facelib/LandmarksProcessor.py

import colorsys
import math
from enum import IntEnum

import cv2
import numpy as np
import numpy.linalg as npla

from core import imagelib
from core import mathlib
from facelib import FaceType
from core.mathlib.umeyama import umeyama

landmarks_2D = np.array([
[ 0.000213256,  0.106454  ], #17
[ 0.0752622,    0.038915  ], #18
[ 0.18113,      0.0187482 ], #19
[ 0.29077,      0.0344891 ], #20
[ 0.393397,     0.0773906 ], #21
[ 0.586856,     0.0773906 ], #22
[ 0.689483,     0.0344891 ], #23
[ 0.799124,     0.0187482 ], #24
[ 0.904991,     0.038915  ], #25
[ 0.98004,      0.106454  ], #26
[ 0.490127,     0.203352  ], #27
[ 0.490127,     0.307009  ], #28
[ 0.490127,     0.409805  ], #29
[ 0.490127,     0.515625  ], #30
[ 0.36688,      0.587326  ], #31
[ 0.426036,     0.609345  ], #32
[ 0.490127,     0.628106  ], #33
[ 0.554217,     0.609345  ], #34
[ 0.613373,     0.587326  ], #35
[ 0.121737,     0.216423  ], #36
[ 0.187122,     0.178758  ], #37
[ 0.265825,     0.179852  ], #38
[ 0.334606,     0.231733  ], #39
[ 0.260918,     0.245099  ], #40
[ 0.182743,     0.244077  ], #41
[ 0.645647,     0.231733  ], #42
[ 0.714428,     0.179852  ], #43
[ 0.793132,     0.178758  ], #44
[ 0.858516,     0.216423  ], #45
[ 0.79751,      0.244077  ], #46
[ 0.719335,     0.245099  ], #47
[ 0.254149,     0.780233  ], #48
[ 0.340985,     0.745405  ], #49
[ 0.428858,     0.727388  ], #50
[ 0.490127,     0.742578  ], #51
[ 0.551395,     0.727388  ], #52
[ 0.639268,     0.745405  ], #53
[ 0.726104,     0.780233  ], #54
[ 0.642159,     0.864805  ], #55
[ 0.556721,     0.902192  ], #56
[ 0.490127,     0.909281  ], #57
[ 0.423532,     0.902192  ], #58
[ 0.338094,     0.864805  ], #59
[ 0.290379,     0.784792  ], #60
[ 0.428096,     0.778746  ], #61
[ 0.490127,     0.785343  ], #62
[ 0.552157,     0.778746  ], #63
[ 0.689874,     0.784792  ], #64
[ 0.553364,     0.824182  ], #65
[ 0.490127,     0.831803  ], #66
[ 0.42689 ,     0.824182  ]  #67
], dtype=np.float32)


landmarks_2D_new = np.array([
[ 0.000213256,  0.106454  ], #17
[ 0.0752622,    0.038915  ], #18
[ 0.18113,      0.0187482 ], #19
[ 0.29077,      0.0344891 ], #20
[ 0.393397,     0.0773906 ], #21
[ 0.586856,     0.0773906 ], #22
[ 0.689483,     0.0344891 ], #23
[ 0.799124,     0.0187482 ], #24
[ 0.904991,     0.038915  ], #25
[ 0.98004,      0.106454  ], #26
[ 0.490127,     0.203352  ], #27
[ 0.490127,     0.307009  ], #28
[ 0.490127,     0.409805  ], #29
[ 0.490127,     0.515625  ], #30
[ 0.36688,      0.587326  ], #31
[ 0.426036,     0.609345  ], #32
[ 0.490127,     0.628106  ], #33
[ 0.554217,     0.609345  ], #34
[ 0.613373,     0.587326  ], #35
[ 0.121737,     0.216423  ], #36
[ 0.187122,     0.178758  ], #37
[ 0.265825,     0.179852  ], #38
[ 0.334606,     0.231733  ], #39
[ 0.260918,     0.245099  ], #40
[ 0.182743,     0.244077  ], #41
[ 0.645647,     0.231733  ], #42
[ 0.714428,     0.179852  ], #43
[ 0.793132,     0.178758  ], #44
[ 0.858516,     0.216423  ], #45
[ 0.79751,      0.244077  ], #46
[ 0.719335,     0.245099  ], #47
[ 0.254149,     0.780233  ], #48
[ 0.726104,     0.780233  ], #54
], dtype=np.float32)

mouth_center_landmarks_2D = np.array([
    [-4.4202591e-07,  4.4916576e-01],  #48
    [ 1.8399176e-01,  3.7537053e-01],  #49
    [ 3.7018123e-01,  3.3719531e-01],  #50
    [ 5.0000089e-01,  3.6938059e-01],  #51
    [ 6.2981832e-01,  3.3719531e-01],  #52
    [ 8.1600773e-01,  3.7537053e-01],  #53
    [ 1.0000000e+00,  4.4916576e-01],  #54
    [ 8.2213330e-01,  6.2836081e-01],  #55
    [ 6.4110327e-01,  7.0757812e-01],  #56
    [ 5.0000089e-01,  7.2259867e-01],  #57
    [ 3.5889623e-01,  7.0757812e-01],  #58
    [ 1.7786618e-01,  6.2836081e-01],  #59
    [ 7.6765373e-02,  4.5882553e-01],  #60
    [ 3.6856663e-01,  4.4601500e-01],  #61
    [ 5.0000089e-01,  4.5999300e-01],  #62
    [ 6.3143289e-01,  4.4601500e-01],  #63
    [ 9.2323411e-01,  4.5882553e-01],  #64
    [ 6.3399029e-01,  5.4228687e-01],  #65
    [ 5.0000089e-01,  5.5843467e-01],  #66
    [ 3.6601129e-01,  5.4228687e-01]   #67
], dtype=np.float32)

