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"""This script defines the parametric 3d face model for Deep3DFaceRecon_pytorch
"""
import numpy as np
import torch
import torch.nn.functional as F
from scipy.io import loadmat
from src.face3d.util.load_mats import transferBFM09
import os
def perspective_projection(focal, center):
# return p.T (N, 3) @ (3, 3)
return np.array([
focal, 0, center,
0, focal, center,
0, 0, 1
]).reshape([3, 3]).astype(np.float32).transpose()
class SH:
def __init__(self):
self.a = [np.pi, 2 * np.pi / np.sqrt(3.), 2 * np.pi / np.sqrt(8.)]
self.c = [1/np.sqrt(4 * np.pi), np.sqrt(3.) / np.sqrt(4 * np.pi), 3 * np.sqrt(5.) / np.sqrt(12 * np.pi)]
class ParametricFaceModel:
def __init__(self,
bfm_folder='./BFM',
recenter=True,
camera_distance=10.,
init_lit=np.array([
0.8, 0, 0, 0, 0, 0, 0, 0, 0
]),
focal=1015.,
center=112.,
is_train=True,
default_name='BFM_model_front.mat'):
if not os.path.isfile(os.path.join(bfm_folder, default_name)):
transferBFM09(bfm_folder)
model = loadmat(os.path.join(bfm_folder, default_name))
# mean face shape. [3*N,1]
self.mean_shape = model['meanshape'].astype(np.float32)
# identity basis. [3*N,80]
self.id_base = model['idBase'].astype(np.float32)
# expression basis. [3*N,64]
self.exp_base = model['exBase'].astype(np.float32)
# mean face texture. [3*N,1] (0-255)
self.mean_tex = model['meantex'].astype(np.float32)
# texture basis. [3*N,80]
self.tex_base = model['texBase'].astype(np.float32)
# face indices for each vertex that lies in. starts from 0. [N,8]
self.point_buf = model['point_buf'].astype(np.int64) - 1
# vertex indices for each face. starts from 0. [F,3]
self.face_buf = model['tri'].astype(np.int64) - 1
# vertex indices for 68 landmarks. starts from 0. [68,1]
self.keypoints = np.squeeze(model['keypoints']).astype(np.int64) - 1
if is_train:
# vertex indices for small face region to compute photometric error. starts from 0.
self.front_mask = np.squeeze(model['frontmask2_idx']).astype(np.int64) - 1
# vertex indices for each face from small face region. starts from 0. [f,3]
self.front_face_buf = model['tri_mask2'].astype(np.int64) - 1
# vertex indices for pre-defined skin region to compute reflectance loss
self.skin_mask = np.squeeze(model['skinmask'])
if recenter:
mean_shape = self.mean_shape.reshape([-1, 3])
mean_shape = mean_shape - np.mean(mean_shape, axis=0, keepdims=True)
self.mean_shape = mean_shape.reshape([-1, 1])
self.persc_proj = perspective_projection(focal, center)
self.device = 'cpu'
self.camera_distance = camera_distance
self.SH = SH()
self.init_lit = init_lit.reshape([1, 1, -1]).astype(np.float32)
def to(self, device):
self.device = device
for key, value in self.__dict__.items():
if type(value).__module__ == np.__name__:
setattr(self, key, torch.tensor(value).to(device))
def compute_shape(self, id_coeff, exp_coeff):
"""
Return:
face_shape -- torch.tensor, size (B, N, 3)
Parameters:
id_coeff -- torch.tensor, size (B, 80), identity coeffs
exp_coeff -- torch.tensor, size (B, 64), expression coeffs
"""
batch_size = id_coeff.shape[0]
id_part = torch.einsum('ij,aj->ai', self.id_base, id_coeff)
exp_part = torch.einsum('ij,aj->ai', self.exp_base, exp_coeff)
face_shape = id_part + exp_part + self.mean_shape.reshape([1, -1])
return face_shape.reshape([batch_size, -1, 3])
def compute_texture(self, tex_coeff, normalize=True):
"""
Return:
face_texture -- torch.tensor, size (B, N, 3), in RGB order, range (0, 1.)
