def edge_quality(n, edges, Tstar, R):
good_edges = 0.0
bad_edges = 0.0
err_bad = 0.0
err_good = 0.0
for edge in edges:
if edge['weight'] < 0.01:
continue
sid = edge['src']
tid = edge['tgt']
Ti = Tstar[sid]
Tj = Tstar[tid]
Tij_gt = Tj.dot(inverse(Ti))
Rij_in = edge['R']
tij_in = edge['t']
Tij_in = pack(Rij_in, tij_in)
aerr_gt = angular_distance_np(Tij_in[np.newaxis, :3, :3],
Tij_gt[np.newaxis, :3, :3]).sum()
Rij = R[tid].dot(R[sid].T)
aerr = np.linalg.norm(Rij - Rij_in, 'fro')**2
if aerr_gt > 30.0:
bad_edges += edge['weight']
err_bad += aerr * edge['weight']
else:
good_edges += edge['weight']
err_good += aerr * edge['weight']
print('Edge Quality: #good=%f, #bad=%f, mean aerr=(%f, %f)' %
(good_edges, bad_edges, err_good / good_edges, err_bad / bad_edges))
def main():
depth_paths, T, pose_paths = getData(args.shapeid)
n = len(depth_paths)
print('found %d clean depth images...' % n)
intrinsic = np.array([[525.0,0,319.5],[0,525.0,239.5],[0,0,1]])
np.random.seed(816)
indices = np.random.permutation(n)
print(indices[:100])
#indices = sorted(indices)
make_dirs(PATH_MAT.format(args.shapeid, 0))
import open3d
pcd_combined = open3d.PointCloud()
for i, idx in enumerate(indices):
import ipdb; ipdb.set_trace()
print('%d / %d' % (i, len(indices)))
mesh = Mesh.read(depth_paths[idx], mode='depth', intrinsic = intrinsic)
pcd = open3d.PointCloud()
pcd.points = open3d.Vector3dVector(mesh.vertex.T)
pcd.transform(inverse(T[idx]))
#pcd = open3d.voxel_down_sample(pcd, voxel_size=0.02)
pcd_combined += pcd
pcd_combined = open3d.voxel_down_sample(pcd_combined, voxel_size=0.02)
sio.savemat(PATH_MAT.format(args.shapeid, i), mdict={
'vertex': mesh.vertex,
'validIdx_rowmajor': mesh.validIdx,
'pose': T[idx],
'depth_path': depth_paths[idx],
'pose_path': pose_paths[idx]})
if i <= 50 and i >= 40:
pcd_combined_down = open3d.voxel_down_sample(pcd_combined, voxel_size=0.02)
open3d.draw_geometries([pcd_combined_down])
pcd_combined_down = open3d.voxel_down_sample(pcd_combined, voxel_size=0.02)
open3d.draw_geometries([pcd_combined_down])
def __init__(self, center, radius, normal, I, scene, loops = 1, pitch = 1):
Shape.__init__(self, scene)
self.center = center
self.radius = radius
self.normal = normal
self.loops = loops
self.pitch = pitch
self.length = loops*pitch
self.I = I
# some consonants
self.C = mu_0*I/pi
self.oner = [[1,0,0], [0,1,0], [0,0,1]]
# rotation matrices for this coil, rotating so norm becomes z axis
self.rotate = self.find_rotmatrix(normal.norm(), vector(0, 0, 1))
self.antiRotate = inverse(self.rotate)
if loops == 1:
self.obj = ring(pos = center, axis = normal*self.length,
radius = radius, thickness = 0.1, display = scene,
material = materials.chrome)
else:
self.obj = helix(pos = center, axis = normal*self.length,
radius = radius, coils = loops, thickness = 0.1,
display = scene, material = materials.chrome)
def error(T, G):
aerrs = []
n = T.shape[0]
terrs = []
for i in range(n):
for j in range(i + 1, n):
Ti = T[i, :, :]
Tj = T[j, :, :]
Gi = G[i, :, :]
Gj = G[j, :, :]
Tij = Tj.dot(inverse(Ti))
Gij = Gj.dot(inverse(Gi))
Rij = Tij[:3, :3]
Rij_gt = Gij[:3, :3]
fro = np.linalg.norm(Rij - Rij_gt, 'fro')
aerr = angular_distance_np(Rij[np.newaxis, :, :],
Rij_gt[np.newaxis, :, :]).sum()
terr = np.linalg.norm(Tij[:3, 3] - Gij[:3, 3], 2)
aerrs.append(aerr)
terrs.append(terr)
return np.mean(aerrs), np.mean(terrs)