# 68 point landmark definitions
landmarks_68_pt = { "mouth": (48,68),
                    "right_eyebrow": (17, 22),
                    "left_eyebrow": (22, 27),
                    "right_eye": (36, 42),
                    "left_eye": (42, 48),
                    "nose": (27, 36), # missed one point
                    "jaw": (0, 17) }

landmarks_68_3D = np.array( [
[-73.393523  , -29.801432   , 47.667532   ], #00
[-72.775014  , -10.949766   , 45.909403   ], #01
[-70.533638  , 7.929818     , 44.842580   ], #02
[-66.850058  , 26.074280    , 43.141114   ], #03
[-59.790187  , 42.564390    , 38.635298   ], #04
[-48.368973  , 56.481080    , 30.750622   ], #05
[-34.121101  , 67.246992    , 18.456453   ], #06
[-17.875411  , 75.056892    , 3.609035    ], #07
[0.098749    , 77.061286    , -0.881698   ], #08
[17.477031   , 74.758448    , 5.181201    ], #09
[32.648966   , 66.929021    , 19.176563   ], #10
[46.372358   , 56.311389    , 30.770570   ], #11
[57.343480   , 42.419126    , 37.628629   ], #12
[64.388482   , 25.455880    , 40.886309   ], #13
[68.212038   , 6.990805     , 42.281449   ], #14
[70.486405   , -11.666193   , 44.142567   ], #15
[71.375822   , -30.365191   , 47.140426   ], #16
[-61.119406  , -49.361602   , 14.254422   ], #17
[-51.287588  , -58.769795   , 7.268147    ], #18
[-37.804800  , -61.996155   , 0.442051    ], #19
[-24.022754  , -61.033399   , -6.606501   ], #20
[-11.635713  , -56.686759   , -11.967398  ], #21
[12.056636   , -57.391033   , -12.051204  ], #22
[25.106256   , -61.902186   , -7.315098   ], #23
[38.338588   , -62.777713   , -1.022953   ], #24
[51.191007   , -59.302347   , 5.349435    ], #25
[60.053851   , -50.190255   , 11.615746   ], #26
[0.653940    , -42.193790   , -13.380835  ], #27
[0.804809    , -30.993721   , -21.150853  ], #28
[0.992204    , -19.944596   , -29.284036  ], #29
[1.226783    , -8.414541    , -36.948060  ], #00
[-14.772472  , 2.598255     , -20.132003  ], #01
[-7.180239   , 4.751589     , -23.536684  ], #02
[0.555920    , 6.562900     , -25.944448  ], #03
[8.272499    , 4.661005     , -23.695741  ], #04
[15.214351   , 2.643046     , -20.858157  ], #05
[-46.047290  , -37.471411   , 7.037989    ], #06
[-37.674688  , -42.730510   , 3.021217    ], #07
[-27.883856  , -42.711517   , 1.353629    ], #08
[-19.648268  , -36.754742   , -0.111088   ], #09
[-28.272965  , -35.134493   , -0.147273   ], #10
[-38.082418  , -34.919043   , 1.476612    ], #11
[19.265868   , -37.032306   , -0.665746   ], #12
[27.894191   , -43.342445   , 0.247660    ], #13
[37.437529   , -43.110822   , 1.696435    ], #14
[45.170805   , -38.086515   , 4.894163    ], #15
[38.196454   , -35.532024   , 0.282961    ], #16
[28.764989   , -35.484289   , -1.172675   ], #17
[-28.916267  , 28.612716    , -2.240310   ], #18
[-17.533194  , 22.172187    , -15.934335  ], #19
[-6.684590   , 19.029051    , -22.611355  ], #20
[0.381001    , 20.721118    , -23.748437  ], #21
[8.375443    , 19.035460    , -22.721995  ], #22
[18.876618   , 22.394109    , -15.610679  ], #23
[28.794412   , 28.079924    , -3.217393   ], #24
[19.057574   , 36.298248    , -14.987997  ], #25
[8.956375    , 39.634575    , -22.554245  ], #26
[0.381549    , 40.395647    , -23.591626  ], #27
[-7.428895   , 39.836405    , -22.406106  ], #28
[-18.160634  , 36.677899    , -15.121907  ], #29
[-24.377490  , 28.677771    , -4.785684   ], #30
[-6.897633   , 25.475976    , -20.893742  ], #31
[0.340663    , 26.014269    , -22.220479  ], #32
[8.444722    , 25.326198    , -21.025520  ], #33
[24.474473   , 28.323008    , -5.712776   ], #34
[8.449166    , 30.596216    , -20.671489  ], #35
[0.205322    , 31.408738    , -21.903670  ], #36 
[-7.198266   , 30.844876    , -20.328022  ]  #37
], dtype=np.float32)

