enabling effective autonomous trajectory planning. We hope our work inspires the community to explore new frontiers in physically-reasonable world modeling and its applications.

We present DreamPolisher, a novel Gaussian Splatting based method with geometric guidance, tailored to learn cross-view consistency and intricate detail from textual descriptions. While recent progress on text-to-3D generation methods have been promising, prevailing methods often fail to ensure view-consistency and textural richness. This problem becomes particularly noticeable for methods that work with text input alone. To address this, we propose a two-stage Gaussian Splatting based approach that enforces geometric consistency among views. Initially, a coarse 3D generation undergoes refinement via geometric optimization. Subsequently, we use a ControlNet driven refiner coupled with the geometric consistency term to improve both texture fidelity and overall consistency of the generated 3D asset. Empirical evaluations across diverse textual prompts spanning various object categories demonstrate the efficacy of DreamPolisher in generating consistent and realistic 3D objects, aligning closely with the semantics of the textual instructions.

Recently, 3D Gaussian splatting (3D-GS) has achieved great success in reconstructing and rendering real-world scenes. To transfer the high rendering quality to generation tasks, a series of research works attempt to generate 3D-Gaussian assets from text. However, the generated assets have not achieved the same quality as those in reconstruction tasks. We observe that Gaussians tend to grow without control as the generation process may cause indeterminacy. Aiming at highly enhancing the generation quality, we propose a novel framework named GaussianDreamerPro. The main idea is to bind Gaussians to reasonable geometry, which evolves over the whole generation process. Along different stages of our framework, both the geometry and appearance can be enriched progressively. The final output asset is constructed with 3D Gaussians bound to mesh, which shows significantly enhanced details and quality compared with previous methods. Notably, the generated asset can also be seamlessly integrated into downstream manipulation pipelines, e.g. animation, composition, and simulation etc., greatly promoting its potential in wide applications. Demos are available at https://taoranyi.com/gaussiandreamerpro/.

In real-life scenarios, humans seek out objects in the 3D world to fulfill their daily needs or intentions. This inspires us to introduce 3D intention grounding, a new task in 3D object detection employing RGB-D, based on human intention, such as "I want something to support my back". Closely related, 3D visual grounding focuses on understanding human reference. To achieve detection based on human intention, it relies on humans to observe the scene, reason out the target that aligns with their intention ("pillow" in this case), and finally provide a reference to the AI system, such as "A pillow on the couch". Instead, 3D intention grounding challenges AI agents to automatically observe, reason and detect the desired target solely based on human intention. To tackle this challenge, we introduce the new Intent3D dataset, consisting of 44,990 intention texts associated with 209 fine-grained classes from 1,042 scenes of the ScanNet dataset. We also establish several baselines based on different language-based 3D object detection models on our benchmark. Finally, we propose IntentNet, our unique approach, designed to tackle this intention-based detection problem. It focuses on three key aspects: intention understanding, reasoning to identify object candidates, and cascaded adaptive learning that leverages the intrinsic priority logic of different losses for multiple objective optimization.

3D room layout estimation by a single panorama using deep neural networks has made great progress. However, previous approaches can not obtain efficient geometry awareness of room layout with the only latitude of boundaries or horizon-depth. We present that using horizon-depth along with room height can obtain omnidirectional-geometry awareness of room layout in both horizontal and vertical directions. In addition, we propose a planar-geometry aware loss function with normals and gradients of normals to supervise the planeness of walls and turning of corners. We propose an efficient network, LGT-Net, for room layout estimation, which contains a novel Transformer architecture called SWG-Transformer to model geometry relations. SWG-Transformer consists of (Shifted) Window Blocks and Global Blocks to combine the local and global geometry relations. Moreover, we design a novel relative position embedding of Transformer to enhance the spatial identification ability for the panorama. Experiments show that the proposed LGT-Net achieves better performance than current state-of-the-arts (SOTA) on benchmark datasets.

Generative models can produce impressively realistic images. This paper demonstrates that generated images have geometric features different from those of real images. We build a set of collections of generated images, prequalified to fool simple, signal-based classifiers into believing they are real. We then show that prequalified generated images can be identified reliably by classifiers that only look at geometric properties. We use three such classifiers. All three classifiers are denied access to image pixels, and look only at derived geometric features. The first classifier looks at the perspective field of the image, the second looks at lines detected in the image, and the third looks at relations between detected objects and shadows. Our procedure detects generated images more reliably than SOTA local signal based detectors, for images from a number of distinct generators. Saliency maps suggest that the classifiers can identify geometric problems reliably. We conclude that current generators cannot reliably reproduce geometric properties of real images.

Deep neural networks are prone to adversarial examples that maliciously alter the network's outcome. Due to the increasing popularity of 3D sensors in safety-critical systems and the vast deployment of deep learning models for 3D point sets, there is a growing interest in adversarial attacks and defenses for such models. So far, the research has focused on the semantic level, namely, deep point cloud classifiers. However, point clouds are also widely used in a geometric-related form that includes encoding and reconstructing the geometry. In this work, we are the first to consider the problem of adversarial examples at a geometric level. In this setting, the question is how to craft a small change to a clean source point cloud that leads, after passing through an autoencoder model, to the reconstruction of a different target shape. Our attack is in sharp contrast to existing semantic attacks on 3D point clouds. While such works aim to modify the predicted label by a classifier, we alter the entire reconstructed geometry. Additionally, we demonstrate the robustness of our attack in the case of defense, where we show that remnant characteristics of the target shape are still present at the output after applying the defense to the adversarial input. Our code is publicly available at https://github.com/itailang/geometric_adv.

We present DecoupledGaussian, a novel system that decouples static objects from their contacted surfaces captured in-the-wild videos, a key prerequisite for realistic Newtonian-based physical simulations. Unlike prior methods focused on synthetic data or elastic jittering along the contact surface, which prevent objects from fully detaching or moving independently, DecoupledGaussian allows for significant positional changes without being constrained by the initial contacted surface. Recognizing the limitations of current 2D inpainting tools for restoring 3D locations, our approach proposes joint Poisson fields to repair and expand the Gaussians of both objects and contacted scenes after separation. This is complemented by a multi-carve strategy to refine the object's geometry. Our system enables realistic simulations of decoupling motions, collisions, and fractures driven by user-specified impulses, supporting complex interactions within and across multiple scenes. We validate DecoupledGaussian through a comprehensive user study and quantitative benchmarks. This system enhances digital interaction with objects and scenes in real-world environments, benefiting industries such as VR, robotics, and autonomous driving. Our project page is at: https://wangmiaowei.github.io/DecoupledGaussian.github.io/.

Extracting planes from a 3D scene is useful for downstream tasks in robotics and augmented reality. In this paper we tackle the problem of estimating the planar surfaces in a scene from posed images. Our first finding is that a surprisingly competitive baseline results from combining popular clustering algorithms with recent improvements in 3D geometry estimation. However, such purely geometric methods are understandably oblivious to plane semantics, which are crucial to discerning distinct planes. To overcome this limitation, we propose a method that predicts multi-view consistent plane embeddings that complement geometry when clustering points into planes. We show through extensive evaluation on the ScanNetV2 dataset that our new method outperforms existing approaches and our strong geometric baseline for the task of plane estimation.

In document image rectification, there exist rich geometric constraints between the distorted image and the ground truth one. However, such geometric constraints are largely ignored in existing advanced solutions, which limits the rectification performance. To this end, we present DocGeoNet for document image rectification by introducing explicit geometric representation. Technically, two typical attributes of the document image are involved in the proposed geometric representation learning, i.e., 3D shape and textlines. Our motivation arises from the insight that 3D shape provides global unwarping cues for rectifying a distorted document image while overlooking the local structure. On the other hand, textlines complementarily provide explicit geometric constraints for local patterns. The learned geometric representation effectively bridges the distorted image and the ground truth one. Extensive experiments show the effectiveness of our framework and demonstrate the superiority of our DocGeoNet over state-of-the-art methods on both the DocUNet Benchmark dataset and our proposed DIR300 test set. The code is available at https://github.com/fh2019ustc/DocGeoNet.

3D visual grounding aims to locate the referred target object in 3D point cloud scenes according to a free-form language description. Previous methods mostly follow a two-stage paradigm, i.e., language-irrelevant detection and cross-modal matching, which is limited by the isolated architecture. In such a paradigm, the detector needs to sample keypoints from raw point clouds due to the inherent properties of 3D point clouds (irregular and large-scale), to generate the corresponding object proposal for each keypoint. However, sparse proposals may leave out the target in detection, while dense proposals may confuse the matching model. Moreover, the language-irrelevant detection stage can only sample a small proportion of keypoints on the target, deteriorating the target prediction. In this paper, we propose a 3D Single-Stage Referred Point Progressive Selection (3D-SPS) method, which progressively selects keypoints with the guidance of language and directly locates the target. Specifically, we propose a Description-aware Keypoint Sampling (DKS) module to coarsely focus on the points of language-relevant objects, which are significant clues for grounding. Besides, we devise a Target-oriented Progressive Mining (TPM) module to finely concentrate on the points of the target, which is enabled by progressive intra-modal relation modeling and inter-modal target mining. 3D-SPS bridges the gap between detection and matching in the 3D visual grounding task, localizing the target at a single stage. Experiments demonstrate that 3D-SPS achieves state-of-the-art performance on both ScanRefer and Nr3D/Sr3D datasets.

We present WonderWorld, a novel framework for interactive 3D scene generation that enables users to interactively specify scene contents and layout and see the created scenes in low latency. The major challenge lies in achieving fast generation of 3D scenes. Existing scene generation approaches fall short of speed as they often require (1) progressively generating many views and depth maps, and (2) time-consuming optimization of the scene geometry representations. We introduce the Fast Layered Gaussian Surfels (FLAGS) as our scene representation and an algorithm to generate it from a single view. Our approach does not need multiple views, and it leverages a geometry-based initialization that significantly reduces optimization time. Another challenge is generating coherent geometry that allows all scenes to be connected. We introduce the guided depth diffusion that allows partial conditioning of depth estimation. WonderWorld generates connected and diverse 3D scenes in less than 10 seconds on a single A6000 GPU, enabling real-time user interaction and exploration. We demonstrate the potential of WonderWorld for user-driven content creation and exploration in virtual environments. We will release full code and software for reproducibility. Project website: https://kovenyu.com/WonderWorld/.

Multi-camera 3D object detection for autonomous driving is a challenging problem that has garnered notable attention from both academia and industry. An obstacle encountered in vision-based techniques involves the precise extraction of geometry-conscious features from RGB images. Recent approaches have utilized geometric-aware image backbones pretrained on depth-relevant tasks to acquire spatial information. However, these approaches overlook the critical aspect of view transformation, resulting in inadequate performance due to the misalignment of spatial knowledge between the image backbone and view transformation. To address this issue, we propose a novel geometric-aware pretraining framework called GAPretrain. Our approach incorporates spatial and structural cues to camera networks by employing the geometric-rich modality as guidance during the pretraining phase. The transference of modal-specific attributes across different modalities is non-trivial, but we bridge this gap by using a unified bird's-eye-view (BEV) representation and structural hints derived from LiDAR point clouds to facilitate the pretraining process. GAPretrain serves as a plug-and-play solution that can be flexibly applied to multiple state-of-the-art detectors. Our experiments demonstrate the effectiveness and generalization ability of the proposed method. We achieve 46.2 mAP and 55.5 NDS on the nuScenes val set using the BEVFormer method, with a gain of 2.7 and 2.1 points, respectively. We also conduct experiments on various image backbones and view transformations to validate the efficacy of our approach. Code will be released at https://github.com/OpenDriveLab/BEVPerception-Survey-Recipe.

Given that visual foundation models (VFMs) are trained on extensive datasets but often limited to 2D images, a natural question arises: how well do they understand the 3D world? With the differences in architecture and training protocols (i.e., objectives, proxy tasks), a unified framework to fairly and comprehensively probe their 3D awareness is urgently needed. Existing works on 3D probing suggest single-view 2.5D estimation (e.g., depth and normal) or two-view sparse 2D correspondence (e.g., matching and tracking). Unfortunately, these tasks ignore texture awareness, and require 3D data as ground-truth, which limits the scale and diversity of their evaluation set. To address these issues, we introduce Feat2GS, which readout 3D Gaussians attributes from VFM features extracted from unposed images. This allows us to probe 3D awareness for geometry and texture via novel view synthesis, without requiring 3D data. Additionally, the disentanglement of 3DGS parameters - geometry (x, alpha, Sigma) and texture (c) - enables separate analysis of texture and geometry awareness. Under Feat2GS, we conduct extensive experiments to probe the 3D awareness of several VFMs, and investigate the ingredients that lead to a 3D aware VFM. Building on these findings, we develop several variants that achieve state-of-the-art across diverse datasets. This makes Feat2GS useful for probing VFMs, and as a simple-yet-effective baseline for novel-view synthesis. Code and data will be made available at https://fanegg.github.io/Feat2GS/.

Foundation models have revolutionized artificial intelligence (AI), offering remarkable capabilities across multi-modal domains. Their ability to precisely locate objects in complex aerial and satellite images, using rich contextual information and detailed object descriptions, is essential for remote sensing (RS). These models can associate textual descriptions with object positions through the Visual Grounding (VG) task, but due to domain-specific challenges, their direct application to RS produces sub-optimal results. To address this, we applied Parameter Efficient Fine Tuning (PEFT) techniques to adapt these models for RS-specific VG tasks. Specifically, we evaluated LoRA placement across different modules in Grounding DINO and used BitFit and adapters to fine-tune the OFA foundation model pre-trained on general-purpose VG datasets. This approach achieved performance comparable to or surpassing current State Of The Art (SOTA) models while significantly reducing computational costs. This study highlights the potential of PEFT techniques to advance efficient and precise multi-modal analysis in RS, offering a practical and cost-effective alternative to full model training.

