bilateral_solver.py

from scipy.sparse import diags
from scipy.sparse.linalg import cg
from scipy.sparse import csr_matrix
from scipy import ndimage
import numpy as np
from PIL import Image


RGB_TO_YUV = np.array([
    [0.299, 0.587, 0.114],
    [-0.168736, -0.331264, 0.5],
    [0.5, -0.418688, -0.081312]])
YUV_TO_RGB = np.array([
    [1.0, 0.0, 1.402],
    [1.0, -0.34414, -0.71414],
    [1.0, 1.772, 0.0]])
YUV_OFFSET = np.array([0, 128.0, 128.0]).reshape(1, 1, -1)
MAX_VAL = 255.0


def rgb2yuv(im):
    return np.tensordot(im, RGB_TO_YUV, ([2], [1])) + YUV_OFFSET


def yuv2rgb(im):
    return np.tensordot(im.astype(float) - YUV_OFFSET, YUV_TO_RGB, ([2], [1]))


def get_valid_idx(valid, candidates):
    """Find which values are present in a list and where they are located"""
    locs = np.searchsorted(valid, candidates)
    # Handle edge case where the candidate is larger than all valid values
    locs = np.clip(locs, 0, len(valid) - 1)
    # Identify which values are actually present
    valid_idx = np.flatnonzero(valid[locs] == candidates)
    locs = locs[valid_idx]
    return valid_idx, locs


class BilateralGrid(object):
    def __init__(self, im, sigma_spatial=32, sigma_luma=8, sigma_chroma=8):
        im_yuv = rgb2yuv(im)
        # Compute 5-dimensional XYLUV bilateral-space coordinates
        Iy, Ix = np.mgrid[:im.shape[0], :im.shape[1]]
        x_coords = (Ix / sigma_spatial).astype(int)
        y_coords = (Iy / sigma_spatial).astype(int)
        luma_coords = (im_yuv[..., 0] / sigma_luma).astype(int)
        chroma_coords = (im_yuv[..., 1:] / sigma_chroma).astype(int)
        coords = np.dstack((x_coords, y_coords, luma_coords, chroma_coords))
        coords_flat = coords.reshape(-1, coords.shape[-1])
        self.npixels, self.dim = coords_flat.shape
        # Hacky "hash vector" for coordinates,
        # Requires all scaled coordinates be < MAX_VAL
        self.hash_vec = (MAX_VAL ** np.arange(self.dim))
        # Construct S and B matrix
        self._compute_factorization(coords_flat)

    def _compute_factorization(self, coords_flat):
        # Hash each coordinate in grid to a unique value
        hashed_coords = self._hash_coords(coords_flat)
        unique_hashes, unique_idx, idx = \
            np.unique(hashed_coords, return_index=True, return_inverse=True)
        # Identify unique set of vertices
        unique_coords = coords_flat[unique_idx]
        self.nvertices = len(unique_coords)
        # Construct sparse splat matrix that maps from pixels to vertices
        self.S = csr_matrix((np.ones(self.npixels), (idx, np.arange(self.npixels))))
        # Construct sparse blur matrices.
        # Note that these represent [1 0 1] blurs, excluding the central element
        self.blurs = []
        for d in range(self.dim):
            blur = 0.0
            for offset in (-1, 1):
                offset_vec = np.zeros((1, self.dim))
                offset_vec[:, d] = offset
                neighbor_hash = self._hash_coords(unique_coords + offset_vec)
                valid_coord, idx = get_valid_idx(unique_hashes, neighbor_hash)
                blur = blur + csr_matrix((np.ones((len(valid_coord),)),
                                          (valid_coord, idx)),
                                         shape=(self.nvertices, self.nvertices))
            self.blurs.append(blur)

    def _hash_coords(self, coord):
        """Hacky function to turn a coordinate into a unique value"""
        return np.dot(coord.reshape(-1, self.dim), self.hash_vec)

    def splat(self, x):
        return self.S.dot(x)