FaceType_to_padding_remove_align = {
    FaceType.HALF: (0.0, False),
    FaceType.MID_FULL: (0.0675, False),
    FaceType.FULL: (0.2109375, False),
    FaceType.FULL_NO_ALIGN: (0.2109375, True),
    FaceType.WHOLE_FACE: (0.40, False),
    FaceType.HEAD: (0.70, False),
    FaceType.HEAD_NO_ALIGN: (0.70, True),
}

def convert_98_to_68(lmrks):
    #jaw
    result = [ lmrks[0] ]
    for i in range(2,16,2):
        result += [ ( lmrks[i] + (lmrks[i-1]+lmrks[i+1])/2 ) / 2  ]
    result += [ lmrks[16] ]
    for i in range(18,32,2):
        result += [ ( lmrks[i] + (lmrks[i-1]+lmrks[i+1])/2 ) / 2  ]
    result += [ lmrks[32] ]

    #eyebrows averaging
    result += [ lmrks[33],
                (lmrks[34]+lmrks[41])/2,
                (lmrks[35]+lmrks[40])/2,
                (lmrks[36]+lmrks[39])/2,
                (lmrks[37]+lmrks[38])/2,
              ]

    result += [ (lmrks[42]+lmrks[50])/2,
                (lmrks[43]+lmrks[49])/2,
                (lmrks[44]+lmrks[48])/2,
                (lmrks[45]+lmrks[47])/2,
                lmrks[46]
              ]

    #nose
    result += list ( lmrks[51:60] )

    #left eye (from our view)
    result += [ lmrks[60],
                lmrks[61],
                lmrks[63],
                lmrks[64],
                lmrks[65],
                lmrks[67] ]

    #right eye
    result += [ lmrks[68],
                lmrks[69],
                lmrks[71],
                lmrks[72],
                lmrks[73],
                lmrks[75] ]

    #mouth
    result += list ( lmrks[76:96] )

    return np.concatenate (result).reshape ( (68,2) )

def transform_points(points, mat, invert=False):
    if invert:
        mat = cv2.invertAffineTransform (mat)
    points = np.expand_dims(points, axis=1)
    points = cv2.transform(points, mat, points.shape)
    points = np.squeeze(points)
    return points

def get_transform_mat (image_landmarks, output_size, face_type, scale=1.0):
    if not isinstance(image_landmarks, np.ndarray):
        image_landmarks = np.array (image_landmarks)


    # estimate landmarks transform from global space to local aligned space with bounds [0..1]
    mat = umeyama( np.concatenate ( [ image_landmarks[17:49] , image_landmarks[54:55] ] ) , landmarks_2D_new, True)[0:2]

    # get corner points in global space
    g_p = transform_points (  np.float32([(0,0),(1,0),(1,1),(0,1),(0.5,0.5) ]) , mat, True)
    g_c = g_p[4]

    # calc diagonal vectors between corners in global space
    tb_diag_vec = (g_p[2]-g_p[0]).astype(np.float32)
    tb_diag_vec /= npla.norm(tb_diag_vec)
    bt_diag_vec = (g_p[1]-g_p[3]).astype(np.float32)
    bt_diag_vec /= npla.norm(bt_diag_vec)

    # calc modifier of diagonal vectors for scale and padding value
    padding, remove_align = FaceType_to_padding_remove_align.get(face_type, 0.0)
    mod = (1.0 / scale)* ( npla.norm(g_p[0]-g_p[2])*(padding*np.sqrt(2.0) + 0.5) )

    if face_type == FaceType.WHOLE_FACE:
        # adjust vertical offset for WHOLE_FACE, 7% below in order to cover more forehead
        vec = (g_p[0]-g_p[3]).astype(np.float32)
        vec_len = npla.norm(vec)
        vec /= vec_len
        g_c += vec*vec_len*0.07

    elif face_type == FaceType.HEAD:
        # assuming image_landmarks are 3D_Landmarks extracted for HEAD,
        # adjust horizontal offset according to estimated yaw        
        yaw = estimate_averaged_yaw(transform_points (image_landmarks, mat, False))
        
        hvec = (g_p[0]-g_p[1]).astype(np.float32)
        hvec_len = npla.norm(hvec)
        hvec /= hvec_len        

        yaw *= np.abs(math.tanh(yaw*2)) # Damp near zero
        
        g_c -= hvec * (yaw * hvec_len / 2.0)                     

        # adjust vertical offset for HEAD, 50% below
        vvec = (g_p[0]-g_p[3]).astype(np.float32)
        vvec_len = npla.norm(vvec)
        vvec /= vvec_len
        g_c += vvec*vvec_len*0.50

    # calc 3 points in global space to estimate 2d affine transform
    if not remove_align:
        l_t = np.array( [ g_c - tb_diag_vec*mod,
                          g_c + bt_diag_vec*mod,
                          g_c + tb_diag_vec*mod ] )
    else:
        # remove_align - face will be centered in the frame but not aligned
        l_t = np.array( [ g_c - tb_diag_vec*mod,
                          g_c + bt_diag_vec*mod,
                          g_c + tb_diag_vec*mod,
                          g_c - bt_diag_vec*mod,
                         ] )

