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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
import numpy as np
import pickle
import torch
import os
class SMPLModel():
def __init__(self, model_path, age):
"""
SMPL model.
Parameter:
---------
model_path: Path to the SMPL model parameters, pre-processed by
`preprocess.py`.
"""
with open(model_path, 'rb') as f:
params = pickle.load(f, encoding='latin1')
self.J_regressor = params['J_regressor']
self.weights = np.asarray(params['weights'])
self.posedirs = np.asarray(params['posedirs'])
self.v_template = np.asarray(params['v_template'])
self.shapedirs = np.asarray(params['shapedirs'])
self.faces = np.asarray(params['f'])
self.kintree_table = np.asarray(params['kintree_table'])
self.pose_shape = [24, 3]
self.beta_shape = [10]
self.trans_shape = [3]
if age == 'kid':
v_template_smil = np.load(
os.path.join(os.path.dirname(model_path),
"smpl/smpl_kid_template.npy"))
v_template_smil -= np.mean(v_template_smil, axis=0)
v_template_diff = np.expand_dims(v_template_smil - self.v_template,
axis=2)
self.shapedirs = np.concatenate(
(self.shapedirs[:, :, :self.beta_shape[0]], v_template_diff),
axis=2)
self.beta_shape[0] += 1
id_to_col = {
self.kintree_table[1, i]: i
for i in range(self.kintree_table.shape[1])
}
self.parent = {
i: id_to_col[self.kintree_table[0, i]]
for i in range(1, self.kintree_table.shape[1])
}
self.pose = np.zeros(self.pose_shape)
self.beta = np.zeros(self.beta_shape)
self.trans = np.zeros(self.trans_shape)
self.verts = None
self.J = None
self.R = None
self.G = None
self.update()
def set_params(self, pose=None, beta=None, trans=None):
"""
Set pose, shape, and/or translation parameters of SMPL model. Verices of the
model will be updated and returned.
Prameters:
---------
pose: Also known as 'theta', a [24,3] matrix indicating child joint rotation
relative to parent joint. For root joint it's global orientation.
Represented in a axis-angle format.
beta: Parameter for model shape. A vector of shape [10]. Coefficients for
PCA component. Only 10 components were released by MPI.
trans: Global translation of shape [3].
Return:
------
Updated vertices.
"""
if pose is not None:
self.pose = pose
if beta is not None:
self.beta = beta
if trans is not None:
self.trans = trans
self.update()
return self.verts
def update(self):
"""
Called automatically when parameters are updated.
"""
# how beta affect body shape
v_shaped = self.shapedirs.dot(self.beta) + self.v_template
# joints location
self.J = self.J_regressor.dot(v_shaped)
pose_cube = self.pose.reshape((-1, 1, 3))
# rotation matrix for each joint
self.R = self.rodrigues(pose_cube)
I_cube = np.broadcast_to(np.expand_dims(np.eye(3), axis=0),
(self.R.shape[0] - 1, 3, 3))
lrotmin = (self.R[1:] - I_cube).ravel()
# how pose affect body shape in zero pose
v_posed = v_shaped + self.posedirs.dot(lrotmin)
# world transformation of each joint
G = np.empty((self.kintree_table.shape[1], 4, 4))
G[0] = self.with_zeros(
np.hstack((self.R[0], self.J[0, :].reshape([3, 1]))))
for i in range(1, self.kintree_table.shape[1]):
G[i] = G[self.parent[i]].dot(
self.with_zeros(
np.hstack([
self.R[i],
((self.J[i, :] - self.J[self.parent[i], :]).reshape(
[3, 1]))
])))
# remove the transformation due to the rest pose
G = G - self.pack(
np.matmul(
G,
np.hstack([self.J, np.zeros([24, 1])]).reshape([24, 4, 1])))
# transformation of each vertex
T = np.tensordot(self.weights, G, axes=[[1], [0]])
rest_shape_h = np.hstack((v_posed, np.ones([v_posed.shape[0], 1])))
v = np.matmul(T, rest_shape_h.reshape([-1, 4, 1])).reshape([-1,
4])[:, :3]
self.verts = v + self.trans.reshape([1, 3])
self.G = G
def rodrigues(self, r):
"""
Rodrigues' rotation formula that turns axis-angle vector into rotation
matrix in a batch-ed manner.
Parameter:
----------
r: Axis-angle rotation vector of shape [batch_size, 1, 3].
Return:
-------
Rotation matrix of shape [batch_size, 3, 3].
