File size: 11,036 Bytes
f12ab4c |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 |
# Copyright (c) 2020, NVIDIA CORPORATION. All rights reserved.
#
# NVIDIA CORPORATION and its licensors retain all intellectual property
# and proprietary rights in and to this software, related documentation
# and any modifications thereto. Any use, reproduction, disclosure or
# distribution of this software and related documentation without an express
# license agreement from NVIDIA CORPORATION is strictly prohibited.
import numpy as np
import tensorflow as tf
import os
import sys
import util
import pathlib
sys.path.insert(0, os.path.join(sys.path[0], '../..')) # for nvdiffrast
import nvdiffrast.tensorflow as dr
#----------------------------------------------------------------------------
# Quaternion math.
#----------------------------------------------------------------------------
# Unit quaternion.
def q_unit():
return np.asarray([1, 0, 0, 0], np.float32)
# Get a random normalized quaternion.
def q_rnd():
u, v, w = np.random.uniform(0.0, 1.0, size=[3])
v *= 2.0 * np.pi
w *= 2.0 * np.pi
return np.asarray([(1.0-u)**0.5 * np.sin(v), (1.0-u)**0.5 * np.cos(v), u**0.5 * np.sin(w), u**0.5 * np.cos(w)], np.float32)
# Get a random quaternion from the octahedral symmetric group S_4.
_r2 = 0.5**0.5
_q_S4 = [[ 1.0, 0.0, 0.0, 0.0], [ 0.0, 1.0, 0.0, 0.0], [ 0.0, 0.0, 1.0, 0.0], [ 0.0, 0.0, 0.0, 1.0],
[-0.5, 0.5, 0.5, 0.5], [-0.5,-0.5,-0.5, 0.5], [ 0.5,-0.5, 0.5, 0.5], [ 0.5, 0.5,-0.5, 0.5],
[ 0.5, 0.5, 0.5, 0.5], [-0.5, 0.5,-0.5, 0.5], [ 0.5,-0.5,-0.5, 0.5], [-0.5,-0.5, 0.5, 0.5],
[ _r2,-_r2, 0.0, 0.0], [ _r2, _r2, 0.0, 0.0], [ 0.0, 0.0, _r2, _r2], [ 0.0, 0.0,-_r2, _r2],
[ 0.0, _r2, _r2, 0.0], [ _r2, 0.0, 0.0,-_r2], [ _r2, 0.0, 0.0, _r2], [ 0.0,-_r2, _r2, 0.0],
[ _r2, 0.0, _r2, 0.0], [ 0.0, _r2, 0.0, _r2], [ _r2, 0.0,-_r2, 0.0], [ 0.0,-_r2, 0.0, _r2]]
def q_rnd_S4():
return np.asarray(_q_S4[np.random.randint(24)], np.float32)
# Quaternion slerp.
def q_slerp(p, q, t):
d = np.dot(p, q)
if d < 0.0:
q = -q
d = -d
if d > 0.999:
a = p + t * (q-p)
return a / np.linalg.norm(a)
t0 = np.arccos(d)
tt = t0 * t
st = np.sin(tt)
st0 = np.sin(t0)
s1 = st / st0
s0 = np.cos(tt) - d*s1
return s0*p + s1*q
# Quaterion scale (slerp vs. identity quaternion).
def q_scale(q, scl):
return q_slerp(q_unit(), q, scl)
# Quaternion product.
def q_mul(p, q):
s1, V1 = p[0], p[1:]
s2, V2 = q[0], q[1:]
s = s1*s2 - np.dot(V1, V2)
V = s1*V2 + s2*V1 + np.cross(V1, V2)
return np.asarray([s, V[0], V[1], V[2]], np.float32)
# Angular difference between two quaternions in degrees.
def q_angle_deg(p, q):
d = np.abs(np.dot(p, q))
d = min(d, 1.0)
return np.degrees(2.0 * np.arccos(d))
# Quaternion product in TensorFlow.
def q_mul_tf(p, q):
a = p[0]*q[0] - p[1]*q[1] - p[2]*q[2] - p[3]*q[3]
b = p[0]*q[1] + p[1]*q[0] + p[2]*q[3] - p[3]*q[2]
c = p[0]*q[2] + p[2]*q[0] + p[3]*q[1] - p[1]*q[3]
d = p[0]*q[3] + p[3]*q[0] + p[1]*q[2] - p[2]*q[1]
return tf.stack([a, b, c, d])