        # get area of face square in global space
        area = mathlib.polygon_area(l_t[:,0], l_t[:,1] )

        # calc side of square
        side = np.float32(math.sqrt(area) / 2)

        # calc 3 points with unrotated square
        l_t = np.array( [ g_c + [-side,-side],
                          g_c + [ side,-side],
                          g_c + [ side, side] ] )

    # calc affine transform from 3 global space points to 3 local space points size of 'output_size'
    pts2 = np.float32(( (0,0),(output_size,0),(output_size,output_size) ))
    mat = cv2.getAffineTransform(l_t,pts2)
    return mat

def get_rect_from_landmarks(image_landmarks):
    mat = get_transform_mat(image_landmarks, 256, FaceType.FULL_NO_ALIGN)

    g_p = transform_points (  np.float32([(0,0),(255,255) ]) , mat, True)

    (l,t,r,b) = g_p[0][0], g_p[0][1], g_p[1][0], g_p[1][1]

    return (l,t,r,b)

def expand_eyebrows(lmrks, eyebrows_expand_mod=1.0):
    if len(lmrks) != 68:
        raise Exception('works only with 68 landmarks')
    lmrks = np.array( lmrks.copy(), dtype=np.int )

    # #nose
    ml_pnt = (lmrks[36] + lmrks[0]) // 2
    mr_pnt = (lmrks[16] + lmrks[45]) // 2

    # mid points between the mid points and eye
    ql_pnt = (lmrks[36] + ml_pnt) // 2
    qr_pnt = (lmrks[45] + mr_pnt) // 2

    # Top of the eye arrays
    bot_l = np.array((ql_pnt, lmrks[36], lmrks[37], lmrks[38], lmrks[39]))
    bot_r = np.array((lmrks[42], lmrks[43], lmrks[44], lmrks[45], qr_pnt))

    # Eyebrow arrays
    top_l = lmrks[17:22]
    top_r = lmrks[22:27]

    # Adjust eyebrow arrays
    lmrks[17:22] = top_l + eyebrows_expand_mod * 0.5 * (top_l - bot_l)
    lmrks[22:27] = top_r + eyebrows_expand_mod * 0.5 * (top_r - bot_r)
    return lmrks




def get_image_hull_mask (image_shape, image_landmarks, eyebrows_expand_mod=1.0 ):
    hull_mask = np.zeros(image_shape[0:2]+(1,),dtype=np.float32)

    lmrks = expand_eyebrows(image_landmarks, eyebrows_expand_mod)

    r_jaw = (lmrks[0:9], lmrks[17:18])
    l_jaw = (lmrks[8:17], lmrks[26:27])
    r_cheek = (lmrks[17:20], lmrks[8:9])
    l_cheek = (lmrks[24:27], lmrks[8:9])
    nose_ridge = (lmrks[19:25], lmrks[8:9],)
    r_eye = (lmrks[17:22], lmrks[27:28], lmrks[31:36], lmrks[8:9])
    l_eye = (lmrks[22:27], lmrks[27:28], lmrks[31:36], lmrks[8:9])
    nose = (lmrks[27:31], lmrks[31:36])
    parts = [r_jaw, l_jaw, r_cheek, l_cheek, nose_ridge, r_eye, l_eye, nose]

    for item in parts:
        merged = np.concatenate(item)
        cv2.fillConvexPoly(hull_mask, cv2.convexHull(merged), (1,) )

    return hull_mask

def get_image_eye_mask (image_shape, image_landmarks):
    if len(image_landmarks) != 68:
        raise Exception('get_image_eye_mask works only with 68 landmarks')

    h,w,c = image_shape

    hull_mask = np.zeros( (h,w,1),dtype=np.float32)

    image_landmarks = image_landmarks.astype(np.int)

    cv2.fillConvexPoly( hull_mask, cv2.convexHull( image_landmarks[36:42]), (1,) )
    cv2.fillConvexPoly( hull_mask, cv2.convexHull( image_landmarks[42:48]), (1,) )

    dilate = h // 32
    hull_mask = cv2.dilate(hull_mask, cv2.getStructuringElement(cv2.MORPH_ELLIPSE,(dilate,dilate)), iterations = 1 )

    blur = h // 16
    blur = blur + (1-blur % 2)
    hull_mask = cv2.GaussianBlur(hull_mask, (blur, blur) , 0)
    hull_mask = hull_mask[...,None]

    return hull_mask

def get_image_mouth_mask (image_shape, image_landmarks):
    if len(image_landmarks) != 68:
        raise Exception('get_image_eye_mask works only with 68 landmarks')

    h,w,c = image_shape

    hull_mask = np.zeros( (h,w,1),dtype=np.float32)

    image_landmarks = image_landmarks.astype(np.int)

    cv2.fillConvexPoly( hull_mask, cv2.convexHull( image_landmarks[60:]), (1,) )

    dilate = h // 32
    hull_mask = cv2.dilate(hull_mask, cv2.getStructuringElement(cv2.MORPH_ELLIPSE,(dilate,dilate)), iterations = 1 )