3D affordance reasoning is essential in associating human instructions with the functional regions of 3D objects, facilitating precise, task-oriented manipulations in embodied AI. However, current methods, which predominantly depend on sparse 3D point clouds, exhibit limited generalizability and robustness due to their sensitivity to coordinate variations and the inherent sparsity of the data. By contrast, 3D Gaussian Splatting (3DGS) delivers high-fidelity, real-time rendering with minimal computational overhead by representing scenes as dense, continuous distributions. This positions 3DGS as a highly effective approach for capturing fine-grained affordance details and improving recognition accuracy. Nevertheless, its full potential remains largely untapped due to the absence of large-scale, 3DGS-specific affordance datasets. To overcome these limitations, we present 3DAffordSplat, the first large-scale, multi-modal dataset tailored for 3DGS-based affordance reasoning. This dataset includes 23,677 Gaussian instances, 8,354 point cloud instances, and 6,631 manually annotated affordance labels, encompassing 21 object categories and 18 affordance types. Building upon this dataset, we introduce AffordSplatNet, a novel model specifically designed for affordance reasoning using 3DGS representations. AffordSplatNet features an innovative cross-modal structure alignment module that exploits structural consistency priors to align 3D point cloud and 3DGS representations, resulting in enhanced affordance recognition accuracy. Extensive experiments demonstrate that the 3DAffordSplat dataset significantly advances affordance learning within the 3DGS domain, while AffordSplatNet consistently outperforms existing methods across both seen and unseen settings, highlighting its robust generalization capabilities.

We introduce DreamPolish, a text-to-3D generation model that excels in producing refined geometry and high-quality textures. In the geometry construction phase, our approach leverages multiple neural representations to enhance the stability of the synthesis process. Instead of relying solely on a view-conditioned diffusion prior in the novel sampled views, which often leads to undesired artifacts in the geometric surface, we incorporate an additional normal estimator to polish the geometry details, conditioned on viewpoints with varying field-of-views. We propose to add a surface polishing stage with only a few training steps, which can effectively refine the artifacts attributed to limited guidance from previous stages and produce 3D objects with more desirable geometry. The key topic of texture generation using pretrained text-to-image models is to find a suitable domain in the vast latent distribution of these models that contains photorealistic and consistent renderings. In the texture generation phase, we introduce a novel score distillation objective, namely domain score distillation (DSD), to guide neural representations toward such a domain. We draw inspiration from the classifier-free guidance (CFG) in textconditioned image generation tasks and show that CFG and variational distribution guidance represent distinct aspects in gradient guidance and are both imperative domains for the enhancement of texture quality. Extensive experiments show our proposed model can produce 3D assets with polished surfaces and photorealistic textures, outperforming existing state-of-the-art methods.

We propose a novel, object-agnostic method for learning a universal policy for dexterous object grasping from realistic point cloud observations and proprioceptive information under a table-top setting, namely UniDexGrasp++. To address the challenge of learning the vision-based policy across thousands of object instances, we propose Geometry-aware Curriculum Learning (GeoCurriculum) and Geometry-aware iterative Generalist-Specialist Learning (GiGSL) which leverage the geometry feature of the task and significantly improve the generalizability. With our proposed techniques, our final policy shows universal dexterous grasping on thousands of object instances with 85.4% and 78.2% success rate on the train set and test set which outperforms the state-of-the-art baseline UniDexGrasp by 11.7% and 11.3%, respectively.

We address the problem of detecting and erasing furniture from a wide angle photograph of a room. Inpainting large regions of an indoor scene often results in geometric inconsistencies of background elements within the inpaint mask. To address this problem, we utilize perceptual information (e.g. instance segmentation, and room layout) to produce a geometrically consistent empty version of a room. We share important details to make this system viable, such as per-plane inpainting, automatic rectification, and texture refinement. We provide detailed ablation along with qualitative examples, justifying our design choices. We show an application of our system by removing real furniture from a room and redecorating it with virtual furniture.

Estimating the pose of an object from a monocular image is an inverse problem fundamental in computer vision. The ill-posed nature of this problem requires incorporating deformation priors to solve it. In practice, many materials do not perceptibly shrink or extend when manipulated, constituting a powerful and well-known prior. Mathematically, this translates to the preservation of the Riemannian metric. Neural networks offer the perfect playground to solve the surface reconstruction problem as they can approximate surfaces with arbitrary precision and allow the computation of differential geometry quantities. This paper presents an approach to inferring continuous deformable surfaces from a sequence of images, which is benchmarked against several techniques and obtains state-of-the-art performance without the need for offline training.

Humans have the ability to reason about geometric patterns in images and scenes from a young age. However, developing large multimodal models (LMMs) capable of similar reasoning remains a challenge, highlighting the need for robust evaluation methods to assess these capabilities. We introduce \Turtle, a benchmark designed to evaluate LMMs' capacity to interpret geometric patterns -- given visual examples, textual instructions, or both -- and generate precise code outputs. Inspired by turtle geometry, a notion used to teach children foundational coding and geometric concepts, TurtleBench features tasks with patterned shapes that have underlying algorithmic logic. Our evaluation reveals that leading LMMs struggle significantly with these tasks, with GPT-4o achieving only 19\% accuracy on the simplest tasks and few-shot prompting only marginally improves their performance (<2%). \Turtle highlights the gap between human and AI performance in intuitive and visual geometrical understanding, setting the stage for future research in this area. \Turtle stands as one of the few benchmarks to evaluate the integration of visual understanding and code generation capabilities in LMMs, setting the stage for future research. Code and Dataset for this paper is provided here: https://github.com/sinaris76/TurtleBench{https://github.com/sinaris76/TurtleBench}

3D Gaussian Splatting (3DGS) integrates the strengths of primitive-based representations and volumetric rendering techniques, enabling real-time, high-quality rendering. However, 3DGS models typically overfit to single-scene training and are highly sensitive to the initialization of Gaussian ellipsoids, heuristically derived from Structure from Motion (SfM) point clouds, which limits both generalization and practicality. To address these limitations, we propose GS-Net, a generalizable, plug-and-play 3DGS module that densifies Gaussian ellipsoids from sparse SfM point clouds, enhancing geometric structure representation. To the best of our knowledge, GS-Net is the first plug-and-play 3DGS module with cross-scene generalization capabilities. Additionally, we introduce the CARLA-NVS dataset, which incorporates additional camera viewpoints to thoroughly evaluate reconstruction and rendering quality. Extensive experiments demonstrate that applying GS-Net to 3DGS yields a PSNR improvement of 2.08 dB for conventional viewpoints and 1.86 dB for novel viewpoints, confirming the method's effectiveness and robustness.

3D Gaussian Splatting (3DGS) has recently attracted wide attentions in various areas such as 3D navigation, Virtual Reality (VR) and 3D simulation, due to its photorealistic and efficient rendering performance. High-quality reconstrution of 3DGS relies on sufficient splats and a reasonable distribution of these splats to fit real geometric surface and texture details, which turns out to be a challenging problem. We present GeoTexDensifier, a novel geometry-texture-aware densification strategy to reconstruct high-quality Gaussian splats which better comply with the geometric structure and texture richness of the scene. Specifically, our GeoTexDensifier framework carries out an auxiliary texture-aware densification method to produce a denser distribution of splats in fully textured areas, while keeping sparsity in low-texture regions to maintain the quality of Gaussian point cloud. Meanwhile, a geometry-aware splitting strategy takes depth and normal priors to guide the splitting sampling and filter out the noisy splats whose initial positions are far from the actual geometric surfaces they aim to fit, under a Validation of Depth Ratio Change checking. With the help of relative monocular depth prior, such geometry-aware validation can effectively reduce the influence of scattered Gaussians to the final rendering quality, especially in regions with weak textures or without sufficient training views. The texture-aware densification and geometry-aware splitting strategies are fully combined to obtain a set of high-quality Gaussian splats. We experiment our GeoTexDensifier framework on various datasets and compare our Novel View Synthesis results to other state-of-the-art 3DGS approaches, with detailed quantitative and qualitative evaluations to demonstrate the effectiveness of our method in producing more photorealistic 3DGS models.

To endow machines with the ability to perceive the real-world in a three dimensional representation as we do as humans is a fundamental and long-standing topic in Artificial Intelligence. Given different types of visual inputs such as images or point clouds acquired by 2D/3D sensors, one important goal is to understand the geometric structure and semantics of the 3D environment. Traditional approaches usually leverage hand-crafted features to estimate the shape and semantics of objects or scenes. However, they are difficult to generalize to novel objects and scenarios, and struggle to overcome critical issues caused by visual occlusions. By contrast, we aim to understand scenes and the objects within them by learning general and robust representations using deep neural networks, trained on large-scale real-world 3D data. To achieve these aims, this thesis makes three core contributions from object-level 3D shape estimation from single or multiple views to scene-level semantic understanding.

Geometric deep learning, i.e., designing neural networks to handle the ubiquitous geometric data such as point clouds and graphs, have achieved great successes in the last decade. One critical inductive bias is that the model can maintain invariance towards various transformations such as translation, rotation, and scaling. The existing graph neural network (GNN) approaches can only maintain permutation-invariance, failing to guarantee invariance with respect to other transformations. Besides GNNs, other works design sophisticated transformation-invariant layers, which are computationally expensive and difficult to be extended. To solve this problem, we revisit why the existing neural networks cannot maintain transformation invariance when handling geometric data. Our findings show that transformation-invariant and distance-preserving initial representations are sufficient to achieve transformation invariance rather than needing sophisticated neural layer designs. Motivated by these findings, we propose Transformation Invariant Neural Networks (TinvNN), a straightforward and general framework for geometric data. Specifically, we realize transformation-invariant and distance-preserving initial point representations by modifying multi-dimensional scaling before feeding the representations into neural networks. We prove that TinvNN can strictly guarantee transformation invariance, being general and flexible enough to be combined with the existing neural networks. Extensive experimental results on point cloud analysis and combinatorial optimization demonstrate the effectiveness and general applicability of our proposed method. Based on the experimental results, we advocate that TinvNN should be considered a new starting point and an essential baseline for further studies of transformation-invariant geometric deep learning.

We introduce CLR-Wire, a novel framework for 3D curve-based wireframe generation that integrates geometry and topology into a unified Continuous Latent Representation. Unlike conventional methods that decouple vertices, edges, and faces, CLR-Wire encodes curves as Neural Parametric Curves along with their topological connectivity into a continuous and fixed-length latent space using an attention-driven variational autoencoder (VAE). This unified approach facilitates joint learning and generation of both geometry and topology. To generate wireframes, we employ a flow matching model to progressively map Gaussian noise to these latents, which are subsequently decoded into complete 3D wireframes. Our method provides fine-grained modeling of complex shapes and irregular topologies, and supports both unconditional generation and generation conditioned on point cloud or image inputs. Experimental results demonstrate that, compared with state-of-the-art generative approaches, our method achieves substantial improvements in accuracy, novelty, and diversity, offering an efficient and comprehensive solution for CAD design, geometric reconstruction, and 3D content creation.

We introduce PhysGaussian, a new method that seamlessly integrates physically grounded Newtonian dynamics within 3D Gaussians to achieve high-quality novel motion synthesis. Employing a custom Material Point Method (MPM), our approach enriches 3D Gaussian kernels with physically meaningful kinematic deformation and mechanical stress attributes, all evolved in line with continuum mechanics principles. A defining characteristic of our method is the seamless integration between physical simulation and visual rendering: both components utilize the same 3D Gaussian kernels as their discrete representations. This negates the necessity for triangle/tetrahedron meshing, marching cubes, "cage meshes," or any other geometry embedding, highlighting the principle of "what you see is what you simulate (WS^2)." Our method demonstrates exceptional versatility across a wide variety of materials--including elastic entities, metals, non-Newtonian fluids, and granular materials--showcasing its strong capabilities in creating diverse visual content with novel viewpoints and movements. Our project page is at: https://xpandora.github.io/PhysGaussian/

Following the advent of NeRFs, 3D Gaussian Splatting (3D-GS) has paved the way to real-time neural rendering overcoming the computational burden of volumetric methods. Following the pioneering work of 3D-GS, several methods have attempted to achieve compressible and high-fidelity performance alternatives. However, by employing a geometry-agnostic optimization scheme, these methods neglect the inherent 3D structure of the scene, thereby restricting the expressivity and the quality of the representation, resulting in various floating points and artifacts. In this work, we propose a structure-aware Gaussian Splatting method (SAGS) that implicitly encodes the geometry of the scene, which reflects to state-of-the-art rendering performance and reduced storage requirements on benchmark novel-view synthesis datasets. SAGS is founded on a local-global graph representation that facilitates the learning of complex scenes and enforces meaningful point displacements that preserve the scene's geometry. Additionally, we introduce a lightweight version of SAGS, using a simple yet effective mid-point interpolation scheme, which showcases a compact representation of the scene with up to 24times size reduction without the reliance on any compression strategies. Extensive experiments across multiple benchmark datasets demonstrate the superiority of SAGS compared to state-of-the-art 3D-GS methods under both rendering quality and model size. Besides, we demonstrate that our structure-aware method can effectively mitigate floating artifacts and irregular distortions of previous methods while obtaining precise depth maps. Project page https://eververas.github.io/SAGS/.