# Convert quaternion to 4x4 rotation matrix. TensorFlow.
def q_to_mtx_tf(q):
r0 = tf.stack([1.0-2.0*q[1]**2 - 2.0*q[2]**2, 2.0*q[0]*q[1] - 2.0*q[2]*q[3], 2.0*q[0]*q[2] + 2.0*q[1]*q[3]])
r1 = tf.stack([2.0*q[0]*q[1] + 2.0*q[2]*q[3], 1.0 - 2.0*q[0]**2 - 2.0*q[2]**2, 2.0*q[1]*q[2] - 2.0*q[0]*q[3]])
r2 = tf.stack([2.0*q[0]*q[2] - 2.0*q[1]*q[3], 2.0*q[1]*q[2] + 2.0*q[0]*q[3], 1.0 - 2.0*q[0]**2 - 2.0*q[1]**2])
rr = tf.transpose(tf.stack([r0, r1, r2]), [1, 0])
rr = tf.concat([rr, tf.convert_to_tensor([[0], [0], [0]], tf.float32)], axis=1) # Pad right column.
rr = tf.concat([rr, tf.convert_to_tensor([[0, 0, 0, 1]], tf.float32)], axis=0) # Pad bottom row.
return rr
#----------------------------------------------------------------------------
# Cube pose fitter.
#----------------------------------------------------------------------------
def fit_pose(max_iter = 10000,
repeats = 1,
log_interval = 10,
display_interval = None,
display_res = 512,
lr_base = 0.01,
lr_falloff = 1.0,
nr_base = 1.0,
nr_falloff = 1e-4,
grad_phase_start = 0.5,
resolution = 256,
out_dir = '.',
log_fn = None,
imgsave_interval = None,
imgsave_fn = None):
if out_dir:
os.makedirs(out_dir, exist_ok=True)
datadir = f'{pathlib.Path(__file__).absolute().parents[1]}/data'
with np.load(f'{datadir}/cube_p.npz') as f:
pos_idx, pos, col_idx, col = f.values()
print("Mesh has %d triangles and %d vertices." % (pos_idx.shape[0], pos.shape[0]))
# Transformation matrix input to TF graph.
mtx_in = tf.placeholder(tf.float32, [4, 4])
# Pose matrix input to TF graph.
pose_in = tf.placeholder(tf.float32, [4]) # Quaternion.
noise_in = tf.placeholder(tf.float32, [4]) # Mollification noise.
# Setup TF graph for reference.
mtx_total = tf.matmul(mtx_in, q_to_mtx_tf(pose_in))
pos_clip = tf.matmul(pos, mtx_total, transpose_b=True)[tf.newaxis, ...]
rast_out, _ = dr.rasterize(pos_clip, pos_idx, resolution=[resolution, resolution], output_db=False)
color, _ = dr.interpolate(col[tf.newaxis, ...], rast_out, col_idx)
color = dr.antialias(color, rast_out, pos_clip, pos_idx)
# Setup TF graph for optimization candidate.
pose_var = tf.get_variable('pose', initializer=tf.zeros_initializer(), shape=[4])
pose_var_in = tf.placeholder(tf.float32, [4])
pose_set = tf.assign(pose_var, pose_var_in)
pose_norm_op = tf.assign(pose_var, pose_var / tf.reduce_sum(pose_var**2)**0.5) # Normalization operation.
pose_total = q_mul_tf(pose_var, noise_in)
mtx_total_opt = tf.matmul(mtx_in, q_to_mtx_tf(pose_total))
pos_clip_opt = tf.matmul(pos, mtx_total_opt, transpose_b=True)[tf.newaxis, ...]
rast_out_opt, _ = dr.rasterize(pos_clip_opt, pos_idx, resolution=[resolution, resolution], output_db=False)
color_opt, _ = dr.interpolate(col[tf.newaxis, ...], rast_out_opt, col_idx)
color_opt = dr.antialias(color_opt, rast_out_opt, pos_clip_opt, pos_idx)
# Image-space loss.
diff = (color_opt - color)**2 # L2 norm.