    blur = h // 16
    blur = blur + (1-blur % 2)
    hull_mask = cv2.GaussianBlur(hull_mask, (blur, blur) , 0)
    hull_mask = hull_mask[...,None]

    return hull_mask
    
def alpha_to_color (img_alpha, color):
    if len(img_alpha.shape) == 2:
        img_alpha = img_alpha[...,None]
    h,w,c = img_alpha.shape
    result = np.zeros( (h,w, len(color) ), dtype=np.float32 )
    result[:,:] = color

    return result * img_alpha



def get_cmask (image_shape, lmrks, eyebrows_expand_mod=1.0):
    h,w,c = image_shape

    hull = get_image_hull_mask (image_shape, lmrks, eyebrows_expand_mod )

    result = np.zeros( (h,w,3), dtype=np.float32 )



    def process(w,h, data ):
        d = {}
        cur_lc = 0
        all_lines = []
        for s, pts_loop_ar in data:
            lines = []
            for pts, loop in pts_loop_ar:
                pts_len = len(pts)
                lines.append ( [ [ pts[i], pts[(i+1) % pts_len ] ]  for i in range(pts_len - (0 if loop else 1) ) ] )
            lines = np.concatenate (lines)

            lc = lines.shape[0]
            all_lines.append(lines)
            d[s] = cur_lc, cur_lc+lc
            cur_lc += lc
        all_lines = np.concatenate (all_lines, 0)

        #calculate signed distance for all points and lines
        line_count = all_lines.shape[0]
        pts_count = w*h

        all_lines = np.repeat ( all_lines[None,...], pts_count, axis=0 ).reshape ( (pts_count*line_count,2,2) )

        pts = np.empty( (h,w,line_count,2), dtype=np.float32 )
        pts[...,1] = np.arange(h)[:,None,None]
        pts[...,0] = np.arange(w)[:,None]
        pts = pts.reshape ( (h*w*line_count, -1) )

        a = all_lines[:,0,:]
        b = all_lines[:,1,:]
        pa = pts-a
        ba = b-a
        ph = np.clip ( np.einsum('ij,ij->i', pa, ba) / np.einsum('ij,ij->i', ba, ba), 0, 1 )
        dists = npla.norm ( pa - ba*ph[...,None], axis=1).reshape ( (h,w,line_count) )

        def get_dists(name, thickness=0):
            s,e = d[name]
            result = dists[...,s:e]
            if thickness != 0:
                result = np.abs(result)-thickness
            return np.min (result, axis=-1)

        return get_dists

    l_eye = lmrks[42:48]
    r_eye = lmrks[36:42]
    l_brow = lmrks[22:27]
    r_brow = lmrks[17:22]
    mouth = lmrks[48:60]

    up_nose = np.concatenate( (lmrks[27:31], lmrks[33:34]) )
    down_nose = lmrks[31:36]
    nose = np.concatenate ( (up_nose, down_nose) )

    gdf = process ( w,h,
                         (
                          ('eyes',  ((l_eye, True), (r_eye, True)) ),
                          ('brows', ((l_brow, False), (r_brow,False)) ),
                          ('up_nose', ((up_nose, False),) ),
                          ('down_nose', ((down_nose, False),) ),
                          ('mouth', ((mouth, True),) ),
                         )
                        )

    eyes_fall_dist = w // 32
    eyes_thickness = max( w // 64, 1 )

    brows_fall_dist = w // 32
    brows_thickness = max( w // 256, 1 )

    nose_fall_dist = w / 12
    nose_thickness = max( w // 96, 1 )

    mouth_fall_dist = w // 32
    mouth_thickness = max( w // 64, 1 )

    eyes_mask = gdf('eyes',eyes_thickness)
    eyes_mask = 1-np.clip( eyes_mask/ eyes_fall_dist, 0, 1)
    #eyes_mask = np.clip ( 1- ( np.sqrt( np.maximum(eyes_mask,0) ) / eyes_fall_dist ), 0, 1)
    #eyes_mask = np.clip ( 1- ( np.cbrt( np.maximum(eyes_mask,0) ) / eyes_fall_dist ), 0, 1)

    brows_mask = gdf('brows', brows_thickness)
    brows_mask = 1-np.clip( brows_mask / brows_fall_dist, 0, 1)
    #brows_mask = np.clip ( 1- ( np.sqrt( np.maximum(brows_mask,0) ) / brows_fall_dist ), 0, 1)

    mouth_mask = gdf('mouth', mouth_thickness)
    mouth_mask = 1-np.clip( mouth_mask / mouth_fall_dist, 0, 1)
    #mouth_mask = np.clip ( 1- ( np.sqrt( np.maximum(mouth_mask,0) ) / mouth_fall_dist ), 0, 1)

    def blend(a,b,k):
        x = np.clip ( 0.5+0.5*(b-a)/k, 0.0, 1.0 )
        return (a-b)*x+b - k*x*(1.0-x)


    #nose_mask = (a-b)*x+b - k*x*(1.0-x)