The scarcity of large-scale 3D-text paired data poses a great challenge on open vocabulary 3D scene understanding, and hence it is popular to leverage internet-scale 2D data and transfer their open vocabulary capabilities to 3D models through knowledge distillation. However, the existing distillation-based 3D scene understanding approaches rely on the representation capacity of 2D models, disregarding the exploration of geometric priors and inherent representational advantages offered by 3D data. In this paper, we propose an effective approach, namely Geometry Guided Self-Distillation (GGSD), to learn superior 3D representations from 2D pre-trained models. Specifically, we first design a geometry guided distillation module to distill knowledge from 2D models, and then leverage the 3D geometric priors to alleviate the inherent noise in 2D models and enhance the representation learning process. Due to the advantages of 3D representation, the performance of the distilled 3D student model can significantly surpass that of the 2D teacher model. This motivates us to further leverage the representation advantages of 3D data through self-distillation. As a result, our proposed GGSD approach outperforms the existing open vocabulary 3D scene understanding methods by a large margin, as demonstrated by our experiments on both indoor and outdoor benchmark datasets.

It has been observed that representations learned by distinct neural networks conceal structural similarities when the models are trained under similar inductive biases. From a geometric perspective, identifying the classes of transformations and the related invariances that connect these representations is fundamental to unlocking applications, such as merging, stitching, and reusing different neural modules. However, estimating task-specific transformations a priori can be challenging and expensive due to several factors (e.g., weights initialization, training hyperparameters, or data modality). To this end, we introduce a versatile method to directly incorporate a set of invariances into the representations, constructing a product space of invariant components on top of the latent representations without requiring prior knowledge about the optimal invariance to infuse. We validate our solution on classification and reconstruction tasks, observing consistent latent similarity and downstream performance improvements in a zero-shot stitching setting. The experimental analysis comprises three modalities (vision, text, and graphs), twelve pretrained foundational models, nine benchmarks, and several architectures trained from scratch.

Recent advances in discriminative and generative pretraining have yielded geometry estimation models with strong generalization capabilities. While discriminative monocular geometry estimation methods rely on large-scale fine-tuning data to achieve zero-shot generalization, several generative-based paradigms show the potential of achieving impressive generalization performance on unseen scenes by leveraging pre-trained diffusion models and fine-tuning on even a small scale of synthetic training data. Frustratingly, these models are trained with different recipes on different datasets, making it hard to find out the critical factors that determine the evaluation performance. Besides, current geometry evaluation benchmarks have two main drawbacks that may prevent the development of the field, i.e., limited scene diversity and unfavorable label quality. To resolve the above issues, (1) we build fair and strong baselines in a unified codebase for evaluating and analyzing the geometry estimation models; (2) we evaluate monocular geometry estimators on more challenging benchmarks for geometry estimation task with diverse scenes and high-quality annotations. Our results reveal that pre-trained using large data, discriminative models such as DINOv2, can outperform generative counterparts with a small amount of high-quality synthetic data under the same training configuration, which suggests that fine-tuning data quality is a more important factor than the data scale and model architecture. Our observation also raises a question: if simply fine-tuning a general vision model such as DINOv2 using a small amount of synthetic depth data produces SOTA results, do we really need complex generative models for depth estimation? We believe this work can propel advancements in geometry estimation tasks as well as a wide range of downstream applications.

Many deep generative models are defined as a push-forward of a Gaussian measure by a continuous generator, such as Generative Adversarial Networks (GANs) or Variational Auto-Encoders (VAEs). This work explores the latent space of such deep generative models. A key issue with these models is their tendency to output samples outside of the support of the target distribution when learning disconnected distributions. We investigate the relationship between the performance of these models and the geometry of their latent space. Building on recent developments in geometric measure theory, we prove a sufficient condition for optimality in the case where the dimension of the latent space is larger than the number of modes. Through experiments on GANs, we demonstrate the validity of our theoretical results and gain new insights into the latent space geometry of these models. Additionally, we propose a truncation method that enforces a simplicial cluster structure in the latent space and improves the performance of GANs.

In the realm of digital creativity, our potential to craft intricate 3D worlds from imagination is often hampered by the limitations of existing digital tools, which demand extensive expertise and efforts. To narrow this disparity, we introduce CLAY, a 3D geometry and material generator designed to effortlessly transform human imagination into intricate 3D digital structures. CLAY supports classic text or image inputs as well as 3D-aware controls from diverse primitives (multi-view images, voxels, bounding boxes, point clouds, implicit representations, etc). At its core is a large-scale generative model composed of a multi-resolution Variational Autoencoder (VAE) and a minimalistic latent Diffusion Transformer (DiT), to extract rich 3D priors directly from a diverse range of 3D geometries. Specifically, it adopts neural fields to represent continuous and complete surfaces and uses a geometry generative module with pure transformer blocks in latent space. We present a progressive training scheme to train CLAY on an ultra large 3D model dataset obtained through a carefully designed processing pipeline, resulting in a 3D native geometry generator with 1.5 billion parameters. For appearance generation, CLAY sets out to produce physically-based rendering (PBR) textures by employing a multi-view material diffusion model that can generate 2K resolution textures with diffuse, roughness, and metallic modalities. We demonstrate using CLAY for a range of controllable 3D asset creations, from sketchy conceptual designs to production ready assets with intricate details. Even first time users can easily use CLAY to bring their vivid 3D imaginations to life, unleashing unlimited creativity.

Representing complex objects with basic geometric primitives has long been a topic in computer vision. Primitive-based representations have the merits of compactness and computational efficiency in higher-level tasks such as physics simulation, collision checking, and robotic manipulation. Unlike previous works which extract polygonal meshes from a signed distance function (SDF), in this paper, we present a novel method, named Marching-Primitives, to obtain a primitive-based abstraction directly from an SDF. Our method grows geometric primitives (such as superquadrics) iteratively by analyzing the connectivity of voxels while marching at different levels of signed distance. For each valid connected volume of interest, we march on the scope of voxels from which a primitive is able to be extracted in a probabilistic sense and simultaneously solve for the parameters of the primitive to capture the underlying local geometry. We evaluate the performance of our method on both synthetic and real-world datasets. The results show that the proposed method outperforms the state-of-the-art in terms of accuracy, and is directly generalizable among different categories and scales. The code is open-sourced at https://github.com/ChirikjianLab/Marching-Primitives.git.

Faithful visualizations of data residing on manifolds must take the underlying geometry into account when producing a flat planar view of the data. In this paper, we extend the classic stochastic neighbor embedding (SNE) algorithm to data on general Riemannian manifolds. We replace standard Gaussian assumptions with Riemannian diffusion counterparts and propose an efficient approximation that only requires access to calculations of Riemannian distances and volumes. We demonstrate that the approach also allows for mapping data from one manifold to another, e.g. from a high-dimensional sphere to a low-dimensional one.

This work investigates the use of smooth neural networks for modeling dynamic variations of implicit surfaces under the level set equation (LSE). For this, it extends the representation of neural implicit surfaces to the space-time R^3times R, which opens up mechanisms for continuous geometric transformations. Examples include evolving an initial surface towards general vector fields, smoothing and sharpening using the mean curvature equation, and interpolations of initial conditions. The network training considers two constraints. A data term is responsible for fitting the initial condition to the corresponding time instant, usually R^3 times {0}. Then, a LSE term forces the network to approximate the underlying geometric evolution given by the LSE, without any supervision. The network can also be initialized based on previously trained initial conditions, resulting in faster convergence compared to the standard approach.

Mapping high-fidelity 3D geometry to a representation that allows for intuitive edits remains an elusive goal in computer vision and graphics. The key challenge is the need to model both continuous and discrete shape variations. Current approaches, such as implicit shape representation, lack straightforward interpretable encoding, while others that employ procedural methods output coarse geometry. We present GeoCode, a technique for 3D shape synthesis using an intuitively editable parameter space. We build a novel program that enforces a complex set of rules and enables users to perform intuitive and controlled high-level edits that procedurally propagate at a low level to the entire shape. Our program produces high-quality mesh outputs by construction. We use a neural network to map a given point cloud or sketch to our interpretable parameter space. Once produced by our procedural program, shapes can be easily modified. Empirically, we show that GeoCode can infer and recover 3D shapes more accurately compared to existing techniques and we demonstrate its ability to perform controlled local and global shape manipulations.

In Marius von Senden's Space and Sight, a newly sighted blind patient describes the experience of a corner as lemon-like, because corners "prick" sight like lemons prick the tongue. Prickliness, here, is a dimension in the feature space of sensory experience, an effect of the perceived on the perceiver that arises where the two interact. In the account of the newly sighted, an effect familiar from one interaction translates to a novel context. Perception serves as the vehicle for generalization, in that an effect shared across different experiences produces a concrete abstraction grounded in those experiences. Cezanne and the post-impressionists, fluent in the language of experience translation, realized that the way to paint a concrete form that best reflected reality was to paint not what they saw, but what it was like to see. We envision a future of creation using AI where what it is like to see is replicable, transferrable, manipulable - part of the artist's palette that is both grounded in a particular context, and generalizable beyond it. An active line of research maps human-interpretable features onto directions in GAN latent space. Supervised and self-supervised approaches that search for anticipated directions or use off-the-shelf classifiers to drive image manipulation in embedding space are limited in the variety of features they can uncover. Unsupervised approaches that discover useful new directions show that the space of perceptually meaningful directions is nowhere close to being fully mapped. As this space is broad and full of creative potential, we want tools for direction discovery that capture the richness and generalizability of human perception. Our approach puts creators in the discovery loop during real-time tool use, in order to identify directions that are perceptually meaningful to them, and generate interpretable image translations along those directions.

Solving Algebra Problems with Geometry Diagrams (APGDs) is still a challenging problem because diagram processing is not studied as intensively as language processing. To work against this challenge, this paper proposes a hologram reasoning scheme and develops a high-performance method for solving APGDs by using this scheme. To reach this goal, it first defines a hologram, being a kind of graph, and proposes a hologram generator to convert a given APGD into a hologram, which represents the entire information of APGD and the relations for solving the problem can be acquired from it by a uniform way. Then HGR, a hologram reasoning method employs a pool of prepared graph models to derive algebraic equations, which is consistent with the geometric theorems. This method is able to be updated by adding new graph models into the pool. Lastly, it employs deep reinforcement learning to enhance the efficiency of model selection from the pool. The entire HGR not only ensures high solution accuracy with fewer reasoning steps but also significantly enhances the interpretability of the solution process by providing descriptions of all reasoning steps. Experimental results demonstrate the effectiveness of HGR in improving both accuracy and interpretability in solving APGDs.

Computer-aided design (CAD) significantly enhances the efficiency, accuracy, and innovation of design processes by enabling precise 2D and 3D modeling, extensive analysis, and optimization. Existing methods for creating CAD models rely on latent vectors or point clouds, which are difficult to obtain and costly to store. Recent advances in Multimodal Large Language Models (MLLMs) have inspired researchers to use natural language instructions and images for CAD model construction. However, these models still struggle with inferring accurate 3D spatial location and orientation, leading to inaccuracies in determining the spatial 3D starting points and extrusion directions for constructing geometries. This work introduces CAD-GPT, a CAD synthesis method with spatial reasoning-enhanced MLLM that takes either a single image or a textual description as input. To achieve precise spatial inference, our approach introduces a 3D Modeling Spatial Mechanism. This method maps 3D spatial positions and 3D sketch plane rotation angles into a 1D linguistic feature space using a specialized spatial unfolding mechanism, while discretizing 2D sketch coordinates into an appropriate planar space to enable precise determination of spatial starting position, sketch orientation, and 2D sketch coordinate translations. Extensive experiments demonstrate that CAD-GPT consistently outperforms existing state-of-the-art methods in CAD model synthesis, both quantitatively and qualitatively.

This paper presents the computational challenge on differential geometry and topology that happened within the ICLR 2021 workshop "Geometric and Topological Representation Learning". The competition asked participants to provide creative contributions to the fields of computational geometry and topology through the open-source repositories Geomstats and Giotto-TDA. The challenge attracted 16 teams in its two month duration. This paper describes the design of the challenge and summarizes its main findings.

Generalizing metric monocular depth estimation presents a significant challenge due to its ill-posed nature, while the entanglement between camera parameters and depth amplifies issues further, hindering multi-dataset training and zero-shot accuracy. This challenge is particularly evident in autonomous vehicles and mobile robotics, where data is collected with fixed camera setups, limiting the geometric diversity. Yet, this context also presents an opportunity: the fixed relationship between the camera and the ground plane imposes additional perspective geometry constraints, enabling depth regression via vertical image positions of objects. However, this cue is highly susceptible to overfitting, thus we propose a novel canonical representation that maintains consistency across varied camera setups, effectively disentangling depth from specific parameters and enhancing generalization across datasets. We also propose a novel architecture that adaptively and probabilistically fuses depths estimated via object size and vertical image position cues. A comprehensive evaluation demonstrates the effectiveness of the proposed approach on five autonomous driving datasets, achieving accurate metric depth estimation for varying resolutions, aspect ratios and camera setups. Notably, we achieve comparable accuracy to existing zero-shot methods, despite training on a single dataset with a single-camera setup.

With their meaningful geometry and their omnipresence in the 3D world, edges are extremely useful primitives in computer vision. 3D edges comprise of lines and curves, and methods to reconstruct them use either multi-view images or point clouds as input. State-of-the-art image-based methods first learn a 3D edge point cloud then fit 3D edges to it. The edge point cloud is obtained by learning a 3D neural implicit edge field from which the 3D edge points are sampled on a specific level set (0 or 1). However, such methods present two important drawbacks: i) it is not realistic to sample points on exact level sets due to float imprecision and training inaccuracies. Instead, they are sampled within a range of levels so the points do not lie accurately on the 3D edges and require further processing. ii) Such implicit representations are computationally expensive and require long training times. In this paper, we address these two limitations and propose a 3D edge mapping that is simpler, more efficient, and preserves accuracy. Our method learns explicitly the 3D edge points and their edge direction hence bypassing the need for point sampling. It casts a 3D edge point as the center of a 3D Gaussian and the edge direction as the principal axis of the Gaussian. Such a representation has the advantage of being not only geometrically meaningful but also compatible with the efficient training optimization defined in Gaussian Splatting. Results show that the proposed method produces edges as accurate and complete as the state-of-the-art while being an order of magnitude faster. Code is released at https://github.com/kunalchelani/EdgeGaussians.

