# 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() #----------------------------------------------------------------------------