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# 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 argparse
import os
import pathlib
import numpy as np
import torch
import imageio
import util
import nvdiffrast.torch 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):
p = p.detach().cpu().numpy()
q = q.detach().cpu().numpy()
d = np.abs(np.dot(p, q))
d = min(d, 1.0)
return np.degrees(2.0 * np.arccos(d))
# Quaternion product
def q_mul_torch(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 torch.stack([a, b, c, d])
# Convert quaternion to 4x4 rotation matrix.
def q_to_mtx(q):
r0 = torch.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 = torch.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 = torch.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 = torch.transpose(torch.stack([r0, r1, r2]), 1, 0)
rr = torch.cat([rr, torch.tensor([[0], [0], [0]], dtype=torch.float32).cuda()], dim=1) # Pad right column.
rr = torch.cat([rr, torch.tensor([[0, 0, 0, 1]], dtype=torch.float32).cuda()], dim=0) # Pad bottom row.
return rr
# Transform vertex positions to clip space
def transform_pos(mtx, pos):
t_mtx = torch.from_numpy(mtx).cuda() if isinstance(mtx, np.ndarray) else mtx
# (x,y,z) -> (x,y,z,1)
posw = torch.cat([pos, torch.ones([pos.shape[0], 1]).cuda()], axis=1)
return torch.matmul(posw, t_mtx.t())[None, ...]
def render(glctx, mtx, pos, pos_idx, col, col_idx, resolution: int):
# Setup TF graph for reference.
pos_clip = transform_pos(mtx, pos)
rast_out, _ = dr.rasterize(glctx, pos_clip, pos_idx, resolution=[resolution, resolution])
color , _ = dr.interpolate(col[None, ...], rast_out, col_idx)
color = dr.antialias(color, rast_out, pos_clip, pos_idx)
return color
#----------------------------------------------------------------------------
# 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 = None,
log_fn = None,
mp4save_interval = None,
mp4save_fn = None):
log_file = None
writer = None
if out_dir:
os.makedirs(out_dir, exist_ok=True)
if log_fn:
log_file = open(out_dir + '/' + log_fn, 'wt')
if mp4save_interval != 0:
writer = imageio.get_writer(f'{out_dir}/{mp4save_fn}', mode='I', fps=30, codec='libx264', bitrate='16M')
else:
mp4save_interval = None
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]))
# Some input geometry contains vertex positions in (N, 4) (with v[:,3]==1). Drop
# the last column in that case.
if pos.shape[1] == 4: pos = pos[:, 0:3]
# Create position/triangle index tensors
pos_idx = torch.from_numpy(pos_idx.astype(np.int32)).cuda()
vtx_pos = torch.from_numpy(pos.astype(np.float32)).cuda()
col_idx = torch.from_numpy(col_idx.astype(np.int32)).cuda()
vtx_col = torch.from_numpy(col.astype(np.float32)).cuda()
glctx = dr.RasterizeGLContext()
for rep in range(repeats):
pose_target = torch.tensor(q_rnd(), device='cuda')
pose_init = q_rnd()
pose_opt = torch.tensor(pose_init / np.sum(pose_init**2)**0.5, dtype=torch.float32, device='cuda', requires_grad=True)
loss_best = np.inf
pose_best = pose_opt.detach().clone()
# Modelview + projection matrix.
mvp = torch.tensor(np.matmul(util.projection(x=0.4), util.translate(0, 0, -3.5)).astype(np.float32), device='cuda')
# Adam optimizer for texture with a learning rate ramp.
optimizer = torch.optim.Adam([pose_opt], betas=(0.9, 0.999), lr=lr_base)
# Render.
for it in range(max_iter + 1):
# Set learning rate.
itf = 1.0 * it / max_iter
nr = nr_base * nr_falloff**itf
lr = lr_base * lr_falloff**itf
for param_group in optimizer.param_groups:
param_group['lr'] = lr
# 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.
# Render.
color = render(glctx, torch.matmul(mvp, q_to_mtx(pose_target)), vtx_pos, pos_idx, vtx_col, col_idx, resolution)
pose_total_opt = q_mul_torch(pose_opt, noise)
mtx_total_opt = torch.matmul(mvp, q_to_mtx(pose_total_opt))
color_opt = render(glctx, mtx_total_opt, vtx_pos, pos_idx, vtx_col, col_idx, resolution)
# Image-space loss.
diff = (color_opt - color)**2 # L2 norm.
diff = torch.tanh(5.0 * torch.max(diff, dim=-1)[0])
loss = torch.mean(diff)
# Measure image-space loss and update best found pose.
loss_val = float(loss)
if (loss_val < loss_best) and (loss_val > 0.0):
pose_best = pose_total_opt.detach().clone()
loss_best = loss_val
if itf < grad_phase_start:
with torch.no_grad(): pose_opt[:] = pose_best
# Print/save log.
if log_interval and (it % log_interval == 0):
err = q_angle_deg(pose_opt, 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")
# Run gradient training step.
if itf >= grad_phase_start:
optimizer.zero_grad()
loss.backward()
optimizer.step()
with torch.no_grad():
pose_opt /= torch.sum(pose_opt**2)**0.5
# Show/save image.
display_image = display_interval and (it % display_interval == 0)
save_mp4 = mp4save_interval and (it % mp4save_interval == 0)
if display_image or save_mp4:
c = color[0].detach().cpu().numpy()
img_ref = color[0].detach().cpu().numpy()
img_opt = color_opt[0].detach().cpu().numpy()
img_best = render(glctx, torch.matmul(mvp, q_to_mtx(pose_best)), vtx_pos, pos_idx, vtx_col, col_idx, resolution)[0].detach().cpu().numpy()
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_mp4:
writer.append_data(np.clip(np.rint(result_image*255.0), 0, 255).astype(np.uint8))
# Done.
if writer is not None:
writer.close()
if log_file:
log_file.close()
#----------------------------------------------------------------------------
def main():
parser = argparse.ArgumentParser(description='Cube pose fitting example')
parser.add_argument('--outdir', help='Specify output directory', default='')
parser.add_argument('--display-interval', type=int, default=0)
parser.add_argument('--mp4save-interval', type=int, default=10)
parser.add_argument('--max-iter', type=int, default=1000)
parser.add_argument('--repeats', type=int, default=1)
args = parser.parse_args()
# Set up logging.
if args.outdir:
out_dir = f'{args.outdir}/pose'
print (f'Saving results under {out_dir}')
else:
out_dir = None
print ('No output directory specified, not saving log or images')
# Run.
fit_pose(
max_iter=args.max_iter,
repeats=args.repeats,
log_interval=100,
display_interval=args.display_interval,
out_dir=out_dir,
log_fn='log.txt',
mp4save_interval=args.mp4save_interval,
mp4save_fn='progress.mp4'
)
# Done.
print("Done.")
#----------------------------------------------------------------------------
if __name__ == "__main__":
main()
#----------------------------------------------------------------------------
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