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# -*- coding: utf-8 -*-
# Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. (MPG) is
# holder of all proprietary rights on this computer program.
# You can only use this computer program if you have closed
# a license agreement with MPG or you get the right to use the computer
# program from someone who is authorized to grant you that right.
# Any use of the computer program without a valid license is prohibited and
# liable to prosecution.
#
# Copyright©2019 Max-Planck-Gesellschaft zur Förderung
# der Wissenschaften e.V. (MPG). acting on behalf of its Max Planck Institute
# for Intelligent Systems. All rights reserved.
#
# Contact: ps-license@tuebingen.mpg.de
from __future__ import absolute_import
from __future__ import print_function
from __future__ import division
from typing import Tuple, List
import numpy as np
import torch
import torch.nn.functional as F
from .utils import rot_mat_to_euler, Tensor
def find_dynamic_lmk_idx_and_bcoords(
vertices: Tensor,
pose: Tensor,
dynamic_lmk_faces_idx: Tensor,
dynamic_lmk_b_coords: Tensor,
neck_kin_chain: List[int],
pose2rot: bool = True,
) -> Tuple[Tensor, Tensor]:
''' Compute the faces, barycentric coordinates for the dynamic landmarks
To do so, we first compute the rotation of the neck around the y-axis
and then use a pre-computed look-up table to find the faces and the
barycentric coordinates that will be used.
Special thanks to Soubhik Sanyal (soubhik.sanyal@tuebingen.mpg.de)
for providing the original TensorFlow implementation and for the LUT.
Parameters
----------
vertices: torch.tensor BxVx3, dtype = torch.float32
The tensor of input vertices
pose: torch.tensor Bx(Jx3), dtype = torch.float32
The current pose of the body model
dynamic_lmk_faces_idx: torch.tensor L, dtype = torch.long
The look-up table from neck rotation to faces
dynamic_lmk_b_coords: torch.tensor Lx3, dtype = torch.float32
The look-up table from neck rotation to barycentric coordinates
neck_kin_chain: list
A python list that contains the indices of the joints that form the
kinematic chain of the neck.
dtype: torch.dtype, optional
Returns
-------
dyn_lmk_faces_idx: torch.tensor, dtype = torch.long
A tensor of size BxL that contains the indices of the faces that
will be used to compute the current dynamic landmarks.
dyn_lmk_b_coords: torch.tensor, dtype = torch.float32
A tensor of size BxL that contains the indices of the faces that
will be used to compute the current dynamic landmarks.
'''
dtype = vertices.dtype
batch_size = vertices.shape[0]
if pose2rot:
aa_pose = torch.index_select(pose.view(batch_size, -1, 3), 1,
neck_kin_chain)
rot_mats = batch_rodrigues(
aa_pose.view(-1, 3)).view(batch_size, -1, 3, 3)
else:
rot_mats = torch.index_select(
pose.view(batch_size, -1, 3, 3), 1, neck_kin_chain)
rel_rot_mat = torch.eye(
3, device=vertices.device, dtype=dtype).unsqueeze_(dim=0).repeat(
batch_size, 1, 1)
for idx in range(len(neck_kin_chain)):
rel_rot_mat = torch.bmm(rot_mats[:, idx], rel_rot_mat)
y_rot_angle = torch.round(
torch.clamp(-rot_mat_to_euler(rel_rot_mat) * 180.0 / np.pi,
max=39)).to(dtype=torch.long)
neg_mask = y_rot_angle.lt(0).to(dtype=torch.long)
mask = y_rot_angle.lt(-39).to(dtype=torch.long)
neg_vals = mask * 78 + (1 - mask) * (39 - y_rot_angle)
y_rot_angle = (neg_mask * neg_vals +
(1 - neg_mask) * y_rot_angle)
dyn_lmk_faces_idx = torch.index_select(dynamic_lmk_faces_idx,
0, y_rot_angle)
dyn_lmk_b_coords = torch.index_select(dynamic_lmk_b_coords,
0, y_rot_angle)
return dyn_lmk_faces_idx, dyn_lmk_b_coords
def vertices2landmarks(
vertices: Tensor,
faces: Tensor,
lmk_faces_idx: Tensor,
lmk_bary_coords: Tensor
) -> Tensor:
''' Calculates landmarks by barycentric interpolation
Parameters
----------
vertices: torch.tensor BxVx3, dtype = torch.float32
The tensor of input vertices
faces: torch.tensor Fx3, dtype = torch.long
The faces of the mesh
lmk_faces_idx: torch.tensor L, dtype = torch.long
The tensor with the indices of the faces used to calculate the
landmarks.