    #nose_mask = np.minimum (up_nose_mask , down_nose_mask )
    #nose_mask = 1-np.clip( nose_mask / nose_fall_dist, 0, 1)

    nose_mask = blend ( gdf('up_nose', nose_thickness), gdf('down_nose', nose_thickness), nose_thickness*3 )
    nose_mask = 1-np.clip( nose_mask / nose_fall_dist, 0, 1)

    up_nose_mask = gdf('up_nose', nose_thickness)
    up_nose_mask = 1-np.clip( up_nose_mask / nose_fall_dist, 0, 1)
    #up_nose_mask = np.clip ( 1- ( np.cbrt( np.maximum(up_nose_mask,0) ) / nose_fall_dist ), 0, 1)

    down_nose_mask = gdf('down_nose', nose_thickness)
    down_nose_mask = 1-np.clip( down_nose_mask / nose_fall_dist, 0, 1)
    #down_nose_mask = np.clip ( 1- ( np.cbrt( np.maximum(down_nose_mask,0) ) / nose_fall_dist ), 0, 1)

    #nose_mask = np.clip( up_nose_mask + down_nose_mask, 0, 1 )
    #nose_mask /= np.max(nose_mask)
    #nose_mask = np.maximum (up_nose_mask , down_nose_mask )
    #nose_mask = down_nose_mask

    #nose_mask = np.zeros_like(nose_mask)

    eyes_mask = eyes_mask * (1-mouth_mask)
    nose_mask = nose_mask * (1-eyes_mask)

    hull_mask = hull[...,0].copy()
    hull_mask = hull_mask * (1-eyes_mask) * (1-brows_mask) * (1-nose_mask) * (1-mouth_mask)

    #eyes_mask = eyes_mask * (1-nose_mask)

    mouth_mask= mouth_mask * (1-nose_mask)

    brows_mask = brows_mask * (1-nose_mask)* (1-eyes_mask )

    hull_mask = alpha_to_color(hull_mask, (0,1,0) )
    eyes_mask = alpha_to_color(eyes_mask, (1,0,0) )
    brows_mask = alpha_to_color(brows_mask, (0,0,1) )
    nose_mask = alpha_to_color(nose_mask, (0,1,1) )
    mouth_mask = alpha_to_color(mouth_mask, (0,0,1) )

    #nose_mask = np.maximum( up_nose_mask, down_nose_mask )

    result = hull_mask + mouth_mask+ nose_mask + brows_mask  + eyes_mask
    result *= hull
    #result = np.clip (result, 0, 1)
    return result

def blur_image_hull_mask (hull_mask):

    maxregion = np.argwhere(hull_mask==1.0)
    miny,minx = maxregion.min(axis=0)[:2]
    maxy,maxx = maxregion.max(axis=0)[:2]
    lenx = maxx - minx;
    leny = maxy - miny;
    masky = int(minx+(lenx//2))
    maskx = int(miny+(leny//2))
    lowest_len = min (lenx, leny)
    ero = int( lowest_len * 0.085 )
    blur = int( lowest_len * 0.10 )

    hull_mask = cv2.erode(hull_mask, cv2.getStructuringElement(cv2.MORPH_ELLIPSE,(ero,ero)), iterations = 1 )
    hull_mask = cv2.blur(hull_mask, (blur, blur) )
    hull_mask = np.expand_dims (hull_mask,-1)

    return hull_mask

mirror_idxs = [
    [0,16],
    [1,15],
    [2,14],
    [3,13],
    [4,12],
    [5,11],
    [6,10],
    [7,9],

    [17,26],
    [18,25],
    [19,24],
    [20,23],
    [21,22],

    [36,45],
    [37,44],
    [38,43],
    [39,42],
    [40,47],
    [41,46],

    [31,35],
    [32,34],

    [50,52],
    [49,53],
    [48,54],
    [59,55],
    [58,56],
    [67,65],
    [60,64],
    [61,63] ]

def mirror_landmarks (landmarks, val):
    result = landmarks.copy()

    for idx in mirror_idxs:
        result [ idx ] = result [ idx[::-1] ]

    result[:,0] = val - result[:,0] - 1
    return result

def get_face_struct_mask (image_shape, image_landmarks, eyebrows_expand_mod=1.0, color=(1,) ):
    mask = np.zeros(image_shape[0:2]+( len(color),),dtype=np.float32)
    lmrks = expand_eyebrows(image_landmarks, eyebrows_expand_mod)
    draw_landmarks (mask, image_landmarks, color=color, draw_circles=False, thickness=2)
    return mask

def draw_landmarks (image, image_landmarks, color=(0,255,0), draw_circles=True, thickness=1, transparent_mask=False):
    if len(image_landmarks) != 68:
        raise Exception('get_image_eye_mask works only with 68 landmarks')

    int_lmrks = np.array(image_landmarks, dtype=np.int)

    jaw = int_lmrks[slice(*landmarks_68_pt["jaw"])]
    right_eyebrow = int_lmrks[slice(*landmarks_68_pt["right_eyebrow"])]
    left_eyebrow = int_lmrks[slice(*landmarks_68_pt["left_eyebrow"])]
    mouth = int_lmrks[slice(*landmarks_68_pt["mouth"])]
    right_eye = int_lmrks[slice(*landmarks_68_pt["right_eye"])]
    left_eye = int_lmrks[slice(*landmarks_68_pt["left_eye"])]
    nose = int_lmrks[slice(*landmarks_68_pt["nose"])]