    def slice(self, y):
        return self.S.T.dot(y)

    def blur(self, x):
        """Blur a bilateral-space vector with a 1 2 1 kernel in each dimension"""
        assert x.shape[0] == self.nvertices
        out = 2 * self.dim * x
        for blur in self.blurs:
            out = out + blur.dot(x)
        return out

    def filter(self, x):
        """Apply bilateral filter to an input x"""
        return self.slice(self.blur(self.splat(x))) / \
               self.slice(self.blur(self.splat(np.ones_like(x))))


def bistochastize(grid, maxiter=10):
    """Compute diagonal matrices to bistochastize a bilateral grid"""
    m = grid.splat(np.ones(grid.npixels))
    n = np.ones(grid.nvertices)
    for i in range(maxiter):
        n = np.sqrt(n * m / grid.blur(n))
    # Correct m to satisfy the assumption of bistochastization regardless
    # of how many iterations have been run.
    m = n * grid.blur(n)
    Dm = diags(m, 0)
    Dn = diags(n, 0)
    return Dn, Dm


class BilateralSolver(object):
    def __init__(self, grid, params):
        self.grid = grid
        self.params = params
        self.Dn, self.Dm = bistochastize(grid)

    def solve(self, x, w):
        # Check that w is a vector or a nx1 matrix
        if w.ndim == 2:
            assert (w.shape[1] == 1)
        elif w.dim == 1:
            w = w.reshape(w.shape[0], 1)
        A_smooth = (self.Dm - self.Dn.dot(self.grid.blur(self.Dn)))
        w_splat = self.grid.splat(w)
        A_data = diags(w_splat[:, 0], 0)
        A = self.params["lam"] * A_smooth + A_data
        xw = x * w
        b = self.grid.splat(xw)
        # Use simple Jacobi preconditioner
        A_diag = np.maximum(A.diagonal(), self.params["A_diag_min"])
        M = diags(1 / A_diag, 0)
        # Flat initialization
        y0 = self.grid.splat(xw) / w_splat
        yhat = np.empty_like(y0)
        for d in range(x.shape[-1]):
            yhat[..., d], info = cg(A, b[..., d], x0=y0[..., d], M=M, maxiter=self.params["cg_maxiter"],
                                    tol=self.params["cg_tol"])
        xhat = self.grid.slice(yhat)
        return xhat


def bilateral_solver_output(
        img: Image.Image,
        target: np.ndarray,
        sigma_spatial=16,
        sigma_luma=16,
        sigma_chroma=8
):
    reference = np.array(img)
    h, w = target.shape
    confidence = np.ones((h, w)) * 0.999

    grid_params = {
        'sigma_luma': sigma_luma,  # Brightness bandwidth
        'sigma_chroma': sigma_chroma,  # Color bandwidth
        'sigma_spatial': sigma_spatial  # Spatial bandwidth
    }

    bs_params = {
        'lam': 256,  # The strength of the smoothness parameter
        'A_diag_min': 1e-5,  # Clamp the diagonal of the A diagonal in the Jacobi preconditioner.
        'cg_tol': 1e-5,  # The tolerance on the convergence in PCG
        'cg_maxiter': 25  # The number of PCG iterations
    }

    grid = BilateralGrid(reference, **grid_params)

    t = target.reshape(-1, 1).astype(np.double)
    c = confidence.reshape(-1, 1).astype(np.double)

    ## output solver, which is a soft value
    output_solver = BilateralSolver(grid, bs_params).solve(t, c).reshape((h, w))

    binary_solver = ndimage.binary_fill_holes(output_solver > 0.5)
    labeled, nr_objects = ndimage.label(binary_solver)

    nb_pixel = [np.sum(labeled == i) for i in range(nr_objects + 1)]
    pixel_order = np.argsort(nb_pixel)
    try:
        binary_solver = labeled == pixel_order[-2]
    except:
        binary_solver = np.ones((h, w), dtype=bool)

    return output_solver, binary_solver