Diffusion models generating images conditionally on text, such as Dall-E 2 and Stable Diffusion, have recently made a splash far beyond the computer vision community. Here, we tackle the related problem of generating point clouds, both unconditionally, and conditionally with images. For the latter, we introduce a novel geometrically-motivated conditioning scheme based on projecting sparse image features into the point cloud and attaching them to each individual point, at every step in the denoising process. This approach improves geometric consistency and yields greater fidelity than current methods relying on unstructured, global latent codes. Additionally, we show how to apply recent continuous-time diffusion schemes. Our method performs on par or above the state of art on conditional and unconditional experiments on synthetic data, while being faster, lighter, and delivering tractable likelihoods. We show it can also scale to diverse indoors scenes.

Using parts of existing models to rebuild new models, commonly termed as example-based modeling, is a classical methodology in the realm of computer graphics. Previous works mostly focus on shape composition, making them very hard to use for realistic composition of 3D objects captured from real-world scenes. This leads to combining multiple NeRFs into a single 3D scene to achieve seamless appearance blending. However, the current SeamlessNeRF method struggles to achieve interactive editing and harmonious stitching for real-world scenes due to its gradient-based strategy and grid-based representation. To this end, we present an example-based modeling method that combines multiple Gaussian fields in a point-based representation using sample-guided synthesis. Specifically, as for composition, we create a GUI to segment and transform multiple fields in real time, easily obtaining a semantically meaningful composition of models represented by 3D Gaussian Splatting (3DGS). For texture blending, due to the discrete and irregular nature of 3DGS, straightforwardly applying gradient propagation as SeamlssNeRF is not supported. Thus, a novel sampling-based cloning method is proposed to harmonize the blending while preserving the original rich texture and content. Our workflow consists of three steps: 1) real-time segmentation and transformation of a Gaussian model using a well-tailored GUI, 2) KNN analysis to identify boundary points in the intersecting area between the source and target models, and 3) two-phase optimization of the target model using sampling-based cloning and gradient constraints. Extensive experimental results validate that our approach significantly outperforms previous works in terms of realistic synthesis, demonstrating its practicality. More demos are available at https://ingra14m.github.io/gs_stitching_website.

Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects--the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra--which have been loosely referred to as "positive geometries". The connection between the geometry and physics is provided by a unique differential form canonically determined by the property of having logarithmic singularities (only) on all the boundaries of the space, with residues on each boundary given by the canonical form on that boundary. In this paper we initiate an exploration of "positive geometries" and "canonical forms" as objects of study in their own right in a more general mathematical setting. We give a precise definition of positive geometries and canonical forms, introduce general methods for finding forms for more complicated positive geometries from simpler ones, and present numerous examples of positive geometries in projective spaces, Grassmannians, and toric, cluster and flag varieties. We also illustrate a number of strategies for computing canonical forms which yield interesting representations for the forms associated with wide classes of positive geometries, ranging from the simplest Amplituhedra to new expressions for the volume of arbitrary convex polytopes.

Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the symmetry group employed is compact or abelian, or both. Recent work has explored enlarging the class of transformations used to the case of Lie groups, principally through the use of their Lie algebra, as well as the group exponential and logarithm maps. The applicability of such methods to larger transformation groups is limited by the fact that depending on the group of interest G, the exponential map may not be surjective. Further limitations are encountered when G is neither compact nor abelian. Using the structure and geometry of Lie groups and their homogeneous spaces, we present a framework by which it is possible to work with such groups primarily focusing on the Lie groups G = GL^{+}(n, R) and G = SL(n, R), as well as their representation as affine transformations R^{n} rtimes G. Invariant integration as well as a global parametrization is realized by decomposing the `larger` groups into subgroups and submanifolds which can be handled individually. Under this framework, we show how convolution kernels can be parametrized to build models equivariant with respect to affine transformations. We evaluate the robustness and out-of-distribution generalisation capability of our model on the standard affine-invariant benchmark classification task, where we outperform all previous equivariant models as well as all Capsule Network proposals.

Grounding language to the visual observations of a navigating agent can be performed using off-the-shelf visual-language models pretrained on Internet-scale data (e.g., image captions). While this is useful for matching images to natural language descriptions of object goals, it remains disjoint from the process of mapping the environment, so that it lacks the spatial precision of classic geometric maps. To address this problem, we propose VLMaps, a spatial map representation that directly fuses pretrained visual-language features with a 3D reconstruction of the physical world. VLMaps can be autonomously built from video feed on robots using standard exploration approaches and enables natural language indexing of the map without additional labeled data. Specifically, when combined with large language models (LLMs), VLMaps can be used to (i) translate natural language commands into a sequence of open-vocabulary navigation goals (which, beyond prior work, can be spatial by construction, e.g., "in between the sofa and TV" or "three meters to the right of the chair") directly localized in the map, and (ii) can be shared among multiple robots with different embodiments to generate new obstacle maps on-the-fly (by using a list of obstacle categories). Extensive experiments carried out in simulated and real world environments show that VLMaps enable navigation according to more complex language instructions than existing methods. Videos are available at https://vlmaps.github.io.

Due to high utility in many applications, from social networks to blockchain to power grids, deep learning on non-Euclidean objects such as graphs and manifolds, coined Geometric Deep Learning (GDL), continues to gain an ever increasing interest. We propose a new L\'evy Flights Graph Convolutional Networks (LFGCN) method for semi-supervised learning, which casts the L\'evy Flights into random walks on graphs and, as a result, allows both to accurately account for the intrinsic graph topology and to substantially improve classification performance, especially for heterogeneous graphs. Furthermore, we propose a new preferential P-DropEdge method based on the Girvan-Newman argument. That is, in contrast to uniform removing of edges as in DropEdge, following the Girvan-Newman algorithm, we detect network periphery structures using information on edge betweenness and then remove edges according to their betweenness centrality. Our experimental results on semi-supervised node classification tasks demonstrate that the LFGCN coupled with P-DropEdge accelerates the training task, increases stability and further improves predictive accuracy of learned graph topology structure. Finally, in our case studies we bring the machinery of LFGCN and other deep networks tools to analysis of power grid networks - the area where the utility of GDL remains untapped.

Shape assembly aims to reassemble parts (or fragments) into a complete object, which is a common task in our daily life. Different from the semantic part assembly (e.g., assembling a chair's semantic parts like legs into a whole chair), geometric part assembly (e.g., assembling bowl fragments into a complete bowl) is an emerging task in computer vision and robotics. Instead of semantic information, this task focuses on geometric information of parts. As the both geometric and pose space of fractured parts are exceptionally large, shape pose disentanglement of part representations is beneficial to geometric shape assembly. In our paper, we propose to leverage SE(3) equivariance for such shape pose disentanglement. Moreover, while previous works in vision and robotics only consider SE(3) equivariance for the representations of single objects, we move a step forward and propose leveraging SE(3) equivariance for representations considering multi-part correlations, which further boosts the performance of the multi-part assembly. Experiments demonstrate the significance of SE(3) equivariance and our proposed method for geometric shape assembly. Project page: https://crtie.github.io/SE-3-part-assembly/

Generative models for 3D object synthesis have seen significant advancements with the incorporation of prior knowledge distilled from 2D diffusion models. Nevertheless, challenges persist in the form of multi-view geometric inconsistencies and slow generation speeds within the existing 3D synthesis frameworks. This can be attributed to two factors: firstly, the deficiency of abundant geometric a priori knowledge in optimization, and secondly, the entanglement issue between geometry and texture in conventional 3D generation methods.In response, we introduce MetaDreammer, a two-stage optimization approach that leverages rich 2D and 3D prior knowledge. In the first stage, our emphasis is on optimizing the geometric representation to ensure multi-view consistency and accuracy of 3D objects. In the second stage, we concentrate on fine-tuning the geometry and optimizing the texture, thereby achieving a more refined 3D object. Through leveraging 2D and 3D prior knowledge in two stages, respectively, we effectively mitigate the interdependence between geometry and texture. MetaDreamer establishes clear optimization objectives for each stage, resulting in significant time savings in the 3D generation process. Ultimately, MetaDreamer can generate high-quality 3D objects based on textual prompts within 20 minutes, and to the best of our knowledge, it is the most efficient text-to-3D generation method. Furthermore, we introduce image control into the process, enhancing the controllability of 3D generation. Extensive empirical evidence confirms that our method is not only highly efficient but also achieves a quality level that is at the forefront of current state-of-the-art 3D generation techniques.

We introduce a pipeline that enhances a general-purpose Vision Language Model, GPT-4V(ision), by integrating observations of human actions to facilitate robotic manipulation. This system analyzes videos of humans performing tasks and creates executable robot programs that incorporate affordance insights. The computation starts by analyzing the videos with GPT-4V to convert environmental and action details into text, followed by a GPT-4-empowered task planner. In the following analyses, vision systems reanalyze the video with the task plan. Object names are grounded using an open-vocabulary object detector, while focus on the hand-object relation helps to detect the moment of grasping and releasing. This spatiotemporal grounding allows the vision systems to further gather affordance data (e.g., grasp type, way points, and body postures). Experiments across various scenarios demonstrate this method's efficacy in achieving real robots' operations from human demonstrations in a zero-shot manner. The prompts of GPT-4V/GPT-4 are available at this project page: https://microsoft.github.io/GPT4Vision-Robot-Manipulation-Prompts/

Maps are a key component in image-based camera localization and visual SLAM systems: they are used to establish geometric constraints between images, correct drift in relative pose estimation, and relocalize cameras after lost tracking. The exact definitions of maps, however, are often application-specific and hand-crafted for different scenarios (e.g. 3D landmarks, lines, planes, bags of visual words). We propose to represent maps as a deep neural net called MapNet, which enables learning a data-driven map representation. Unlike prior work on learning maps, MapNet exploits cheap and ubiquitous sensory inputs like visual odometry and GPS in addition to images and fuses them together for camera localization. Geometric constraints expressed by these inputs, which have traditionally been used in bundle adjustment or pose-graph optimization, are formulated as loss terms in MapNet training and also used during inference. In addition to directly improving localization accuracy, this allows us to update the MapNet (i.e., maps) in a self-supervised manner using additional unlabeled video sequences from the scene. We also propose a novel parameterization for camera rotation which is better suited for deep-learning based camera pose regression. Experimental results on both the indoor 7-Scenes dataset and the outdoor Oxford RobotCar dataset show significant performance improvement over prior work. The MapNet project webpage is https://goo.gl/mRB3Au.

3D geometric information is essential for manipulation tasks, as robots need to perceive the 3D environment, reason about spatial relationships, and interact with intricate spatial configurations. Recent research has increasingly focused on the explicit extraction of 3D features, while still facing challenges such as the lack of large-scale robotic 3D data and the potential loss of spatial geometry. To address these limitations, we propose the Lift3D framework, which progressively enhances 2D foundation models with implicit and explicit 3D robotic representations to construct a robust 3D manipulation policy. Specifically, we first design a task-aware masked autoencoder that masks task-relevant affordance patches and reconstructs depth information, enhancing the 2D foundation model's implicit 3D robotic representation. After self-supervised fine-tuning, we introduce a 2D model-lifting strategy that establishes a positional mapping between the input 3D points and the positional embeddings of the 2D model. Based on the mapping, Lift3D utilizes the 2D foundation model to directly encode point cloud data, leveraging large-scale pretrained knowledge to construct explicit 3D robotic representations while minimizing spatial information loss. In experiments, Lift3D consistently outperforms previous state-of-the-art methods across several simulation benchmarks and real-world scenarios.

We propose transferability from Large Geometric Vicinity (LGV), a new technique to increase the transferability of black-box adversarial attacks. LGV starts from a pretrained surrogate model and collects multiple weight sets from a few additional training epochs with a constant and high learning rate. LGV exploits two geometric properties that we relate to transferability. First, models that belong to a wider weight optimum are better surrogates. Second, we identify a subspace able to generate an effective surrogate ensemble among this wider optimum. Through extensive experiments, we show that LGV alone outperforms all (combinations of) four established test-time transformations by 1.8 to 59.9 percentage points. Our findings shed new light on the importance of the geometry of the weight space to explain the transferability of adversarial examples.

Empirically validating new 3D-printing related algorithms and implementations requires testing data representative of inputs encountered in the wild. An ideal benchmarking dataset should not only draw from the same distribution of shapes people print in terms of class (e.g., toys, mechanisms, jewelry), representation type (e.g., triangle soup meshes) and complexity (e.g., number of facets), but should also capture problems and artifacts endemic to 3D printing models (e.g., self-intersections, non-manifoldness). We observe that the contextual and geometric characteristics of 3D printing models differ significantly from those used for computer graphics applications, not to mention standard models (e.g., Stanford bunny, Armadillo, Fertility). We present a new dataset of 10,000 models collected from an online 3D printing model-sharing database. Via analysis of both geometric (e.g., triangle aspect ratios, manifoldness) and contextual (e.g., licenses, tags, classes) characteristics, we demonstrate that this dataset represents a more concise summary of real-world models used for 3D printing compared to existing datasets. To facilitate future research endeavors, we also present an online query interface to select subsets of the dataset according to project-specific characteristics. The complete dataset and per-model statistical data are freely available to the public.

Knot diagrams are among the most common visual tools in topology. Computer programs now make it possible to draw, manipulate and render them digitally, which proves to be useful in knot theory teaching and research. Still, an openly available tool to manipulate knot diagrams in a real-time, interactive way is yet to be developed. We introduce a method of operating on the geometry of the knot diagram itself without any underlying three-dimensional structure that can underpin such an application. This allows us to directly interact with vector graphics knot diagrams while at the same time computing knot invariants in ways proposed by previous work. An implementation of this method is provided.