def __get_label__(Rij, tij, Ti, Tj):
""" Measure Quality of Edge """
Ristar, tistar = decompose(Ti)
Rjstar, tjstar = decompose(Tj)
Tij_gt = Tj.dot(inverse(Ti))
Tij_in = pack(Rij, tij)
label = 0.0
err_R = angular_distance_np(Rij[np.newaxis, :, :],
Rjstar.dot(Ristar.T)[np.newaxis, :, :]).sum()
err_T = np.linalg.norm(Tij_gt[:3, 3] - Tij_in[:3, 3], 2)
if (err_R < 30.0) and (err_T < 0.2):
label = 1.0
else:
label = 0.0
return label
def getData(shapeid):
depth_paths = []
poses = []
pose_paths = []
frames = glob.glob(PATH_DEPTH.format(shapeid, '*'))
frames.sort()
for i, frame in enumerate(frames):
frameid = frame.split('/')[-1].split('.')[0]
depth_path = PATH_DEPTH.format(shapeid, frameid)
#tmp = cv2.resize(cv2.imread(imgsPath, 2)/1000., (64,64))
#AuthenticdepthMap.append(tmp.reshape(1,tmp.shape[0],tmp.shape[1],1))
pose_fp = PATH_POSE.format(shapeid, frameid)
flag = True
try:
tmp = np.loadtxt(pose_fp)
assert abs(tmp[3, 3] -
1.0) < 1e-4, 'bottom right corner should be one'
assert (abs(tmp[3, :3]) < 1e-4).all(), '[3, :3] should be zero'
R = tmp[:3, :3]
assert np.linalg.det(R) > 0.01, 'determinant should be 1'
assert np.linalg.norm(
R.dot(R.T) - np.eye(3),
'fro')**2 < 1e-4, 'should be a rotation matrix'
project_R = project_so(R)
assert np.linalg.norm(
R - project_R,
'fro')**2 < 1e-4, 'projection onto SO3 should be identical'
tmp[:3, :3] = project_R
tmp = inverse(tmp)
except Exception as e:
print('error on {}: {}'.format(pose_fp, e))
#print(R.dot(R.T))
#print(np.linalg.norm(R.dot(R.T) - np.eye(3), 'fro'))
flag = False
if not flag:
print('ignoring frame {}'.format(frameid))
continue
poses.append(tmp)
depth_paths.append(depth_path)
pose_paths.append(pose_fp)
if len(poses) == 0:
T = None
else:
T = np.concatenate(poses).reshape(-1, 4, 4)
return depth_paths, T, pose_paths
def compute_sigma(mat_file1, mat_file2, txt, output_mat):
mat1 = sio.loadmat(mat_file1)
mat2 = sio.loadmat(mat_file2)
v1 = mat1['vertex'] # [3, n]
v2 = mat2['vertex'] # [3, n]
Tij = read_super4pcs(txt)
Tij_gt = mat2['pose'].dot(inverse(mat1['pose']))
Rij = Tij[:3, :3]
tij = Tij[:3, 3]
v1 = Rij.dot(v1) + tij[:, np.newaxis]
tree = NN(n_neighbors=1, algorithm='kd_tree').fit(v1.T)
distances, _ = tree.kneighbors(v2.T)
distances = distances[distances < 0.2]
d = {}
d['sigma'] = np.median(distances)
d['Tij'] = Tij
d['aerr'] = angular_distance_np(Tij[np.newaxis, :3, :3], Tij_gt[np.newaxis, :3, :3]).sum()
d['terr'] = np.linalg.norm(Tij[:3, 3]- Tij_gt[:3, 3], 2)
d['src'] = mat_file1
d['tgt'] = mat_file2
sio.savemat(output_mat, mdict=d, do_compression=True)
def reweightEdges(n, edges, R, t, sigma_r, sigma_t, plot=False):
theta1 = 4
terrs = []
if plot:
plots = []
for edge in edges:
i = edge['src']
j = edge['tgt']
Rij = edge['R']
tij = edge['t']
Tij_in = pack(Rij, tij)
Ti = pack(R[i], t[i])
Tj = pack(R[j], t[j])
Tij_rec = Tj.dot(inverse(Ti))
weight = edge['predicted_weight']
if weight < 0.01:
weight = 0.00
if weight > 1.0:
weight = 1.0
aerr_fro = np.linalg.norm(Tij_rec[:3, :3] - Tij_in[:3, :3],
'fro') * sigmoid((0.5 - weight) * 5)
terr_fro = np.linalg.norm(Tij_rec[:3, 3] - Tij_in[:3, 3], 2) * sigmoid(
(0.5 - weight) * 5)
#fro2 = aerr_fro ** 2 + terr_fro ** 2
edge['rotation_weight'] = (sigma_r**theta1) / (sigma_r**theta1 +
aerr_fro**(theta1))
edge['translation_weight'] = (sigma_t**theta1) / (sigma_t**theta1 +
terr_fro**(theta1))
if plot:
plots.append([aerr_fro, edge['rotation_weight']])
if plot:
plots = np.array(plots)
import matplotlib.pyplot as plt
plt.scatter(plots[:, 0], plots[:, 1])
plt.show()
def generate_synthetic(n, sigma):
T = np.zeros((n, 4, 4))
X = so.rvs(dim=3, size=n)
T[:, :3, :3] = X
# u, sigma, v = np.linalg.svd(T[0])
T[:, :3, 3] = np.random.randn(n, 3)
T[0, :3, 3] = 0.0
T[:, 3, 3] = 1
edges = []
for i in range(n):
for j in range(n):
if i <= j:
continue
Tij = T[j].dot(inverse(T[i]))
Rij, tij = decompose(Tij)
Rij = Rij + np.random.randn(3, 3) * sigma
Rij = project_so(Rij)
tij = tij + np.random.randn(3) * sigma
Tij = pack(Rij, tij)
edge = {'src': i, 'tgt': j, 'R': Rij, 't': tij, 'weight': 1.0}
edges.append(edge)
edges = np.array(edges)
return n, edges, T
def __init__(self, center, radius, normal, I, scene, loops=1, pitch=1):
Shape.__init__(self, scene)
self.center = center
self.radius = radius
self.normal = normal
self.loops = loops
self.pitch = pitch
self.length = loops * pitch
self.I = I
# some consonants
self.C = mu_0 * I / pi
self.oner = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
# rotation matrices for this coil, rotating so norm becomes z axis
self.rotate = self.find_rotmatrix(normal.norm(), vector(0, 0, 1))
self.antiRotate = inverse(self.rotate)
if loops == 1:
self.obj = ring(pos=center,
axis=normal * self.length,
radius=radius,
thickness=0.1,
display=scene,
material=materials.chrome)
else:
self.obj = helix(pos=center,
axis=normal * self.length,
radius=radius,
coils=loops,
thickness=0.1,
display=scene,
material=materials.chrome)
def IterativeTransfSync(n,
edges,
eps0=-1,
decay=0.8,
Tstar=None,
max_iter=10000,
cheat=False,
scheme='reweight'):
if scheme == 'reweight':
reweight = True
else:
reweight = False
if cheat:
for edge in edges:
#if edge['weight'] < 0.5:
# continue
sid = edge['src']
tid = edge['tgt']
Ti = Tstar[sid]
Tj = Tstar[tid]
Tij_gt = Tj.dot(inverse(Ti))
Rij = edge['R']
tij = edge['t']
Tij = pack(Rij, tij)
aerr = angular_distance_np(Tij[np.newaxis, :3, :3],
Tij_gt[np.newaxis, :3, :3]).sum()
terr = np.linalg.norm(Tij[:3, 3] - Tij_gt[:3, 3], 2)
#p = 0.9
if aerr > 30.0 or terr > 0.2:
weight = 0.0 #coin(0.02)
else:
weight = 1.0 #coin(0.9)
edge['predicted_weight'] = weight
edge['translation_weight'] = weight
edge['rotation_weight'] = weight
""" Edge Quality """
good_edges = 0.0
bad_edges = 0.0
err_bad = 0.0
err_good = 0.0
for edge in edges:
if edge['predicted_weight'] < 0.5:
continue
sid = edge['src']
tid = edge['tgt']
Ti = Tstar[sid]
Tj = Tstar[tid]
Tij_gt = Tj.dot(inverse(Ti))
Rij = edge['R']
tij = edge['t']
Tij = pack(Rij, tij)
aerr = angular_distance_np(Tij[np.newaxis, :3, :3],
Tij_gt[np.newaxis, :3, :3]).sum()
terr = np.linalg.norm(Tij[:3, 3] - Tij_gt[:3, 3], 2)
if aerr > 30.0 or terr > 0.2:
#print(sid, tid, edge['predicted_weight'])
bad_edges += 1
err_bad += aerr * edge['predicted_weight']
else:
good_edges += 1
err_good += aerr * edge['predicted_weight']
print('Edge Quality: #good=%f, #bad=%f' % (good_edges, bad_edges))
itr = 0
while itr < max_iter:
R, t, eigengap = TransfSync(n, edges)
#edge_quality(n, edges, Tstar, R)
T = np.array([pack(R[i], t[i]) for i in range(n)])
err_gt = -1.0
if Tstar is not None:
aerr_gt, terr_gt = error(T, Tstar)
if not reweight:
if eps0 < -0.5:
eps0 = max_existing_err(n, edges, R, t)
if reweight:
reweightEdges(n, edges, R, t, sigma_r=0.01, sigma_t=0.01)