diff = tf.tanh(5.0 * tf.reduce_max(diff, axis=-1)) # Add some oomph to the loss.
loss = tf.reduce_mean(diff)
lr_in = tf.placeholder(tf.float32, [])
train_op = tf.train.AdamOptimizer(lr_in, 0.9, 0.999).minimize(loss, var_list=[pose_var])
# Open log file.
log_file = open(out_dir + '/' + log_fn, 'wt') if log_fn else None
# Repeats.
for rep in range(repeats):
# Optimize.
util.init_uninitialized_vars()
loss_best = np.inf
pose_best = None
for it in range(max_iter + 1):
# Modelview + projection matrix.
mvp = np.matmul(util.projection(x=0.4), util.translate(0, 0, -3.5)).astype(np.float32)
# Learning and noise rate scheduling.
itf = 1.0 * it / max_iter
lr = lr_base * lr_falloff**itf
nr = nr_base * nr_falloff**itf
# Noise input.
if itf >= grad_phase_start:
noise = q_unit()
else:
noise = q_scale(q_rnd(), nr)
noise = q_mul(noise, q_rnd_S4()) # Orientation noise.
# Initialize optimization.
if it == 0:
pose_target = q_rnd()
util.run(pose_set, {pose_var_in: q_rnd()})
util.run(pose_norm_op)
util.run(loss, {mtx_in: mvp, pose_in: pose_target, noise_in: noise}) # Pipecleaning pass.
# Run gradient training step.
if itf >= grad_phase_start:
util.run(train_op, {mtx_in: mvp, pose_in: pose_target, noise_in: noise, lr_in: lr})
util.run(pose_norm_op)
# Measure image-space loss and update best found pose.
loss_val = util.run(loss, {mtx_in: mvp, pose_in: pose_target, noise_in: noise, lr_in: lr})
if loss_val < loss_best:
pose_best = util.run(pose_total, {noise_in: noise})
if loss_val > 0.0:
loss_best = loss_val
else:
# Return to best pose in the greedy phase.
if itf < grad_phase_start:
util.run(pose_set, {pose_var_in: pose_best})
# Print/save log.
if log_interval and (it % log_interval == 0):
err = q_angle_deg(util.run(pose_var), pose_target)
ebest = q_angle_deg(pose_best, pose_target)
s = "rep=%d,iter=%d,err=%f,err_best=%f,loss=%f,loss_best=%f,lr=%f,nr=%f" % (rep, it, err, ebest, loss_val, loss_best, lr, nr)
print(s)
if log_file:
log_file.write(s + "\n")
# Show/save image.
display_image = display_interval and (it % display_interval == 0)
save_image = imgsave_interval and (it % imgsave_interval == 0)
if display_image or save_image:
img_ref, img_opt = util.run([color, color_opt], {mtx_in: mvp, pose_in: pose_target, noise_in: noise})
img_best, = util.run([color_opt], {mtx_in: mvp, pose_in: pose_best, noise_in: q_unit()})
img_ref = img_ref[0]
img_opt = img_opt[0]
img_best = img_best[0]
result_image = np.concatenate([img_ref, img_best, img_opt], axis=1)
if display_image:
util.display_image(result_image, size=display_res, title='(%d) %d / %d' % (rep, it, max_iter))
if save_image:
util.save_image(out_dir + '/' + (imgsave_fn % (rep, it)), result_image)
# All repeats done.
if log_file:
log_file.close()
#----------------------------------------------------------------------------
# Main function.
#----------------------------------------------------------------------------
def main():
display_interval = 0
repeats = 1
def usage():
print("Usage: python pose.py [-v] [repeats]")
exit()
for a in sys.argv[1:]:
if a == '-v':
display_interval = 10
elif a.isascii() and a.isdecimal():
repeats = int(a)
else:
usage()
if repeats <= 0:
usage()
# Initialize TensorFlow.
util.init_tf()
# Run.
fit_pose(max_iter=1000, repeats=repeats, log_interval=100, display_interval=display_interval, out_dir='out/pose', log_fn='log.txt', imgsave_interval=1000, imgsave_fn='img_%03d_%06d.png')
# Done.
print("Done.")
#----------------------------------------------------------------------------
if __name__ == "__main__":
main()
#----------------------------------------------------------------------------
|