3D-aware Generative Adversarial Networks (GANs) have shown remarkable progress in learning to generate multi-view-consistent images and 3D geometries of scenes from collections of 2D images via neural volume rendering. Yet, the significant memory and computational costs of dense sampling in volume rendering have forced 3D GANs to adopt patch-based training or employ low-resolution rendering with post-processing 2D super resolution, which sacrifices multiview consistency and the quality of resolved geometry. Consequently, 3D GANs have not yet been able to fully resolve the rich 3D geometry present in 2D images. In this work, we propose techniques to scale neural volume rendering to the much higher resolution of native 2D images, thereby resolving fine-grained 3D geometry with unprecedented detail. Our approach employs learning-based samplers for accelerating neural rendering for 3D GAN training using up to 5 times fewer depth samples. This enables us to explicitly "render every pixel" of the full-resolution image during training and inference without post-processing superresolution in 2D. Together with our strategy to learn high-quality surface geometry, our method synthesizes high-resolution 3D geometry and strictly view-consistent images while maintaining image quality on par with baselines relying on post-processing super resolution. We demonstrate state-of-the-art 3D gemetric quality on FFHQ and AFHQ, setting a new standard for unsupervised learning of 3D shapes in 3D GANs.

Geometry and color information provided by the point clouds are both crucial for 3D scene understanding. Two pieces of information characterize the different aspects of point clouds, but existing methods lack an elaborate design for the discrimination and relevance. Hence we explore a 3D self-supervised paradigm that can better utilize the relations of point cloud information. Specifically, we propose a universal 3D scene pre-training framework via Geometry-Color Contrast (Point-GCC), which aligns geometry and color information using a Siamese network. To take care of actual application tasks, we design (i) hierarchical supervision with point-level contrast and reconstruct and object-level contrast based on the novel deep clustering module to close the gap between pre-training and downstream tasks; (ii) architecture-agnostic backbone to adapt for various downstream models. Benefiting from the object-level representation associated with downstream tasks, Point-GCC can directly evaluate model performance and the result demonstrates the effectiveness of our methods. Transfer learning results on a wide range of tasks also show consistent improvements across all datasets. e.g., new state-of-the-art object detection results on SUN RGB-D and S3DIS datasets. Codes will be released at https://github.com/Asterisci/Point-GCC.

We investigate the problem of training generative models on a very sparse collection of 3D models. We use geometrically motivated energies to augment and thus boost a sparse collection of example (training) models. We analyze the Hessian of the as-rigid-as-possible (ARAP) energy to sample from and project to the underlying (local) shape space, and use the augmented dataset to train a variational autoencoder (VAE). We iterate the process of building latent spaces of VAE and augmenting the associated dataset, to progressively reveal a richer and more expressive generative space for creating geometrically and semantically valid samples. Our framework allows us to train generative 3D models even with a small set of good quality 3D models, which are typically hard to curate. We extensively evaluate our method against a set of strong baselines, provide ablation studies and demonstrate application towards establishing shape correspondences. We present multiple examples of interesting and meaningful shape variations even when starting from as few as 3-10 training shapes.

Image-based 3D reconstruction has increasingly stunning results over the past few years with the latest improvements in computer vision and graphics. Geometry and topology are two fundamental concepts when dealing with 3D mesh structures. But the latest often remains a side issue in the 3D mesh-based reconstruction literature. Indeed, performing per-vertex elementary displacements over a 3D sphere mesh only impacts its geometry and leaves the topological structure unchanged and fixed. Whereas few attempts propose to update the geometry and the topology, all need to lean on costly 3D ground-truth to determine the faces/edges to prune. We present in this work a method that aims to refine the topology of any 3D mesh through a face-pruning strategy that extensively relies upon 2D alpha masks and camera pose information. Our solution leverages a differentiable renderer that renders each face as a 2D soft map. Its pixel intensity reflects the probability of being covered during the rendering process by such a face. Based on the 2D soft-masks available, our method is thus able to quickly highlight all the incorrectly rendered faces for a given viewpoint. Because our module is agnostic to the network that produces the 3D mesh, it can be easily plugged into any self-supervised image-based (either synthetic or natural) 3D reconstruction pipeline to get complex meshes with a non-spherical topology.

In this paper, we focus on 3D scene inpainting, where parts of an input image set, captured from different viewpoints, are masked out. The main challenge lies in generating plausible image completions that are geometrically consistent across views. Most recent work addresses this challenge by combining generative models with a 3D radiance field to fuse information across a relatively dense set of viewpoints. However, a major drawback of these methods is that they often produce blurry images due to the fusion of inconsistent cross-view images. To avoid blurry inpaintings, we eschew the use of an explicit or implicit radiance field altogether and instead fuse cross-view information in a learned space. In particular, we introduce a geometry-aware conditional generative model, capable of multi-view consistent inpainting using reference-based geometric and appearance cues. A key advantage of our approach over existing methods is its unique ability to inpaint masked scenes with a limited number of views (i.e., few-view inpainting), whereas previous methods require relatively large image sets for their 3D model fitting step. Empirically, we evaluate and compare our scene-centric inpainting method on two datasets, SPIn-NeRF and NeRFiller, which contain images captured at narrow and wide baselines, respectively, and achieve state-of-the-art 3D inpainting performance on both. Additionally, we demonstrate the efficacy of our approach in the few-view setting compared to prior methods.

How should representations from complementary sensors be integrated for autonomous driving? Geometry-based sensor fusion has shown great promise for perception tasks such as object detection and motion forecasting. However, for the actual driving task, the global context of the 3D scene is key, e.g. a change in traffic light state can affect the behavior of a vehicle geometrically distant from that traffic light. Geometry alone may therefore be insufficient for effectively fusing representations in end-to-end driving models. In this work, we demonstrate that imitation learning policies based on existing sensor fusion methods under-perform in the presence of a high density of dynamic agents and complex scenarios, which require global contextual reasoning, such as handling traffic oncoming from multiple directions at uncontrolled intersections. Therefore, we propose TransFuser, a novel Multi-Modal Fusion Transformer, to integrate image and LiDAR representations using attention. We experimentally validate the efficacy of our approach in urban settings involving complex scenarios using the CARLA urban driving simulator. Our approach achieves state-of-the-art driving performance while reducing collisions by 76% compared to geometry-based fusion.

Knowledge graph embedding (KGE) is an increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.

Although polygon meshes have been a standard representation in geometry processing, their irregular and combinatorial nature hinders their suitability for learning-based applications. In this work, we introduce a novel learnable mesh representation through a set of local 3D sample Points and their associated Normals and Quadric error metrics (QEM) w.r.t. the underlying shape, which we denote PoNQ. A global mesh is directly derived from PoNQ by efficiently leveraging the knowledge of the local quadric errors. Besides marking the first use of QEM within a neural shape representation, our contribution guarantees both topological and geometrical properties by ensuring that a PoNQ mesh does not self-intersect and is always the boundary of a volume. Notably, our representation does not rely on a regular grid, is supervised directly by the target surface alone, and also handles open surfaces with boundaries and/or sharp features. We demonstrate the efficacy of PoNQ through a learning-based mesh prediction from SDF grids and show that our method surpasses recent state-of-the-art techniques in terms of both surface and edge-based metrics.

The widespread use of vector graphics creates a significant demand for vectorization methods. While recent learning-based techniques have shown their capability to create vector images of clear topology, filling these primitives with gradients remains a challenge. In this paper, we propose a segmentation-guided vectorization framework to convert raster images into concise vector graphics with radial gradient fills. With the guidance of an embedded gradient-aware segmentation subroutine, our approach progressively appends gradient-filled B\'ezier paths to the output, where primitive parameters are initiated with our newly designed initialization technique and are optimized to minimize our novel loss function. We build our method on a differentiable renderer with traditional segmentation algorithms to develop it as a model-free tool for raster-to-vector conversion. It is tested on various inputs to demonstrate its feasibility, independent of datasets, to synthesize vector graphics with improved visual quality and layer-wise topology compared to prior work.

The recently developed Sora model [1] has exhibited remarkable capabilities in video generation, sparking intense discussions regarding its ability to simulate real-world phenomena. Despite its growing popularity, there is a lack of established metrics to evaluate its fidelity to real-world physics quantitatively. In this paper, we introduce a new benchmark that assesses the quality of the generated videos based on their adherence to real-world physics principles. We employ a method that transforms the generated videos into 3D models, leveraging the premise that the accuracy of 3D reconstruction is heavily contingent on the video quality. From the perspective of 3D reconstruction, we use the fidelity of the geometric constraints satisfied by the constructed 3D models as a proxy to gauge the extent to which the generated videos conform to real-world physics rules. Project page: https://sora-geometrical-consistency.github.io/

We introduce RealmDreamer, a technique for generation of general forward-facing 3D scenes from text descriptions. Our technique optimizes a 3D Gaussian Splatting representation to match complex text prompts. We initialize these splats by utilizing the state-of-the-art text-to-image generators, lifting their samples into 3D, and computing the occlusion volume. We then optimize this representation across multiple views as a 3D inpainting task with image-conditional diffusion models. To learn correct geometric structure, we incorporate a depth diffusion model by conditioning on the samples from the inpainting model, giving rich geometric structure. Finally, we finetune the model using sharpened samples from image generators. Notably, our technique does not require video or multi-view data and can synthesize a variety of high-quality 3D scenes in different styles, consisting of multiple objects. Its generality additionally allows 3D synthesis from a single image.

Generating photorealistic images with controllable camera pose and scene contents is essential for many applications including AR/VR and simulation. Despite the fact that rapid progress has been made in 3D-aware generative models, most existing methods focus on object-centric images and are not applicable to generating urban scenes for free camera viewpoint control and scene editing. To address this challenging task, we propose UrbanGIRAFFE, which uses a coarse 3D panoptic prior, including the layout distribution of uncountable stuff and countable objects, to guide a 3D-aware generative model. Our model is compositional and controllable as it breaks down the scene into stuff, objects, and sky. Using stuff prior in the form of semantic voxel grids, we build a conditioned stuff generator that effectively incorporates the coarse semantic and geometry information. The object layout prior further allows us to learn an object generator from cluttered scenes. With proper loss functions, our approach facilitates photorealistic 3D-aware image synthesis with diverse controllability, including large camera movement, stuff editing, and object manipulation. We validate the effectiveness of our model on both synthetic and real-world datasets, including the challenging KITTI-360 dataset.

Spatial intelligence is a critical component of embodied AI, promoting robots to understand and interact with their environments. While recent advances have enhanced the ability of VLMs to perceive object locations and positional relationships, they still lack the capability to precisely understand object orientations-a key requirement for tasks involving fine-grained manipulations. Addressing this limitation not only requires geometric reasoning but also an expressive and intuitive way to represent orientation. In this context, we propose that natural language offers a more flexible representation space than canonical frames, making it particularly suitable for instruction-following robotic systems. In this paper, we introduce the concept of semantic orientation, which defines object orientations using natural language in a reference-frame-free manner (e.g., the ''plug-in'' direction of a USB or the ''handle'' direction of a knife). To support this, we construct OrienText300K, a large-scale dataset of 3D models annotated with semantic orientations that link geometric understanding to functional semantics. By integrating semantic orientation into a VLM system, we enable robots to generate manipulation actions with both positional and orientational constraints. Extensive experiments in simulation and real world demonstrate that our approach significantly enhances robotic manipulation capabilities, e.g., 48.7% accuracy on Open6DOR and 74.9% accuracy on SIMPLER.

Recent advances in large-scale pretraining have yielded visual foundation models with strong capabilities. Not only can recent models generalize to arbitrary images for their training task, their intermediate representations are useful for other visual tasks such as detection and segmentation. Given that such models can classify, delineate, and localize objects in 2D, we ask whether they also represent their 3D structure? In this work, we analyze the 3D awareness of visual foundation models. We posit that 3D awareness implies that representations (1) encode the 3D structure of the scene and (2) consistently represent the surface across views. We conduct a series of experiments using task-specific probes and zero-shot inference procedures on frozen features. Our experiments reveal several limitations of the current models. Our code and analysis can be found at https://github.com/mbanani/probe3d.

The integration of language and 3D perception is crucial for developing embodied agents and robots that comprehend and interact with the physical world. While large language models (LLMs) have demonstrated impressive language understanding and generation capabilities, their adaptation to 3D environments (3D-LLMs) remains in its early stages. A primary challenge is the absence of large-scale datasets that provide dense grounding between language and 3D scenes. In this paper, we introduce 3D-GRAND, a pioneering large-scale dataset comprising 40,087 household scenes paired with 6.2 million densely-grounded scene-language instructions. Our results show that instruction tuning with 3D-GRAND significantly enhances grounding capabilities and reduces hallucinations in 3D-LLMs. As part of our contributions, we propose a comprehensive benchmark 3D-POPE to systematically evaluate hallucination in 3D-LLMs, enabling fair comparisons among future models. Our experiments highlight a scaling effect between dataset size and 3D-LLM performance, emphasizing the critical role of large-scale 3D-text datasets in advancing embodied AI research. Notably, our results demonstrate early signals for effective sim-to-real transfer, indicating that models trained on large synthetic data can perform well on real-world 3D scans. Through 3D-GRAND and 3D-POPE, we aim to equip the embodied AI community with essential resources and insights, setting the stage for more reliable and better-grounded 3D-LLMs. Project website: https://3d-grand.github.io

We present a computational framework that transforms single images into 3D physical objects. The visual geometry of a physical object in an image is determined by three orthogonal attributes: mechanical properties, external forces, and rest-shape geometry. Existing single-view 3D reconstruction methods often overlook this underlying composition, presuming rigidity or neglecting external forces. Consequently, the reconstructed objects fail to withstand real-world physical forces, resulting in instability or undesirable deformation -- diverging from their intended designs as depicted in the image. Our optimization framework addresses this by embedding physical compatibility into the reconstruction process. We explicitly decompose the three physical attributes and link them through static equilibrium, which serves as a hard constraint, ensuring that the optimized physical shapes exhibit desired physical behaviors. Evaluations on a dataset collected from Objaverse demonstrate that our framework consistently enhances the physical realism of 3D models over existing methods. The utility of our framework extends to practical applications in dynamic simulations and 3D printing, where adherence to physical compatibility is paramount.