    # open shapes
    cv2.polylines(image, tuple(np.array([v]) for v in ( right_eyebrow, jaw, left_eyebrow, np.concatenate((nose, [nose[-6]])) )),
                  False, color, thickness=thickness, lineType=cv2.LINE_AA)
    # closed shapes
    cv2.polylines(image, tuple(np.array([v]) for v in (right_eye, left_eye, mouth)),
                  True, color, thickness=thickness, lineType=cv2.LINE_AA)

    if draw_circles:
        # the rest of the cicles
        for x, y in np.concatenate((right_eyebrow, left_eyebrow, mouth, right_eye, left_eye, nose), axis=0):
            cv2.circle(image, (x, y), 1, color, 1, lineType=cv2.LINE_AA)
        # jaw big circles
        for x, y in jaw:
            cv2.circle(image, (x, y), 2, color, lineType=cv2.LINE_AA)

    if transparent_mask:
        mask = get_image_hull_mask (image.shape, image_landmarks)
        image[...] = ( image * (1-mask) + image * mask / 2 )[...]

def draw_rect_landmarks (image, rect, image_landmarks, face_type, face_size=256, transparent_mask=False, landmarks_color=(0,255,0)):
    draw_landmarks(image, image_landmarks, color=landmarks_color, transparent_mask=transparent_mask)
    imagelib.draw_rect (image, rect, (255,0,0), 2 )

    image_to_face_mat = get_transform_mat (image_landmarks, face_size, face_type)
    points = transform_points ( [ (0,0), (0,face_size-1), (face_size-1, face_size-1), (face_size-1,0) ], image_to_face_mat, True)
    imagelib.draw_polygon (image, points, (0,0,255), 2)

    points = transform_points ( [ ( int(face_size*0.05), 0), ( int(face_size*0.1), int(face_size*0.1) ), ( 0, int(face_size*0.1) ) ], image_to_face_mat, True)
    imagelib.draw_polygon (image, points, (0,0,255), 2)

def calc_face_pitch(landmarks):
    if not isinstance(landmarks, np.ndarray):
        landmarks = np.array (landmarks)
    t = ( (landmarks[6][1]-landmarks[8][1]) + (landmarks[10][1]-landmarks[8][1]) ) / 2.0
    b = landmarks[8][1]
    return float(b-t)

def estimate_averaged_yaw(landmarks):
    # Works much better than solvePnP if landmarks from "3DFAN"
    if not isinstance(landmarks, np.ndarray):
        landmarks = np.array (landmarks)
    l = ( (landmarks[27][0]-landmarks[0][0]) + (landmarks[28][0]-landmarks[1][0]) + (landmarks[29][0]-landmarks[2][0]) ) / 3.0   
    r = ( (landmarks[16][0]-landmarks[27][0]) + (landmarks[15][0]-landmarks[28][0]) + (landmarks[14][0]-landmarks[29][0]) ) / 3.0
    return float(r-l)
    
def estimate_pitch_yaw_roll(aligned_landmarks, size=256):
    """
    returns pitch,yaw,roll [-pi/2...+pi/2]
    """
    shape = (size,size)
    focal_length = shape[1]
    camera_center = (shape[1] / 2, shape[0] / 2)
    camera_matrix = np.array(
        [[focal_length, 0, camera_center[0]],
         [0, focal_length, camera_center[1]],
         [0, 0, 1]], dtype=np.float32)

    (_, rotation_vector, _) = cv2.solvePnP(
        np.concatenate( (landmarks_68_3D[:27],   landmarks_68_3D[30:36]) , axis=0) ,
        np.concatenate( (aligned_landmarks[:27], aligned_landmarks[30:36]) , axis=0).astype(np.float32),
        camera_matrix,
        np.zeros((4, 1)) )

    pitch, yaw, roll = mathlib.rotationMatrixToEulerAngles( cv2.Rodrigues(rotation_vector)[0] )
   
    half_pi = math.pi / 2.0
    pitch = np.clip ( pitch, -half_pi, half_pi )
    yaw   = np.clip ( yaw ,  -half_pi, half_pi )
    roll  = np.clip ( roll,  -half_pi, half_pi )

    return -pitch, yaw, roll

#if remove_align:
#    bbox = transform_points ( [ (0,0), (0,output_size), (output_size, output_size), (output_size,0) ], mat, True)
#    #import code
#    #code.interact(local=dict(globals(), **locals()))
#    area = mathlib.polygon_area(bbox[:,0], bbox[:,1] )
#    side = math.sqrt(area) / 2
#    center = transform_points ( [(output_size/2,output_size/2)], mat, True)
#    pts1 = np.float32(( center+[-side,-side], center+[side,-side], center+[side,-side] ))
#    pts2 = np.float32([[0,0],[output_size,0],[0,output_size]])
#    mat = cv2.getAffineTransform(pts1,pts2)
#if full_face_align_top and (face_type == FaceType.FULL or face_type == FaceType.FULL_NO_ALIGN):
#    #lmrks2 = expand_eyebrows(image_landmarks)
#    #lmrks2_ = transform_points( [ lmrks2[19], lmrks2[24] ], mat, False )
#    #y_diff = np.float32( (0,np.min(lmrks2_[:,1])) )
#    #y_diff = transform_points( [ np.float32( (0,0) ), y_diff], mat, True)
#    #y_diff = y_diff[1]-y_diff[0]
#
#    x_diff = np.float32((0,0))
#
#    lmrks2_ = transform_points( [ image_landmarks[0], image_landmarks[16] ], mat, False )
#    if lmrks2_[0,0] < 0:
#        x_diff = lmrks2_[0,0]
#        x_diff = transform_points( [ np.float32( (0,0) ), np.float32((x_diff,0)) ], mat, True)
#        x_diff = x_diff[1]-x_diff[0]
#    elif lmrks2_[1,0] >= output_size:
#        x_diff = lmrks2_[1,0]-(output_size-1)
#        x_diff = transform_points( [ np.float32( (0,0) ), np.float32((x_diff,0)) ], mat, True)
#        x_diff = x_diff[1]-x_diff[0]
#
#    mat = cv2.getAffineTransform( l_t+y_diff+x_diff ,pts2)