Parameters:
tex_coeff -- torch.tensor, size (B, 80)
"""
batch_size = tex_coeff.shape[0]
face_texture = torch.einsum('ij,aj->ai', self.tex_base, tex_coeff) + self.mean_tex
if normalize:
face_texture = face_texture / 255.
return face_texture.reshape([batch_size, -1, 3])
def compute_norm(self, face_shape):
"""
Return:
vertex_norm -- torch.tensor, size (B, N, 3)
Parameters:
face_shape -- torch.tensor, size (B, N, 3)
"""
v1 = face_shape[:, self.face_buf[:, 0]]
v2 = face_shape[:, self.face_buf[:, 1]]
v3 = face_shape[:, self.face_buf[:, 2]]
e1 = v1 - v2
e2 = v2 - v3
face_norm = torch.cross(e1, e2, dim=-1)
face_norm = F.normalize(face_norm, dim=-1, p=2)
face_norm = torch.cat([face_norm, torch.zeros(face_norm.shape[0], 1, 3).to(self.device)], dim=1)
vertex_norm = torch.sum(face_norm[:, self.point_buf], dim=2)
vertex_norm = F.normalize(vertex_norm, dim=-1, p=2)
return vertex_norm
def compute_color(self, face_texture, face_norm, gamma):
"""
Return:
face_color -- torch.tensor, size (B, N, 3), range (0, 1.)
Parameters:
face_texture -- torch.tensor, size (B, N, 3), from texture model, range (0, 1.)
face_norm -- torch.tensor, size (B, N, 3), rotated face normal
gamma -- torch.tensor, size (B, 27), SH coeffs
"""
batch_size = gamma.shape[0]
v_num = face_texture.shape[1]
a, c = self.SH.a, self.SH.c
gamma = gamma.reshape([batch_size, 3, 9])
gamma = gamma + self.init_lit
gamma = gamma.permute(0, 2, 1)
Y = torch.cat([
a[0] * c[0] * torch.ones_like(face_norm[..., :1]).to(self.device),
-a[1] * c[1] * face_norm[..., 1:2],
a[1] * c[1] * face_norm[..., 2:],
-a[1] * c[1] * face_norm[..., :1],
a[2] * c[2] * face_norm[..., :1] * face_norm[..., 1:2],
-a[2] * c[2] * face_norm[..., 1:2] * face_norm[..., 2:],
0.5 * a[2] * c[2] / np.sqrt(3.) * (3 * face_norm[..., 2:] ** 2 - 1),
-a[2] * c[2] * face_norm[..., :1] * face_norm[..., 2:],
0.5 * a[2] * c[2] * (face_norm[..., :1] ** 2 - face_norm[..., 1:2] ** 2)
], dim=-1)
r = Y @ gamma[..., :1]
g = Y @ gamma[..., 1:2]
b = Y @ gamma[..., 2:]
face_color = torch.cat([r, g, b], dim=-1) * face_texture
return face_color
def compute_rotation(self, angles):
"""
Return:
rot -- torch.tensor, size (B, 3, 3) pts @ trans_mat
Parameters:
angles -- torch.tensor, size (B, 3), radian
"""
batch_size = angles.shape[0]
ones = torch.ones([batch_size, 1]).to(self.device)
zeros = torch.zeros([batch_size, 1]).to(self.device)
x, y, z = angles[:, :1], angles[:, 1:2], angles[:, 2:],
rot_x = torch.cat([
ones, zeros, zeros,
zeros, torch.cos(x), -torch.sin(x),
zeros, torch.sin(x), torch.cos(x)
], dim=1).reshape([batch_size, 3, 3])
rot_y = torch.cat([
torch.cos(y), zeros, torch.sin(y),
zeros, ones, zeros,
-torch.sin(y), zeros, torch.cos(y)
], dim=1).reshape([batch_size, 3, 3])
rot_z = torch.cat([
torch.cos(z), -torch.sin(z), zeros,
torch.sin(z), torch.cos(z), zeros,
zeros, zeros, ones
], dim=1).reshape([batch_size, 3, 3])
rot = rot_z @ rot_y @ rot_x
return rot.permute(0, 2, 1)
def to_camera(self, face_shape):
face_shape[..., -1] = self.camera_distance - face_shape[..., -1]
return face_shape
def to_image(self, face_shape):
"""
Return:
face_proj -- torch.tensor, size (B, N, 2), y direction is opposite to v direction
Parameters:
face_shape -- torch.tensor, size (B, N, 3)
"""
# to image_plane
face_proj = face_shape @ self.persc_proj
face_proj = face_proj[..., :2] / face_proj[..., 2:]
return face_proj
def transform(self, face_shape, rot, trans):
"""
Return:
face_shape -- torch.tensor, size (B, N, 3) pts @ rot + trans
Parameters:
face_shape -- torch.tensor, size (B, N, 3)
rot -- torch.tensor, size (B, 3, 3)
trans -- torch.tensor, size (B, 3)
"""
return face_shape @ rot + trans.unsqueeze(1)
def get_landmarks(self, face_proj):
"""
Return:
face_lms -- torch.tensor, size (B, 68, 2)
Parameters:
face_proj -- torch.tensor, size (B, N, 2)
"""
return face_proj[:, self.keypoints]
def split_coeff(self, coeffs):
"""
Return:
coeffs_dict -- a dict of torch.tensors
Parameters:
coeffs -- torch.tensor, size (B, 256)
"""
id_coeffs = coeffs[:, :80]
exp_coeffs = coeffs[:, 80: 144]
tex_coeffs = coeffs[:, 144: 224]
angles = coeffs[:, 224: 227]
gammas = coeffs[:, 227: 254]
translations = coeffs[:, 254:]
return {
'id': id_coeffs,
'exp': exp_coeffs,
'tex': tex_coeffs,
'angle': angles,
'gamma': gammas,
'trans': translations
}
def compute_for_render(self, coeffs):
"""
Return:
face_vertex -- torch.tensor, size (B, N, 3), in camera coordinate
face_color -- torch.tensor, size (B, N, 3), in RGB order
landmark -- torch.tensor, size (B, 68, 2), y direction is opposite to v direction
Parameters:
coeffs -- torch.tensor, size (B, 257)
"""
coef_dict = self.split_coeff(coeffs)
face_shape = self.compute_shape(coef_dict['id'], coef_dict['exp'])
rotation = self.compute_rotation(coef_dict['angle'])
face_shape_transformed = self.transform(face_shape, rotation, coef_dict['trans'])
face_vertex = self.to_camera(face_shape_transformed)
face_proj = self.to_image(face_vertex)
landmark = self.get_landmarks(face_proj)
face_texture = self.compute_texture(coef_dict['tex'])
face_norm = self.compute_norm(face_shape)
face_norm_roted = face_norm @ rotation
face_color = self.compute_color(face_texture, face_norm_roted, coef_dict['gamma'])
return face_vertex, face_texture, face_color, landmark
def compute_for_render_woRotation(self, coeffs):
"""
Return:
face_vertex -- torch.tensor, size (B, N, 3), in camera coordinate
face_color -- torch.tensor, size (B, N, 3), in RGB order
landmark -- torch.tensor, size (B, 68, 2), y direction is opposite to v direction
Parameters:
coeffs -- torch.tensor, size (B, 257)
"""
coef_dict = self.split_coeff(coeffs)
face_shape = self.compute_shape(coef_dict['id'], coef_dict['exp'])
#rotation = self.compute_rotation(coef_dict['angle'])
#face_shape_transformed = self.transform(face_shape, rotation, coef_dict['trans'])
face_vertex = self.to_camera(face_shape)
face_proj = self.to_image(face_vertex)
landmark = self.get_landmarks(face_proj)
face_texture = self.compute_texture(coef_dict['tex'])
face_norm = self.compute_norm(face_shape)
face_norm_roted = face_norm # @ rotation
face_color = self.compute_color(face_texture, face_norm_roted, coef_dict['gamma'])
return face_vertex, face_texture, face_color, landmark
if __name__ == '__main__':
transferBFM09() |