A comprehensive semantic understanding of a scene is important for many applications - but in what space should diverse semantic information (e.g., objects, scene categories, material types, texture, etc.) be grounded and what should be its structure? Aspiring to have one unified structure that hosts diverse types of semantics, we follow the Scene Graph paradigm in 3D, generating a 3D Scene Graph. Given a 3D mesh and registered panoramic images, we construct a graph that spans the entire building and includes semantics on objects (e.g., class, material, and other attributes), rooms (e.g., scene category, volume, etc.) and cameras (e.g., location, etc.), as well as the relationships among these entities. However, this process is prohibitively labor heavy if done manually. To alleviate this we devise a semi-automatic framework that employs existing detection methods and enhances them using two main constraints: I. framing of query images sampled on panoramas to maximize the performance of 2D detectors, and II. multi-view consistency enforcement across 2D detections that originate in different camera locations.

A central question for neuroscience is how to characterize brain representations of perceptual and cognitive content. An ideal characterization should distinguish different functional regions with robustness to noise and idiosyncrasies of individual brains that do not correspond to computational differences. Previous studies have characterized brain representations by their representational geometry, which is defined by the representational dissimilarity matrix (RDM), a summary statistic that abstracts from the roles of individual neurons (or responses channels) and characterizes the discriminability of stimuli. Here we explore a further step of abstraction: from the geometry to the topology of brain representations. We propose topological representational similarity analysis (tRSA), an extension of representational similarity analysis (RSA) that uses a family of geo-topological summary statistics that generalizes the RDM to characterize the topology while de-emphasizing the geometry. We evaluate this new family of statistics in terms of the sensitivity and specificity for model selection using both simulations and functional MRI (fMRI) data. In the simulations, the ground truth is a data-generating layer representation in a neural network model and the models are the same and other layers in different model instances (trained from different random seeds). In fMRI, the ground truth is a visual area and the models are the same and other areas measured in different subjects. Results show that topology-sensitive characterizations of population codes are robust to noise and interindividual variability and maintain excellent sensitivity to the unique representational signatures of different neural network layers and brain regions.

Computer use agents automate digital tasks by directly interacting with graphical user interfaces (GUIs) on computers and mobile devices, offering significant potential to enhance human productivity by completing an open-ended space of user queries. However, current agents face significant challenges: imprecise grounding of GUI elements, difficulties with long-horizon task planning, and performance bottlenecks from relying on single generalist models for diverse cognitive tasks. To this end, we introduce Agent S2, a novel compositional framework that delegates cognitive responsibilities across various generalist and specialist models. We propose a novel Mixture-of-Grounding technique to achieve precise GUI localization and introduce Proactive Hierarchical Planning, dynamically refining action plans at multiple temporal scales in response to evolving observations. Evaluations demonstrate that Agent S2 establishes new state-of-the-art (SOTA) performance on three prominent computer use benchmarks. Specifically, Agent S2 achieves 18.9% and 32.7% relative improvements over leading baseline agents such as Claude Computer Use and UI-TARS on the OSWorld 15-step and 50-step evaluation. Moreover, Agent S2 generalizes effectively to other operating systems and applications, surpassing previous best methods by 52.8% on WindowsAgentArena and by 16.52% on AndroidWorld relatively. Code available at https://github.com/simular-ai/Agent-S.

Graph coarsening is a technique for solving large-scale graph problems by working on a smaller version of the original graph, and possibly interpolating the results back to the original graph. It has a long history in scientific computing and has recently gained popularity in machine learning, particularly in methods that preserve the graph spectrum. This work studies graph coarsening from a different perspective, developing a theory for preserving graph distances and proposing a method to achieve this. The geometric approach is useful when working with a collection of graphs, such as in graph classification and regression. In this study, we consider a graph as an element on a metric space equipped with the Gromov--Wasserstein (GW) distance, and bound the difference between the distance of two graphs and their coarsened versions. Minimizing this difference can be done using the popular weighted kernel K-means method, which improves existing spectrum-preserving methods with the proper choice of the kernel. The study includes a set of experiments to support the theory and method, including approximating the GW distance, preserving the graph spectrum, classifying graphs using spectral information, and performing regression using graph convolutional networks. Code is available at https://github.com/ychen-stat-ml/GW-Graph-Coarsening .

Learning about the three-dimensional world from two-dimensional images is a fundamental problem in computer vision. An ideal neural network architecture for such tasks would leverage the fact that objects can be rotated and translated in three dimensions to make predictions about novel images. However, imposing SO(3)-equivariance on two-dimensional inputs is difficult because the group of three-dimensional rotations does not have a natural action on the two-dimensional plane. Specifically, it is possible that an element of SO(3) will rotate an image out of plane. We show that an algorithm that learns a three-dimensional representation of the world from two dimensional images must satisfy certain geometric consistency properties which we formulate as SO(2)-equivariance constraints. We use the induced and restricted representations of SO(2) on SO(3) to construct and classify architectures which satisfy these geometric consistency constraints. We prove that any architecture which respects said consistency constraints can be realized as an instance of our construction. We show that three previously proposed neural architectures for 3D pose prediction are special cases of our construction. We propose a new algorithm that is a learnable generalization of previously considered methods. We test our architecture on three pose predictions task and achieve SOTA results on both the PASCAL3D+ and SYMSOL pose estimation tasks.

We propose a unified framework that integrates object detection (OD) and visual grounding (VG) for remote sensing (RS) imagery. To support conventional OD and establish an intuitive prior for VG task, we fine-tune an open-set object detector using referring expression data, framing it as a partially supervised OD task. In the first stage, we construct a graph representation of each image, comprising object queries, class embeddings, and proposal locations. Then, our task-aware architecture processes this graph to perform the VG task. The model consists of: (i) a multi-branch network that integrates spatial, visual, and categorical features to generate task-aware proposals, and (ii) an object reasoning network that assigns probabilities across proposals, followed by a soft selection mechanism for final referring object localization. Our model demonstrates superior performance on the OPT-RSVG and DIOR-RSVG datasets, achieving significant improvements over state-of-the-art methods while retaining classical OD capabilities. The code will be available in our repository: https://github.com/rd20karim/MB-ORES.

Affordance, defined as the potential actions that an object offers, is crucial for robotic manipulation tasks. A deep understanding of affordance can lead to more intelligent AI systems. For example, such knowledge directs an agent to grasp a knife by the handle for cutting and by the blade when passing it to someone. In this paper, we present a streamlined affordance learning system that encompasses data collection, effective model training, and robot deployment. First, we collect training data from egocentric videos in an automatic manner. Different from previous methods that focus only on the object graspable affordance and represent it as coarse heatmaps, we cover both graspable (e.g., object handles) and functional affordances (e.g., knife blades, hammer heads) and extract data with precise segmentation masks. We then propose an effective model, termed Geometry-guided Affordance Transformer (GKT), to train on the collected data. GKT integrates an innovative Depth Feature Injector (DFI) to incorporate 3D shape and geometric priors, enhancing the model's understanding of affordances. To enable affordance-oriented manipulation, we further introduce Aff-Grasp, a framework that combines GKT with a grasp generation model. For comprehensive evaluation, we create an affordance evaluation dataset with pixel-wise annotations, and design real-world tasks for robot experiments. The results show that GKT surpasses the state-of-the-art by 15.9% in mIoU, and Aff-Grasp achieves high success rates of 95.5% in affordance prediction and 77.1% in successful grasping among 179 trials, including evaluations with seen, unseen objects, and cluttered scenes.

The two-stage object pose estimation paradigm first detects semantic keypoints on the image and then estimates the 6D pose by minimizing reprojection errors. Despite performing well on standard benchmarks, existing techniques offer no provable guarantees on the quality and uncertainty of the estimation. In this paper, we inject two fundamental changes, namely conformal keypoint detection and geometric uncertainty propagation, into the two-stage paradigm and propose the first pose estimator that endows an estimation with provable and computable worst-case error bounds. On one hand, conformal keypoint detection applies the statistical machinery of inductive conformal prediction to convert heuristic keypoint detections into circular or elliptical prediction sets that cover the groundtruth keypoints with a user-specified marginal probability (e.g., 90%). Geometric uncertainty propagation, on the other, propagates the geometric constraints on the keypoints to the 6D object pose, leading to a Pose UnceRtainty SEt (PURSE) that guarantees coverage of the groundtruth pose with the same probability. The PURSE, however, is a nonconvex set that does not directly lead to estimated poses and uncertainties. Therefore, we develop RANdom SAmple averaGing (RANSAG) to compute an average pose and apply semidefinite relaxation to upper bound the worst-case errors between the average pose and the groundtruth. On the LineMOD Occlusion dataset we demonstrate: (i) the PURSE covers the groundtruth with valid probabilities; (ii) the worst-case error bounds provide correct uncertainty quantification; and (iii) the average pose achieves better or similar accuracy as representative methods based on sparse keypoints.

Buildings are primary components of cities, often featuring repeated elements such as windows and doors. Traditional 3D building asset creation is labor-intensive and requires specialized skills to develop design rules. Recent generative models for building creation often overlook these patterns, leading to low visual fidelity and limited scalability. Drawing inspiration from procedural modeling techniques used in the gaming and visual effects industry, our method, Proc-GS, integrates procedural code into the 3D Gaussian Splatting (3D-GS) framework, leveraging their advantages in high-fidelity rendering and efficient asset management from both worlds. By manipulating procedural code, we can streamline this process and generate an infinite variety of buildings. This integration significantly reduces model size by utilizing shared foundational assets, enabling scalable generation with precise control over building assembly. We showcase the potential for expansive cityscape generation while maintaining high rendering fidelity and precise control on both real and synthetic cases.

Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a ``noising'' stage, whereby a diffusion is used to gradually add Gaussian noise to data, and a generative model, which entails a ``denoising'' process defined by approximating the time-reversal of the diffusion. Existing SGMs assume that data is supported on a Euclidean space, i.e. a manifold with flat geometry. In many domains such as robotics, geoscience or protein modelling, data is often naturally described by distributions living on Riemannian manifolds and current SGM techniques are not appropriate. We introduce here Riemannian Score-based Generative Models (RSGMs), a class of generative models extending SGMs to Riemannian manifolds. We demonstrate our approach on a variety of manifolds, and in particular with earth and climate science spherical data.

Informally, the 'linear representation hypothesis' is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does "linear representation" actually mean? And, how do we make sense of geometric notions (e.g., cosine similarity or projection) in the representation space? To answer these, we use the language of counterfactuals to give two formalizations of "linear representation", one in the output (word) representation space, and one in the input (sentence) space. We then prove these connect to linear probing and model steering, respectively. To make sense of geometric notions, we use the formalization to identify a particular (non-Euclidean) inner product that respects language structure in a sense we make precise. Using this causal inner product, we show how to unify all notions of linear representation. In particular, this allows the construction of probes and steering vectors using counterfactual pairs. Experiments with LLaMA-2 demonstrate the existence of linear representations of concepts, the connection to interpretation and control, and the fundamental role of the choice of inner product.

We provide a mapping between past null and future null infinity in three-dimensional flat space, using symmetry considerations. From this we derive a mapping between the corresponding asymptotic symmetry groups. By studying the metric at asymptotic regions, we find that the mapping is energy preserving and yields an infinite number of conservation laws.

Existing 3D vision-language (3D-VL) benchmarks fall short in evaluating 3D-VL models, creating a "mist" that obscures rigorous insights into model capabilities and 3D-VL tasks. This mist persists due to three key limitations. First, flawed test data, like ambiguous referential text in the grounding task, can yield incorrect and unreliable test results. Second, oversimplified metrics such as simply averaging accuracy per question answering (QA) pair, cannot reveal true model capability due to their vulnerability to language variations. Third, existing benchmarks isolate the grounding and QA tasks, disregarding the underlying coherence that QA should be based on solid grounding capabilities. To unveil the "mist", we propose Beacon3D, a benchmark for 3D-VL grounding and QA tasks, delivering a perspective shift in the evaluation of 3D-VL understanding. Beacon3D features (i) high-quality test data with precise and natural language, (ii) object-centric evaluation with multiple tests per object to ensure robustness, and (iii) a novel chain-of-analysis paradigm to address language robustness and model performance coherence across grounding and QA. Our evaluation of state-of-the-art 3D-VL models on Beacon3D reveals that (i) object-centric evaluation elicits true model performance and particularly weak generalization in QA; (ii) grounding-QA coherence remains fragile in current 3D-VL models, and (iii) incorporating large language models (LLMs) to 3D-VL models, though as a prevalent practice, hinders grounding capabilities and has yet to elevate QA capabilities. We hope Beacon3D and our comprehensive analysis could benefit the 3D-VL community towards faithful developments.