"""
def get_averaged_transform_mat (img_landmarks,
                                img_landmarks_prev,
                                img_landmarks_next,
                                average_frame_count,
                                average_center_frame_count,
                                output_size, face_type, scale=1.0):

    l_c_list = []
    tb_diag_vec_list = []
    bt_diag_vec_list = []
    mod_list = []

    count = max(average_frame_count,average_center_frame_count)
    for i in range ( -count, count+1, 1 ):
        if i < 0:
            lmrks = img_landmarks_prev[i] if -i < len(img_landmarks_prev) else None
        elif i > 0:
            lmrks = img_landmarks_next[i] if i < len(img_landmarks_next) else None
        else:
            lmrks = img_landmarks

        if lmrks is None:
            continue

        l_c, tb_diag_vec, bt_diag_vec, mod = get_transform_mat_data (lmrks, face_type, scale=scale)

        if i >= -average_frame_count and i <= average_frame_count:
            tb_diag_vec_list.append(tb_diag_vec)
            bt_diag_vec_list.append(bt_diag_vec)
            mod_list.append(mod)

        if i >= -average_center_frame_count and i <= average_center_frame_count:
            l_c_list.append(l_c)

    tb_diag_vec = np.mean( np.array(tb_diag_vec_list), axis=0 )
    bt_diag_vec = np.mean( np.array(bt_diag_vec_list), axis=0 )
    mod         = np.mean( np.array(mod_list), axis=0 )
    l_c         = np.mean( np.array(l_c_list), axis=0 )

    return get_transform_mat_by_data (l_c, tb_diag_vec, bt_diag_vec, mod, output_size, face_type)


def get_transform_mat (image_landmarks, output_size, face_type, scale=1.0):
    if not isinstance(image_landmarks, np.ndarray):
        image_landmarks = np.array (image_landmarks)

    # get face padding value for FaceType
    padding, remove_align = FaceType_to_padding_remove_align.get(face_type, 0.0)

    # estimate landmarks transform from global space to local aligned space with bounds [0..1]
    mat = umeyama( np.concatenate ( [ image_landmarks[17:49] , image_landmarks[54:55] ] ) , landmarks_2D_new, True)[0:2]

    # get corner points in global space
    l_p = transform_points (  np.float32([(0,0),(1,0),(1,1),(0,1),(0.5,0.5)]) , mat, True)
    l_c = l_p[4]

    # calc diagonal vectors between corners in global space
    tb_diag_vec = (l_p[2]-l_p[0]).astype(np.float32)
    tb_diag_vec /= npla.norm(tb_diag_vec)
    bt_diag_vec = (l_p[1]-l_p[3]).astype(np.float32)
    bt_diag_vec /= npla.norm(bt_diag_vec)

    # calc modifier of diagonal vectors for scale and padding value
    mod = (1.0 / scale)* ( npla.norm(l_p[0]-l_p[2])*(padding*np.sqrt(2.0) + 0.5) )

    # calc 3 points in global space to estimate 2d affine transform
    if not remove_align:
        l_t = np.array( [ np.round( l_c - tb_diag_vec*mod ),
                          np.round( l_c + bt_diag_vec*mod ),
                          np.round( l_c + tb_diag_vec*mod ) ] )
    else:
        # remove_align - face will be centered in the frame but not aligned
        l_t = np.array( [ np.round( l_c - tb_diag_vec*mod ),
                          np.round( l_c + bt_diag_vec*mod ),
                          np.round( l_c + tb_diag_vec*mod ),
                          np.round( l_c - bt_diag_vec*mod ),
                         ] )

        # get area of face square in global space
        area = mathlib.polygon_area(l_t[:,0], l_t[:,1] )

        # calc side of square
        side = np.float32(math.sqrt(area) / 2)

        # calc 3 points with unrotated square
        l_t = np.array( [ np.round( l_c + [-side,-side] ),
                          np.round( l_c + [ side,-side] ),
                          np.round( l_c + [ side, side] ) ] )

    # calc affine transform from 3 global space points to 3 local space points size of 'output_size'
    pts2 = np.float32(( (0,0),(output_size,0),(output_size,output_size) ))
    mat = cv2.getAffineTransform(l_t,pts2)

    return mat
"""