"""
theta = np.linalg.norm(r, axis=(1, 2), keepdims=True)
# avoid zero divide
theta = np.maximum(theta, np.finfo(np.float64).tiny)
r_hat = r / theta
cos = np.cos(theta)
z_stick = np.zeros(theta.shape[0])
m = np.dstack([
z_stick, -r_hat[:, 0, 2], r_hat[:, 0, 1], r_hat[:, 0, 2], z_stick,
-r_hat[:, 0, 0], -r_hat[:, 0, 1], r_hat[:, 0, 0], z_stick
]).reshape([-1, 3, 3])
i_cube = np.broadcast_to(np.expand_dims(np.eye(3), axis=0),
[theta.shape[0], 3, 3])
A = np.transpose(r_hat, axes=[0, 2, 1])
B = r_hat
dot = np.matmul(A, B)
R = cos * i_cube + (1 - cos) * dot + np.sin(theta) * m
return R
def with_zeros(self, x):
"""
Append a [0, 0, 0, 1] vector to a [3, 4] matrix.
Parameter:
---------
x: Matrix to be appended.
Return:
------
Matrix after appending of shape [4,4]
"""
return np.vstack((x, np.array([[0.0, 0.0, 0.0, 1.0]])))
def pack(self, x):
"""
Append zero matrices of shape [4, 3] to vectors of [4, 1] shape in a batched
manner.
Parameter:
----------
x: Matrices to be appended of shape [batch_size, 4, 1]
Return:
------
Matrix of shape [batch_size, 4, 4] after appending.
"""
return np.dstack((np.zeros((x.shape[0], 4, 3)), x))
def save_to_obj(self, path):
"""
Save the SMPL model into .obj file.
Parameter:
---------
path: Path to save.
"""
with open(path, 'w') as fp:
for v in self.verts:
fp.write('v %f %f %f\n' % (v[0], v[1], v[2]))
for f in self.faces + 1:
fp.write('f %d %d %d\n' % (f[0], f[1], f[2]))
class TetraSMPLModel():
def __init__(self,
model_path,
model_addition_path,
age='adult',
v_template=None):
"""
SMPL model.
Parameter:
---------
model_path: Path to the SMPL model parameters, pre-processed by
`preprocess.py`.
"""
with open(model_path, 'rb') as f:
params = pickle.load(f, encoding='latin1')
self.J_regressor = params['J_regressor']
self.weights = np.asarray(params['weights'])
self.posedirs = np.asarray(params['posedirs'])
if v_template is not None:
self.v_template = v_template
else:
self.v_template = np.asarray(params['v_template'])
self.shapedirs = np.asarray(params['shapedirs'])
self.faces = np.asarray(params['f'])
self.kintree_table = np.asarray(params['kintree_table'])
params_added = np.load(model_addition_path)
self.v_template_added = params_added['v_template_added']
self.weights_added = params_added['weights_added']
self.shapedirs_added = params_added['shapedirs_added']
self.posedirs_added = params_added['posedirs_added']
self.tetrahedrons = params_added['tetrahedrons']
id_to_col = {
self.kintree_table[1, i]: i
for i in range(self.kintree_table.shape[1])
}
self.parent = {
i: id_to_col[self.kintree_table[0, i]]
for i in range(1, self.kintree_table.shape[1])
}
self.pose_shape = [24, 3]
self.beta_shape = [10]
self.trans_shape = [3]
if age == 'kid':
v_template_smil = np.load(
os.path.join(os.path.dirname(model_path),
"smpl/smpl_kid_template.npy"))
v_template_smil -= np.mean(v_template_smil, axis=0)
v_template_diff = np.expand_dims(v_template_smil - self.v_template,
axis=2)
self.shapedirs = np.concatenate(
(self.shapedirs[:, :, :self.beta_shape[0]], v_template_diff),
axis=2)
self.beta_shape[0] += 1
self.pose = np.zeros(self.pose_shape)
self.beta = np.zeros(self.beta_shape)
self.trans = np.zeros(self.trans_shape)
self.verts = None
self.verts_added = None
self.J = None
self.R = None
self.G = None
self.update()
def set_params(self, pose=None, beta=None, trans=None):
"""
Set pose, shape, and/or translation parameters of SMPL model. Verices of the
model will be updated and returned.
Prameters:
---------
pose: Also known as 'theta', a [24,3] matrix indicating child joint rotation
relative to parent joint. For root joint it's global orientation.
Represented in a axis-angle format.
beta: Parameter for model shape. A vector of shape [10]. Coefficients for
PCA component. Only 10 components were released by MPI.
trans: Global translation of shape [3].
Return:
------
Updated vertices.
"""
if torch.is_tensor(pose):
pose = pose.detach().cpu().numpy()
if torch.is_tensor(beta):
beta = beta.detach().cpu().numpy()
if pose is not None:
self.pose = pose
if beta is not None:
self.beta = beta
if trans is not None:
self.trans = trans
self.update()
return self.verts
def update(self):
"""
Called automatically when parameters are updated.