In this work, we recover the underlying 3D structure of non-geometrically consistent scenes. We focus our analysis on hand-drawn images from cartoons and anime. Many cartoons are created by artists without a 3D rendering engine, which means that any new image of a scene is hand-drawn. The hand-drawn images are usually faithful representations of the world, but only in a qualitative sense, since it is difficult for humans to draw multiple perspectives of an object or scene 3D consistently. Nevertheless, people can easily perceive 3D scenes from inconsistent inputs! In this work, we correct for 2D drawing inconsistencies to recover a plausible 3D structure such that the newly warped drawings are consistent with each other. Our pipeline consists of a user-friendly annotation tool, camera pose estimation, and image deformation to recover a dense structure. Our method warps images to obey a perspective camera model, enabling our aligned results to be plugged into novel-view synthesis reconstruction methods to experience cartoons from viewpoints never drawn before. Our project page is https://toon3d.studio/.

Novel view synthesis has demonstrated impressive progress recently, with 3D Gaussian splatting (3DGS) offering efficient training time and photorealistic real-time rendering. However, reliance on Cartesian coordinates limits 3DGS's performance on distant objects, which is important for reconstructing unbounded outdoor environments. We found that, despite its ultimate simplicity, using homogeneous coordinates, a concept on the projective geometry, for the 3DGS pipeline remarkably improves the rendering accuracies of distant objects. We therefore propose Homogeneous Gaussian Splatting (HoGS) incorporating homogeneous coordinates into the 3DGS framework, providing a unified representation for enhancing near and distant objects. HoGS effectively manages both expansive spatial positions and scales particularly in outdoor unbounded environments by adopting projective geometry principles. Experiments show that HoGS significantly enhances accuracy in reconstructing distant objects while maintaining high-quality rendering of nearby objects, along with fast training speed and real-time rendering capability. Our implementations are available on our project page https://kh129.github.io/hogs/.

While perspective is a well-studied topic in art, it is generally taken for granted in images. However, for the recent wave of high-quality image synthesis methods such as latent diffusion models, perspective accuracy is not an explicit requirement. Since these methods are capable of outputting a wide gamut of possible images, it is difficult for these synthesized images to adhere to the principles of linear perspective. We introduce a novel geometric constraint in the training process of generative models to enforce perspective accuracy. We show that outputs of models trained with this constraint both appear more realistic and improve performance of downstream models trained on generated images. Subjective human trials show that images generated with latent diffusion models trained with our constraint are preferred over images from the Stable Diffusion V2 model 70% of the time. SOTA monocular depth estimation models such as DPT and PixelFormer, fine-tuned on our images, outperform the original models trained on real images by up to 7.03% in RMSE and 19.3% in SqRel on the KITTI test set for zero-shot transfer.

We present layered ray intersections (LaRI), a new method for unseen geometry reasoning from a single image. Unlike conventional depth estimation that is limited to the visible surface, LaRI models multiple surfaces intersected by the camera rays using layered point maps. Benefiting from the compact and layered representation, LaRI enables complete, efficient, and view-aligned geometric reasoning to unify object- and scene-level tasks. We further propose to predict the ray stopping index, which identifies valid intersecting pixels and layers from LaRI's output. We build a complete training data generation pipeline for synthetic and real-world data, including 3D objects and scenes, with necessary data cleaning steps and coordination between rendering engines. As a generic method, LaRI's performance is validated in two scenarios: It yields comparable object-level results to the recent large generative model using 4% of its training data and 17% of its parameters. Meanwhile, it achieves scene-level occluded geometry reasoning in only one feed-forward.

Affordance denotes the potential interactions inherent in objects. The perception of affordance can enable intelligent agents to navigate and interact with new environments efficiently. Weakly supervised affordance grounding teaches agents the concept of affordance without costly pixel-level annotations, but with exocentric images. Although recent advances in weakly supervised affordance grounding yielded promising results, there remain challenges including the requirement for paired exocentric and egocentric image dataset, and the complexity in grounding diverse affordances for a single object. To address them, we propose INTeraction Relationship-aware weakly supervised Affordance grounding (INTRA). Unlike prior arts, INTRA recasts this problem as representation learning to identify unique features of interactions through contrastive learning with exocentric images only, eliminating the need for paired datasets. Moreover, we leverage vision-language model embeddings for performing affordance grounding flexibly with any text, designing text-conditioned affordance map generation to reflect interaction relationship for contrastive learning and enhancing robustness with our text synonym augmentation. Our method outperformed prior arts on diverse datasets such as AGD20K, IIT-AFF, CAD and UMD. Additionally, experimental results demonstrate that our method has remarkable domain scalability for synthesized images / illustrations and is capable of performing affordance grounding for novel interactions and objects.

The popularity of pre-trained large models has revolutionized downstream tasks across diverse fields, such as language, vision, and multi-modality. To minimize the adaption cost for downstream tasks, many Parameter-Efficient Fine-Tuning (PEFT) techniques are proposed for language and 2D image pre-trained models. However, the specialized PEFT method for 3D pre-trained models is still under-explored. To this end, we introduce Point-PEFT, a novel framework for adapting point cloud pre-trained models with minimal learnable parameters. Specifically, for a pre-trained 3D model, we freeze most of its parameters, and only tune the newly added PEFT modules on downstream tasks, which consist of a Point-prior Prompt and a Geometry-aware Adapter. The Point-prior Prompt adopts a set of learnable prompt tokens, for which we propose to construct a memory bank with domain-specific knowledge, and utilize a parameter-free attention to enhance the prompt tokens. The Geometry-aware Adapter aims to aggregate point cloud features within spatial neighborhoods to capture fine-grained geometric information through local interactions. Extensive experiments indicate that our Point-PEFT can achieve better performance than the full fine-tuning on various downstream tasks, while using only 5% of the trainable parameters, demonstrating the efficiency and effectiveness of our approach. Code is released at https://github.com/Ivan-Tang-3D/Point-PEFT.

Generative models have shown great promise in generating 3D geometric systems, which is a fundamental problem in many natural science domains such as molecule and protein design. However, existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. In this work, we propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories. Modeling such distribution is challenging as it requires capturing both the complex spatial interactions with physical symmetries and temporal correspondence encapsulated in the dynamics. We theoretically justify that diffusion models with equivariant temporal kernels can lead to density with desired symmetry, and develop a novel transition kernel leveraging SE(3)-equivariant spatial convolution and temporal attention. Furthermore, to induce an expressive trajectory distribution for conditional generation, we introduce a generalized learnable geometric prior into the forward diffusion process to enhance temporal conditioning. We conduct extensive experiments on both unconditional and conditional generation in various scenarios, including physical simulation, molecular dynamics, and pedestrian motion. Empirical results on a wide suite of metrics demonstrate that GeoTDM can generate realistic geometric trajectories with significantly higher quality.

The cascade of 2D geometric transformations were exploited to model relations between entities in a knowledge graph (KG), leading to an effective KG embedding (KGE) model, CompoundE. Furthermore, the rotation in the 3D space was proposed as a new KGE model, Rotate3D, by leveraging its non-commutative property. Inspired by CompoundE and Rotate3D, we leverage 3D compound geometric transformations, including translation, rotation, scaling, reflection, and shear and propose a family of KGE models, named CompoundE3D, in this work. CompoundE3D allows multiple design variants to match rich underlying characteristics of a KG. Since each variant has its own advantages on a subset of relations, an ensemble of multiple variants can yield superior performance. The effectiveness and flexibility of CompoundE3D are experimentally verified on four popular link prediction datasets.

In this paper, we propose Img2CAD, the first approach to our knowledge that uses 2D image inputs to generate CAD models with editable parameters. Unlike existing AI methods for 3D model generation using text or image inputs often rely on mesh-based representations, which are incompatible with CAD tools and lack editability and fine control, Img2CAD enables seamless integration between AI-based 3D reconstruction and CAD software. We have identified an innovative intermediate representation called Structured Visual Geometry (SVG), characterized by vectorized wireframes extracted from objects. This representation significantly enhances the performance of generating conditioned CAD models. Additionally, we introduce two new datasets to further support research in this area: ABC-mono, the largest known dataset comprising over 200,000 3D CAD models with rendered images, and KOCAD, the first dataset featuring real-world captured objects alongside their ground truth CAD models, supporting further research in conditioned CAD model generation.

Recent advances in 3D X-ray Computed Tomographic (CT) sensors have stimulated research efforts to unveil the extremely complex micro-scale processes that control the activity of soil microorganisms. Voxel-based description (up to hundreds millions voxels) of the pore space can be extracted, from grey level 3D CT scanner images, by means of simple image processing tools. Classical methods for numerical simulation of biological dynamics using mesh of voxels, such as Lattice Boltzmann Model (LBM), are too much time consuming. Thus, the use of more compact and reliable geometrical representations of pore space can drastically decrease the computational cost of the simulations. Several recent works propose basic analytic volume primitives (e.g. spheres, generalized cylinders, ellipsoids) to define a piece-wise approximation of pore space for numerical simulation of draining, diffusion and microbial decomposition. Such approaches work well but the drawback is that it generates approximation errors. In the present work, we study another alternative where pore space is described by means of geometrically relevant connected subsets of voxels (regions) computed from the curvilinear skeleton. Indeed, many works use the curvilinear skeleton (3D medial axis) for analyzing and partitioning 3D shapes within various domains (medicine, material sciences, petroleum engineering, etc.) but only a few ones in soil sciences. Within the context of soil sciences, most studies dealing with 3D medial axis focus on the determination of pore throats. Here, we segment pore space using curvilinear skeleton in order to achieve numerical simulation of microbial decomposition (including diffusion processes). We validate simulation outputs by comparison with other methods using different pore space geometrical representations (balls, voxels).

In this paper, we introduce a novel geometry-aware self-training framework for room layout estimation models on unseen scenes with unlabeled data. Our approach utilizes a ray-casting formulation to aggregate multiple estimates from different viewing positions, enabling the computation of reliable pseudo-labels for self-training. In particular, our ray-casting approach enforces multi-view consistency along all ray directions and prioritizes spatial proximity to the camera view for geometry reasoning. As a result, our geometry-aware pseudo-labels effectively handle complex room geometries and occluded walls without relying on assumptions such as Manhattan World or planar room walls. Evaluation on publicly available datasets, including synthetic and real-world scenarios, demonstrates significant improvements in current state-of-the-art layout models without using any human annotation.

Inverse graphics -- the task of inverting an image into physical variables that, when rendered, enable reproduction of the observed scene -- is a fundamental challenge in computer vision and graphics. Disentangling an image into its constituent elements, such as the shape, color, and material properties of the objects of the 3D scene that produced it, requires a comprehensive understanding of the environment. This requirement limits the ability of existing carefully engineered approaches to generalize across domains. Inspired by the zero-shot ability of large language models (LLMs) to generalize to novel contexts, we investigate the possibility of leveraging the broad world knowledge encoded in such models in solving inverse-graphics problems. To this end, we propose the Inverse-Graphics Large Language Model (IG-LLM), an inverse-graphics framework centered around an LLM, that autoregressively decodes a visual embedding into a structured, compositional 3D-scene representation. We incorporate a frozen pre-trained visual encoder and a continuous numeric head to enable end-to-end training. Through our investigation, we demonstrate the potential of LLMs to facilitate inverse graphics through next-token prediction, without the use of image-space supervision. Our analysis opens up new possibilities for precise spatial reasoning about images that exploit the visual knowledge of LLMs. We will release our code and data to ensure the reproducibility of our investigation and to facilitate future research at https://ig-llm.is.tue.mpg.de/

3D scene generation conditioned on text prompts has significantly progressed due to the development of 2D diffusion generation models. However, the textual description of 3D scenes is inherently inaccurate and lacks fine-grained control during training, leading to implausible scene generation. As an intuitive and feasible solution, the 3D layout allows for precise specification of object locations within the scene. To this end, we present a text-to-scene generation method (namely, Layout2Scene) using additional semantic layout as the prompt to inject precise control of 3D object positions. Specifically, we first introduce a scene hybrid representation to decouple objects and backgrounds, which is initialized via a pre-trained text-to-3D model. Then, we propose a two-stage scheme to optimize the geometry and appearance of the initialized scene separately. To fully leverage 2D diffusion priors in geometry and appearance generation, we introduce a semantic-guided geometry diffusion model and a semantic-geometry guided diffusion model which are finetuned on a scene dataset. Extensive experiments demonstrate that our method can generate more plausible and realistic scenes as compared to state-of-the-art approaches. Furthermore, the generated scene allows for flexible yet precise editing, thereby facilitating multiple downstream applications.

Scene representations using 3D Gaussian primitives have produced excellent results in modeling the appearance of static and dynamic 3D scenes. Many graphics applications, however, demand the ability to manipulate both the appearance and the physical properties of objects. We introduce Feature Splatting, an approach that unifies physics-based dynamic scene synthesis with rich semantics from vision language foundation models that are grounded by natural language. Our first contribution is a way to distill high-quality, object-centric vision-language features into 3D Gaussians, that enables semi-automatic scene decomposition using text queries. Our second contribution is a way to synthesize physics-based dynamics from an otherwise static scene using a particle-based simulator, in which material properties are assigned automatically via text queries. We ablate key techniques used in this pipeline, to illustrate the challenge and opportunities in using feature-carrying 3D Gaussians as a unified format for appearance, geometry, material properties and semantics grounded on natural language. Project website: https://feature-splatting.github.io/

3D shape modeling is labor-intensive, time-consuming, and requires years of expertise. To facilitate 3D shape modeling, we propose a 3D shape generation network that takes a 3D VR sketch as a condition. We assume that sketches are created by novices without art training and aim to reconstruct geometrically realistic 3D shapes of a given category. To handle potential sketch ambiguity, our method creates multiple 3D shapes that align with the original sketch's structure. We carefully design our method, training the model step-by-step and leveraging multi-modal 3D shape representation to support training with limited training data. To guarantee the realism of generated 3D shapes we leverage the normalizing flow that models the distribution of the latent space of 3D shapes. To encourage the fidelity of the generated 3D shapes to an input sketch, we propose a dedicated loss that we deploy at different stages of the training process. The code is available at https://github.com/Rowl1ng/3Dsketch2shape.