lmk_bary_coords: torch.tensor Lx3, dtype = torch.float32
The tensor of barycentric coordinates that are used to interpolate
the landmarks
Returns
-------
landmarks: torch.tensor BxLx3, dtype = torch.float32
The coordinates of the landmarks for each mesh in the batch
'''
# Extract the indices of the vertices for each face
# BxLx3
batch_size, num_verts = vertices.shape[:2]
device = vertices.device
lmk_faces = torch.index_select(faces, 0, lmk_faces_idx.view(-1)).view(
batch_size, -1, 3)
lmk_faces += torch.arange(
batch_size, dtype=torch.long, device=device).view(-1, 1, 1) * num_verts
lmk_vertices = vertices.view(-1, 3)[lmk_faces].view(
batch_size, -1, 3, 3)
landmarks = torch.einsum('blfi,blf->bli', [lmk_vertices, lmk_bary_coords])
return landmarks
def lbs(
betas: Tensor,
pose: Tensor,
v_template: Tensor,
shapedirs: Tensor,
posedirs: Tensor,
J_regressor: Tensor,
parents: Tensor,
lbs_weights: Tensor,
pose2rot: bool = True,
return_affine_mat = False,
) -> Tuple[Tensor, Tensor]:
''' Performs Linear Blend Skinning with the given shape and pose parameters
Parameters
----------
betas : torch.tensor BxNB
The tensor of shape parameters
pose : torch.tensor Bx(J + 1) * 3
The pose parameters in axis-angle format
v_template torch.tensor BxVx3
The template mesh that will be deformed
shapedirs : torch.tensor 1xNB
The tensor of PCA shape displacements
posedirs : torch.tensor Px(V * 3)
The pose PCA coefficients
J_regressor : torch.tensor JxV
The regressor array that is used to calculate the joints from
the position of the vertices
parents: torch.tensor J
The array that describes the kinematic tree for the model
lbs_weights: torch.tensor N x V x (J + 1)
The linear blend skinning weights that represent how much the
rotation matrix of each part affects each vertex
pose2rot: bool, optional
Flag on whether to convert the input pose tensor to rotation
matrices. The default value is True. If False, then the pose tensor
should already contain rotation matrices and have a size of
Bx(J + 1)x9
dtype: torch.dtype, optional
Returns
-------
verts: torch.tensor BxVx3
The vertices of the mesh after applying the shape and pose
displacements.
joints: torch.tensor BxJx3
The joints of the model
'''
batch_size = max(betas.shape[0], pose.shape[0])
device, dtype = betas.device, betas.dtype
# Add shape contribution
v_shaped = v_template + blend_shapes(betas, shapedirs)
# Get the joints
# NxJx3 array
J = vertices2joints(J_regressor, v_shaped)
# 3. Add pose blend shapes
# N x J x 3 x 3
ident = torch.eye(3, dtype=dtype, device=device)
if pose2rot:
rot_mats = batch_rodrigues(pose.view(-1, 3)).view(
[batch_size, -1, 3, 3])
pose_feature = (rot_mats[:, 1:, :, :] - ident).view([batch_size, -1])
# (N x P) x (P, V * 3) -> N x V x 3
pose_offsets = torch.matmul(
pose_feature, posedirs).view(batch_size, -1, 3)
else:
pose_feature = pose[:, 1:].view(batch_size, -1, 3, 3) - ident
rot_mats = pose.view(batch_size, -1, 3, 3)
pose_offsets = torch.matmul(pose_feature.view(batch_size, -1),
posedirs).view(batch_size, -1, 3)
v_posed = pose_offsets + v_shaped
# 4. Get the global joint location
J_transformed, A = batch_rigid_transform(rot_mats, J, parents, dtype=dtype)
# 5. Do skinning:
# W is N x V x (J + 1)
W = lbs_weights.unsqueeze(dim=0).expand([batch_size, -1, -1])
# (N x V x (J + 1)) x (N x (J + 1) x 16)
num_joints = J_regressor.shape[0]
T = torch.matmul(W, A.view(batch_size, num_joints, 16)) \
.view(batch_size, -1, 4, 4)
homogen_coord = torch.ones([batch_size, v_posed.shape[1], 1],
dtype=dtype, device=device)
v_posed_homo = torch.cat([v_posed, homogen_coord], dim=2)
v_homo = torch.matmul(T, torch.unsqueeze(v_posed_homo, dim=-1))
verts = v_homo[:, :, :3, 0]
if return_affine_mat:
return verts, J_transformed, A
else:
return verts, J_transformed
def vertices2joints(J_regressor: Tensor, vertices: Tensor) -> Tensor:
''' Calculates the 3D joint locations from the vertices
Parameters
----------
J_regressor : torch.tensor JxV
The regressor array that is used to calculate the joints from the
position of the vertices
vertices : torch.tensor BxVx3
The tensor of mesh vertices
Returns
-------
torch.tensor BxJx3
The location of the joints
'''
return torch.einsum('bik,ji->bjk', [vertices, J_regressor])
def blend_shapes(betas: Tensor, shape_disps: Tensor) -> Tensor:
''' Calculates the per vertex displacement due to the blend shapes
Parameters
----------
betas : torch.tensor Bx(num_betas)
Blend shape coefficients
shape_disps: torch.tensor Vx3x(num_betas)
Blend shapes
Returns
-------
torch.tensor BxVx3
The per-vertex displacement due to shape deformation
'''