else:
truncatedWeightPredict(n, edges, R, t, eps0)
mindeg, numedges, err_sum = computeStats(n, edges, R, t)
print(
'iter=%d, avg(err^2)=%f, eigengap=%f, #edges=%d, min_deg=%f, eps0=%f, aerr_gt=%f, terr_gt=%f'
% (itr, err_sum / numedges, eigengap, numedges, mindeg, eps0,
aerr_gt, terr_gt))
""" Skip idle iterations """
if reweight:
itr += 1
else:
max_err = max_existing_err(n, edges, R, t)
while (itr < max_iter) and (eps0 > max_err):
eps0 = eps0 * decay
itr += 1
if mindeg == 0:
break
if err_sum <= 1e-2:
break
return T
if __name__ == "__main__":
voxel_size = 0.02 # means 5cm for the dataset
import argparse
parser = argparse.ArgumentParser(
description='Baseline Algorithm: Fast Global Registration')
parser.add_argument('files', type=str, nargs='+', help='src, tgt, output')
args = parser.parse_args()
src_mat = sio.loadmat(args.files[0])
tgt_mat = sio.loadmat(args.files[1])
src_pose = src_mat['pose']
tgt_pose = tgt_mat['pose']
src = src_mat['vertex']
tgt = tgt_mat['vertex']
Tij = tgt_pose.dot(inverse(src_pose))
src_pc = open3d.PointCloud()
src_pc.points = open3d.Vector3dVector(src.T)
tgt_pc = open3d.PointCloud()
tgt_pc.points = open3d.Vector3dVector(tgt.T)
#source, target, source_down, target_down, source_fpfh, target_fpfh = \
# prepare_dataset(voxel_size)
#draw_registration_result(src_pc, tgt_pc, Tij)
open3d.estimate_normals(src_pc,
search_param=open3d.KDTreeSearchParamHybrid(
radius=0.2, max_nn=60))
open3d.estimate_normals(tgt_pc,
search_param=open3d.KDTreeSearchParamHybrid(
radius=0.2, max_nn=60))
source_down, source_fpfh = preprocess_point_cloud(src_pc, voxel_size)
sigmas = []
for line in lines:
summary_mat = '%s/relative_pose/summary/%s/%s/%s.mat' % (data_path, dataset, source, line)
summary_mat = sio.loadmat(summary_mat)
T = summary_mat['T']
Tstar = summary_mat['Tstar']
aerr = summary_mat['aerr']
terr = summary_mat['terr']
sigma = summary_mat['sigma']
n = Tstar.shape[0]
n = 30
for i in range(n):
for j in range(i+1, n):
Tij = T[i*4:(i+1)*4, j*4:(j+1)*4]
Tij_gt = Tstar[j, :, :].dot(inverse(Tstar[i, :, :]))
terr_ij = np.linalg.norm((Tij_gt - Tij)[:3, 3], 2)
assert abs(terr_ij - terr[i, j]) < 1e-4
terrs.append(terr_ij)
aerr_ij = angular_distance_np(Tij_gt[np.newaxis, :3, :3], Tij[np.newaxis, :3, :3]).sum()
assert abs(aerr_ij - aerr[i, j]) < 1e-4
aerrs.append(aerr_ij)
sigmas.append(sigma[i, j])
aerrs = np.array(aerrs)
terrs = np.array(terrs)
sigmas = np.array(sigmas)
for sigma_threshold in [0.1, 0.2]:
valid_indices = np.where(sigmas < sigma_threshold)[0]
terr = np.zeros((n, n)) + 10000000.0
RLlist = reader.list_relative_poses(dataset, source, sceneid)
if len(RLlist) < 4950:
continue
top = 0
bottom = 0
for mat in reader.list_relative_poses(dataset, source, sceneid):
s = sio.loadmat(mat)
src, tgt = mat.split('/')[-1].split('.')[0].split('_')[:2]
sid = scanid_map[src]
tid = scanid_map[tgt]
Tij = s['Tij']
if sid > tid:
tmp = sid; sid = tid; tid = tmp
Tij = inverse(Tij)
assert sid < tid
sigma[sid, tid] = s['sigma']
aerr[sid, tid] = s['aerr']
terr[sid, tid] = s['terr']
if s['aerr'] < 15.0 and s['terr'] < 0.2:
top += 1.0
bottom += 1.0
T[sid*4:(sid+1)*4, tid*4:(tid+1)*4] = Tij
Tstar = np.zeros((n, 4, 4))
for i, scanid in enumerate(scanids):
scan = reader.read_scan(dataset, sceneid, scanid, variable_names=['pose'])
Tstar[i, :, :] = scan['pose']
print(sceneid, 'good ratio=', top / bottom)