"""
# how beta affect body shape
v_shaped = self.shapedirs.dot(self.beta) + self.v_template
v_shaped_added = self.shapedirs_added.dot(
self.beta) + self.v_template_added
# joints location
self.J = self.J_regressor.dot(v_shaped)
pose_cube = self.pose.reshape((-1, 1, 3))
# rotation matrix for each joint
self.R = self.rodrigues(pose_cube)
I_cube = np.broadcast_to(np.expand_dims(np.eye(3), axis=0),
(self.R.shape[0] - 1, 3, 3))
lrotmin = (self.R[1:] - I_cube).ravel()
# how pose affect body shape in zero pose
v_posed = v_shaped + self.posedirs.dot(lrotmin)
v_posed_added = v_shaped_added + self.posedirs_added.dot(lrotmin)
# world transformation of each joint
G = np.empty((self.kintree_table.shape[1], 4, 4))
G[0] = self.with_zeros(
np.hstack((self.R[0], self.J[0, :].reshape([3, 1]))))
for i in range(1, self.kintree_table.shape[1]):
G[i] = G[self.parent[i]].dot(
self.with_zeros(
np.hstack([
self.R[i],
((self.J[i, :] - self.J[self.parent[i], :]).reshape(
[3, 1]))
])))
# remove the transformation due to the rest pose
G = G - self.pack(
np.matmul(
G,
np.hstack([self.J, np.zeros([24, 1])]).reshape([24, 4, 1])))
self.G = G
# transformation of each vertex
T = np.tensordot(self.weights, G, axes=[[1], [0]])
rest_shape_h = np.hstack((v_posed, np.ones([v_posed.shape[0], 1])))
v = np.matmul(T, rest_shape_h.reshape([-1, 4, 1])).reshape([-1,
4])[:, :3]
self.verts = v + self.trans.reshape([1, 3])
T_added = np.tensordot(self.weights_added, G, axes=[[1], [0]])
rest_shape_added_h = np.hstack(
(v_posed_added, np.ones([v_posed_added.shape[0], 1])))
v_added = np.matmul(T_added,
rest_shape_added_h.reshape([-1, 4,
1])).reshape([-1, 4
])[:, :3]
self.verts_added = v_added + self.trans.reshape([1, 3])
def rodrigues(self, r):
"""
Rodrigues' rotation formula that turns axis-angle vector into rotation
matrix in a batch-ed manner.
Parameter:
----------
r: Axis-angle rotation vector of shape [batch_size, 1, 3].
Return:
-------
Rotation matrix of shape [batch_size, 3, 3].
"""
theta = np.linalg.norm(r, axis=(1, 2), keepdims=True)
# avoid zero divide
theta = np.maximum(theta, np.finfo(np.float64).tiny)
r_hat = r / theta
cos = np.cos(theta)
z_stick = np.zeros(theta.shape[0])
m = np.dstack([
z_stick, -r_hat[:, 0, 2], r_hat[:, 0, 1], r_hat[:, 0, 2], z_stick,
-r_hat[:, 0, 0], -r_hat[:, 0, 1], r_hat[:, 0, 0], z_stick
]).reshape([-1, 3, 3])
i_cube = np.broadcast_to(np.expand_dims(np.eye(3), axis=0),
[theta.shape[0], 3, 3])
A = np.transpose(r_hat, axes=[0, 2, 1])
B = r_hat
dot = np.matmul(A, B)
R = cos * i_cube + (1 - cos) * dot + np.sin(theta) * m
return R
def with_zeros(self, x):
"""
Append a [0, 0, 0, 1] vector to a [3, 4] matrix.
Parameter:
---------
x: Matrix to be appended.
Return:
------
Matrix after appending of shape [4,4]
"""
return np.vstack((x, np.array([[0.0, 0.0, 0.0, 1.0]])))
def pack(self, x):
"""
Append zero matrices of shape [4, 3] to vectors of [4, 1] shape in a batched
manner.
Parameter:
----------
x: Matrices to be appended of shape [batch_size, 4, 1]
Return:
------
Matrix of shape [batch_size, 4, 4] after appending.
"""
return np.dstack((np.zeros((x.shape[0], 4, 3)), x))
def save_mesh_to_obj(self, path):
"""
Save the SMPL model into .obj file.
Parameter:
---------
path: Path to save.
"""
with open(path, 'w') as fp:
for v in self.verts:
fp.write('v %f %f %f\n' % (v[0], v[1], v[2]))
for f in self.faces + 1:
fp.write('f %d %d %d\n' % (f[0], f[1], f[2]))
def save_tetrahedron_to_obj(self, path):
"""
Save the tetrahedron SMPL model into .obj file.
Parameter:
---------
path: Path to save.
"""
with open(path, 'w') as fp:
for v in self.verts:
fp.write('v %f %f %f 1 0 0\n' % (v[0], v[1], v[2]))
for va in self.verts_added:
fp.write('v %f %f %f 0 0 1\n' % (va[0], va[1], va[2]))
for t in self.tetrahedrons + 1:
fp.write('f %d %d %d\n' % (t[0], t[2], t[1]))
fp.write('f %d %d %d\n' % (t[0], t[3], t[2]))
fp.write('f %d %d %d\n' % (t[0], t[1], t[3]))
fp.write('f %d %d %d\n' % (t[1], t[2], t[3]))
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