Existing multi-view image generation methods often make invasive modifications to pre-trained text-to-image (T2I) models and require full fine-tuning, leading to (1) high computational costs, especially with large base models and high-resolution images, and (2) degradation in image quality due to optimization difficulties and scarce high-quality 3D data. In this paper, we propose the first adapter-based solution for multi-view image generation, and introduce MV-Adapter, a versatile plug-and-play adapter that enhances T2I models and their derivatives without altering the original network structure or feature space. By updating fewer parameters, MV-Adapter enables efficient training and preserves the prior knowledge embedded in pre-trained models, mitigating overfitting risks. To efficiently model the 3D geometric knowledge within the adapter, we introduce innovative designs that include duplicated self-attention layers and parallel attention architecture, enabling the adapter to inherit the powerful priors of the pre-trained models to model the novel 3D knowledge. Moreover, we present a unified condition encoder that seamlessly integrates camera parameters and geometric information, facilitating applications such as text- and image-based 3D generation and texturing. MV-Adapter achieves multi-view generation at 768 resolution on Stable Diffusion XL (SDXL), and demonstrates adaptability and versatility. It can also be extended to arbitrary view generation, enabling broader applications. We demonstrate that MV-Adapter sets a new quality standard for multi-view image generation, and opens up new possibilities due to its efficiency, adaptability and versatility.

It is inherently ambiguous to lift 2D results from pre-trained diffusion models to a 3D world for text-to-3D generation. 2D diffusion models solely learn view-agnostic priors and thus lack 3D knowledge during the lifting, leading to the multi-view inconsistency problem. We find that this problem primarily stems from geometric inconsistency, and avoiding misplaced geometric structures substantially mitigates the problem in the final outputs. Therefore, we improve the consistency by aligning the 2D geometric priors in diffusion models with well-defined 3D shapes during the lifting, addressing the vast majority of the problem. This is achieved by fine-tuning the 2D diffusion model to be viewpoint-aware and to produce view-specific coordinate maps of canonically oriented 3D objects. In our process, only coarse 3D information is used for aligning. This "coarse" alignment not only resolves the multi-view inconsistency in geometries but also retains the ability in 2D diffusion models to generate detailed and diversified high-quality objects unseen in the 3D datasets. Furthermore, our aligned geometric priors (AGP) are generic and can be seamlessly integrated into various state-of-the-art pipelines, obtaining high generalizability in terms of unseen shapes and visual appearance while greatly alleviating the multi-view inconsistency problem. Our method represents a new state-of-the-art performance with an 85+% consistency rate by human evaluation, while many previous methods are around 30%. Our project page is https://sweetdreamer3d.github.io/

Legged robots have the potential to expand the reach of autonomy beyond paved roads. In this work, we consider the difficult problem of locomotion on challenging terrains using a single forward-facing depth camera. Due to the partial observability of the problem, the robot has to rely on past observations to infer the terrain currently beneath it. To solve this problem, we follow the paradigm in computer vision that explicitly models the 3D geometry of the scene and propose Neural Volumetric Memory (NVM), a geometric memory architecture that explicitly accounts for the SE(3) equivariance of the 3D world. NVM aggregates feature volumes from multiple camera views by first bringing them back to the ego-centric frame of the robot. We test the learned visual-locomotion policy on a physical robot and show that our approach, which explicitly introduces geometric priors during training, offers superior performance than more na\"ive methods. We also include ablation studies and show that the representations stored in the neural volumetric memory capture sufficient geometric information to reconstruct the scene. Our project page with videos is https://rchalyang.github.io/NVM .

This paper introduces a new interpretation of the Variational Autoencoder framework by taking a fully geometric point of view. We argue that vanilla VAE models unveil naturally a Riemannian structure in their latent space and that taking into consideration those geometrical aspects can lead to better interpolations and an improved generation procedure. This new proposed sampling method consists in sampling from the uniform distribution deriving intrinsically from the learned Riemannian latent space and we show that using this scheme can make a vanilla VAE competitive and even better than more advanced versions on several benchmark datasets. Since generative models are known to be sensitive to the number of training samples we also stress the method's robustness in the low data regime.

We introduce Cosmos, a framework for object-centric world modeling that is designed for compositional generalization (CG), i.e., high performance on unseen input scenes obtained through the composition of known visual "atoms." The central insight behind Cosmos is the use of a novel form of neurosymbolic grounding. Specifically, the framework introduces two new tools: (i) neurosymbolic scene encodings, which represent each entity in a scene using a real vector computed using a neural encoder, as well as a vector of composable symbols describing attributes of the entity, and (ii) a neurosymbolic attention mechanism that binds these entities to learned rules of interaction. Cosmos is end-to-end differentiable; also, unlike traditional neurosymbolic methods that require representations to be manually mapped to symbols, it computes an entity's symbolic attributes using vision-language foundation models. Through an evaluation that considers two different forms of CG on an established blocks-pushing domain, we show that the framework establishes a new state-of-the-art for CG in world modeling.

In this paper, we introduce Geometry-Inverse-Meet-Pixel-Insert, short for GEO, an exceptionally versatile image editing technique designed to cater to customized user requirements at both local and global scales. Our approach seamlessly integrates text prompts and image prompts to yield diverse and precise editing outcomes. Notably, our method operates without the need for training and is driven by two key contributions: (i) a novel geometric accumulation loss that enhances DDIM inversion to faithfully preserve pixel space geometry and layout, and (ii) an innovative boosted image prompt technique that combines pixel-level editing for text-only inversion with latent space geometry guidance for standard classifier-free reversion. Leveraging the publicly available Stable Diffusion model, our approach undergoes extensive evaluation across various image types and challenging prompt editing scenarios, consistently delivering high-fidelity editing results for real images.

Text-to-3D generation from a single-view image is a popular but challenging task in 3D vision. Although numerous methods have been proposed, existing works still suffer from the inconsistency issues, including 1) semantic inconsistency, 2) geometric inconsistency, and 3) saturation inconsistency, resulting in distorted, overfitted, and over-saturated generations. In light of the above issues, we present Consist3D, a three-stage framework Chasing for semantic-, geometric-, and saturation-Consistent Text-to-3D generation from a single image, in which the first two stages aim to learn parameterized consistency tokens, and the last stage is for optimization. Specifically, the semantic encoding stage learns a token independent of views and estimations, promoting semantic consistency and robustness. Meanwhile, the geometric encoding stage learns another token with comprehensive geometry and reconstruction constraints under novel-view estimations, reducing overfitting and encouraging geometric consistency. Finally, the optimization stage benefits from the semantic and geometric tokens, allowing a low classifier-free guidance scale and therefore preventing oversaturation. Experimental results demonstrate that Consist3D produces more consistent, faithful, and photo-realistic 3D assets compared to previous state-of-the-art methods. Furthermore, Consist3D also allows background and object editing through text prompts.

When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often involve the absence of shape parametrization during the inference stage, leaving us with only mesh discretizations as available data. Learning simulations from such mesh-based representations poses significant challenges, with recent advances relying heavily on deep graph neural networks to overcome the limitations of conventional machine learning approaches. Despite their promising results, graph neural networks exhibit certain drawbacks, including their dependency on extensive datasets and limitations in providing built-in predictive uncertainties or handling large meshes. In this work, we propose a machine learning method that do not rely on graph neural networks. Complex geometrical shapes and variations with fixed topology are dealt with using well-known mesh morphing onto a common support, combined with classical dimensionality reduction techniques and Gaussian processes. The proposed methodology can easily deal with large meshes without the need for explicit shape parameterization and provides crucial predictive uncertainties, which are essential for informed decision-making. In the considered numerical experiments, the proposed method is competitive with respect to existing graph neural networks, regarding training efficiency and accuracy of the predictions.

The abundance of data has given machine learning considerable momentum in natural sciences and engineering, though modeling of physical processes is often difficult. A particularly tough problem is the efficient representation of geometric boundaries. Triangularized geometric boundaries are well understood and ubiquitous in engineering applications. However, it is notoriously difficult to integrate them into machine learning approaches due to their heterogeneity with respect to size and orientation. In this work, we introduce an effective theory to model particle-boundary interactions, which leads to our new Boundary Graph Neural Networks (BGNNs) that dynamically modify graph structures to obey boundary conditions. The new BGNNs are tested on complex 3D granular flow processes of hoppers, rotating drums and mixers, which are all standard components of modern industrial machinery but still have complicated geometry. BGNNs are evaluated in terms of computational efficiency as well as prediction accuracy of particle flows and mixing entropies. BGNNs are able to accurately reproduce 3D granular flows within simulation uncertainties over hundreds of thousands of simulation timesteps. Most notably, in our experiments, particles stay within the geometric objects without using handcrafted conditions or restrictions.

Recent vision-only perception models for autonomous driving achieved promising results by encoding multi-view image features into Bird's-Eye-View (BEV) space. A critical step and the main bottleneck of these methods is transforming image features into the BEV coordinate frame. This paper focuses on leveraging geometry information, such as depth, to model such feature transformation. Existing works rely on non-parametric depth distribution modeling leading to significant memory consumption, or ignore the geometry information to address this problem. In contrast, we propose to use parametric depth distribution modeling for feature transformation. We first lift the 2D image features to the 3D space defined for the ego vehicle via a predicted parametric depth distribution for each pixel in each view. Then, we aggregate the 3D feature volume based on the 3D space occupancy derived from depth to the BEV frame. Finally, we use the transformed features for downstream tasks such as object detection and semantic segmentation. Existing semantic segmentation methods do also suffer from an hallucination problem as they do not take visibility information into account. This hallucination can be particularly problematic for subsequent modules such as control and planning. To mitigate the issue, our method provides depth uncertainty and reliable visibility-aware estimations. We further leverage our parametric depth modeling to present a novel visibility-aware evaluation metric that, when taken into account, can mitigate the hallucination problem. Extensive experiments on object detection and semantic segmentation on the nuScenes datasets demonstrate that our method outperforms existing methods on both tasks.

3D semantic scene understanding is a fundamental challenge in computer vision. It enables mobile agents to autonomously plan and navigate arbitrary environments. SSC formalizes this challenge as jointly estimating dense geometry and semantic information from sparse observations of a scene. Current methods for SSC are generally trained on 3D ground truth based on aggregated LiDAR scans. This process relies on special sensors and annotation by hand which are costly and do not scale well. To overcome this issue, our work presents the first self-supervised approach to SSC called S4C that does not rely on 3D ground truth data. Our proposed method can reconstruct a scene from a single image and only relies on videos and pseudo segmentation ground truth generated from off-the-shelf image segmentation network during training. Unlike existing methods, which use discrete voxel grids, we represent scenes as implicit semantic fields. This formulation allows querying any point within the camera frustum for occupancy and semantic class. Our architecture is trained through rendering-based self-supervised losses. Nonetheless, our method achieves performance close to fully supervised state-of-the-art methods. Additionally, our method demonstrates strong generalization capabilities and can synthesize accurate segmentation maps for far away viewpoints.

Spatio-temporal Human-Object Interaction (ST-HOI) understanding aims at detecting HOIs from videos, which is crucial for activity understanding. However, existing whole-body-object interaction video benchmarks overlook the truth that open-world objects are diverse, that is, they usually provide limited and predefined object classes. Therefore, we introduce a new open-world benchmark: Grounding Interacted Objects (GIO) including 1,098 interacted objects class and 290K interacted object boxes annotation. Accordingly, an object grounding task is proposed expecting vision systems to discover interacted objects. Even though today's detectors and grounding methods have succeeded greatly, they perform unsatisfactorily in localizing diverse and rare objects in GIO. This profoundly reveals the limitations of current vision systems and poses a great challenge. Thus, we explore leveraging spatio-temporal cues to address object grounding and propose a 4D question-answering framework (4D-QA) to discover interacted objects from diverse videos. Our method demonstrates significant superiority in extensive experiments compared to current baselines. Data and code will be publicly available at https://github.com/DirtyHarryLYL/HAKE-AVA.

We present a method for 3D reconstruction only using calibrated multi-view surface azimuth maps. Our method, multi-view azimuth stereo, is effective for textureless or specular surfaces, which are difficult for conventional multi-view stereo methods. We introduce the concept of tangent space consistency: Multi-view azimuth observations of a surface point should be lifted to the same tangent space. Leveraging this consistency, we recover the shape by optimizing a neural implicit surface representation. Our method harnesses the robust azimuth estimation capabilities of photometric stereo methods or polarization imaging while bypassing potentially complex zenith angle estimation. Experiments using azimuth maps from various sources validate the accurate shape recovery with our method, even without zenith angles.

Transformers have been recently explored for 3D point cloud understanding with impressive progress achieved. A large number of points, over 0.1 million, make the global self-attention infeasible for point cloud data. Thus, most methods propose to apply the transformer in a local region, e.g., spherical or cubic window. However, it still contains a large number of Query-Key pairs, which requires high computational costs. In addition, previous methods usually learn the query, key, and value using a linear projection without modeling the local 3D geometric structure. In this paper, we attempt to reduce the costs and model the local geometry prior by developing a new transformer block, named ConDaFormer. Technically, ConDaFormer disassembles the cubic window into three orthogonal 2D planes, leading to fewer points when modeling the attention in a similar range. The disassembling operation is beneficial to enlarging the range of attention without increasing the computational complexity, but ignores some contexts. To provide a remedy, we develop a local structure enhancement strategy that introduces a depth-wise convolution before and after the attention. This scheme can also capture the local geometric information. Taking advantage of these designs, ConDaFormer captures both long-range contextual information and local priors. The effectiveness is demonstrated by experimental results on several 3D point cloud understanding benchmarks. Code is available at https://github.com/LHDuan/ConDaFormer .