# Displacement[b, m, k] = sum_{l} betas[b, l] * shape_disps[m, k, l]
# i.e. Multiply each shape displacement by its corresponding beta and
# then sum them.
blend_shape = torch.einsum('bl,mkl->bmk', [betas, shape_disps])
return blend_shape
def batch_rodrigues(
rot_vecs: Tensor,
epsilon: float = 1e-8,
) -> Tensor:
''' Calculates the rotation matrices for a batch of rotation vectors
Parameters
----------
rot_vecs: torch.tensor Nx3
array of N axis-angle vectors
Returns
-------
R: torch.tensor Nx3x3
The rotation matrices for the given axis-angle parameters
'''
batch_size = rot_vecs.shape[0]
device, dtype = rot_vecs.device, rot_vecs.dtype
angle = torch.norm(rot_vecs + 1e-8, dim=1, keepdim=True)
rot_dir = rot_vecs / angle
cos = torch.unsqueeze(torch.cos(angle), dim=1)
sin = torch.unsqueeze(torch.sin(angle), dim=1)
# Bx1 arrays
rx, ry, rz = torch.split(rot_dir, 1, dim=1)
K = torch.zeros((batch_size, 3, 3), dtype=dtype, device=device)
zeros = torch.zeros((batch_size, 1), dtype=dtype, device=device)
K = torch.cat([zeros, -rz, ry, rz, zeros, -rx, -ry, rx, zeros], dim=1) \
.view((batch_size, 3, 3))
ident = torch.eye(3, dtype=dtype, device=device).unsqueeze(dim=0)
rot_mat = ident + sin * K + (1 - cos) * torch.bmm(K, K)
return rot_mat
def transform_mat(R: Tensor, t: Tensor) -> Tensor:
''' Creates a batch of transformation matrices
Args:
- R: Bx3x3 array of a batch of rotation matrices
- t: Bx3x1 array of a batch of translation vectors
Returns:
- T: Bx4x4 Transformation matrix
'''
# No padding left or right, only add an extra row
return torch.cat([F.pad(R, [0, 0, 0, 1]),
F.pad(t, [0, 0, 0, 1], value=1)], dim=2)
def batch_rigid_transform(
rot_mats: Tensor,
joints: Tensor,
parents: Tensor,
dtype=torch.float32
) -> Tensor:
"""
Applies a batch of rigid transformations to the joints
Parameters
----------
rot_mats : torch.tensor BxNx3x3
Tensor of rotation matrices
joints : torch.tensor BxNx3
Locations of joints
parents : torch.tensor BxN
The kinematic tree of each object
dtype : torch.dtype, optional:
The data type of the created tensors, the default is torch.float32
Returns
-------
posed_joints : torch.tensor BxNx3
The locations of the joints after applying the pose rotations
rel_transforms : torch.tensor BxNx4x4
The relative (with respect to the root joint) rigid transformations
for all the joints
"""
joints = torch.unsqueeze(joints, dim=-1)
rel_joints = joints.clone()
rel_joints[:, 1:] -= joints[:, parents[1:]]
transforms_mat = transform_mat(
rot_mats.reshape(-1, 3, 3),
rel_joints.reshape(-1, 3, 1)).reshape(-1, joints.shape[1], 4, 4)
transform_chain = [transforms_mat[:, 0]]
for i in range(1, parents.shape[0]):
# Subtract the joint location at the rest pose
# No need for rotation, since it's identity when at rest
curr_res = torch.matmul(transform_chain[parents[i]],
transforms_mat[:, i])
transform_chain.append(curr_res)
transforms = torch.stack(transform_chain, dim=1)
# The last column of the transformations contains the posed joints
posed_joints = transforms[:, :, :3, 3]
joints_homogen = F.pad(joints, [0, 0, 0, 1])
rel_transforms = transforms - F.pad(
torch.matmul(transforms, joints_homogen), [3, 0, 0, 0, 0, 0, 0, 0])
return posed_joints, rel_transforms
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