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registration.py
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"""
registration toolbox (algorithm for some registration algorithm)
Implemented: fast_global_registration
teaser
"""
import open3d
import numpy as np
import torch
from torch_points3d.utils.geometry import get_trans
from torch_geometric.nn import knn
def get_matches(feat_source, feat_target, sym=False):
matches = knn(feat_target, feat_source, k=1).T
if sym:
match_inv = knn(feat_source, feat_target, k=1).T
mask = match_inv[matches[:, 1], 1] == torch.arange(matches.shape[0], device=feat_source.device)
return matches[mask]
else:
return matches
def estimate_transfo(xyz, xyz_target):
"""
estimate the rotation and translation using Kabsch algorithm
Parameters:
xyz :
xyz_target:
"""
assert xyz.shape == xyz.shape
xyz_c = xyz - xyz.mean(0)
xyz_target_c = xyz_target - xyz_target.mean(0)
Q = xyz_c.T.mm(xyz_target_c) / len(xyz)
U, S, V = torch.svd(Q)
d = torch.det(V.mm(U.T))
diag = torch.diag(torch.tensor([1, 1, d], device=xyz.device))
R = V.mm(diag).mm(U.T)
t = xyz_target.mean(0) - R @ xyz.mean(0)
T = torch.eye(4, device=xyz.device)
T[:3, :3] = R
T[:3, 3] = t
return T
def get_geman_mclure_weight(xyz, xyz_target, mu):
"""
compute the weights defined here for the iterative reweighted least square.
http://vladlen.info/papers/fast-global-registration.pdf
"""
norm2 = torch.norm(xyz_target - xyz, dim=1) ** 2
return (mu / (mu + norm2)).view(-1, 1)
def get_matrix_system(xyz, xyz_target, weight):
"""
Build matrix of size 3N x 6 and b of size 3N
xyz size N x 3
xyz_target size N x 3
weight size N
the matrix is minus cross product matrix concatenate with the identity (rearanged).
"""
assert xyz.shape == xyz_target.shape
A_x = torch.zeros(xyz.shape[0], 6, device=xyz.device)
A_y = torch.zeros(xyz.shape[0], 6, device=xyz.device)
A_z = torch.zeros(xyz.shape[0], 6, device=xyz.device)
b_x = weight.view(-1) * (xyz_target[:, 0] - xyz[:, 0])
b_y = weight.view(-1) * (xyz_target[:, 1] - xyz[:, 1])
b_z = weight.view(-1) * (xyz_target[:, 2] - xyz[:, 2])
A_x[:, 1] = weight.view(-1) * xyz[:, 2]
A_x[:, 2] = -weight.view(-1) * xyz[:, 1]
A_x[:, 3] = weight.view(-1) * 1
A_y[:, 0] = -weight.view(-1) * xyz[:, 2]
A_y[:, 2] = weight.view(-1) * xyz[:, 0]
A_y[:, 4] = weight.view(-1) * 1
A_z[:, 0] = weight.view(-1) * xyz[:, 1]
A_z[:, 1] = -weight.view(-1) * xyz[:, 0]
A_z[:, 5] = weight.view(-1) * 1
return torch.cat([A_x, A_y, A_z], 0), torch.cat([b_x, b_y, b_z], 0).view(-1, 1)
def fast_global_registration(xyz, xyz_target, mu_init=1, num_iter=20):
"""
estimate the rotation and translation using Fast Global Registration algorithm (M estimator for robust estimation)
http://vladlen.info/papers/fast-global-registration.pdf
"""
assert xyz.shape == xyz_target.shape
T_res = torch.eye(4, device=xyz.device)
mu = mu_init
source = xyz.clone()
weight = torch.ones(len(source), 1, device=xyz.device)
for i in range(num_iter):
if i > 0 and i % 5 == 0:
mu /= 2.0
A, b = get_matrix_system(source, xyz_target, weight)
x = torch.linalg.solve(A.T.mm(A), A.T @ b)
T = get_trans(x.view(-1))
source = source.mm(T[:3, :3].T) + T[:3, 3]
T_res = T @ T_res
weight = get_geman_mclure_weight(source, xyz_target, mu)
return T_res
def teaser_pp_registration(
xyz,
xyz_target,
noise_bound=0.05,
cbar2=1,
rotation_gnc_factor=1.4,
rotation_max_iterations=100,
rotation_cost_threshold=1e-12,
):
assert xyz.shape == xyz_target.shape
import teaserpp_python
# Populating the parameters
solver_params = teaserpp_python.RobustRegistrationSolver.Params()
solver_params.cbar2 = cbar2
solver_params.noise_bound = noise_bound
solver_params.estimate_scaling = False
solver_params.rotation_estimation_algorithm = (
teaserpp_python.RobustRegistrationSolver.ROTATION_ESTIMATION_ALGORITHM.GNC_TLS
)
solver_params.rotation_gnc_factor = rotation_gnc_factor
solver_params.rotation_max_iterations = rotation_max_iterations
solver_params.rotation_cost_threshold = rotation_cost_threshold
solver = teaserpp_python.RobustRegistrationSolver(solver_params)
solver.solve(xyz.T.detach().cpu().numpy(), xyz_target.T.detach().cpu().numpy())
solution = solver.getSolution()
T_res = torch.eye(4, device=xyz.device)
T_res[:3, :3] = torch.from_numpy(solution.rotation).to(xyz.device)
T_res[:3, 3] = torch.from_numpy(solution.translation).to(xyz.device)
return T_res
def ransac_registration(xyz, xyz_target, distance_threshold=0.05, num_iterations=80000):
"""
use Open3D version of RANSAC
"""
pcd = open3d.geometry.PointCloud()
pcd.points = open3d.utility.Vector3dVector(xyz.detach().cpu().numpy())
pcd_t = open3d.geometry.PointCloud()
pcd_t.points = open3d.utility.Vector3dVector(xyz_target.detach().cpu().numpy())
rang = np.arange(len(xyz))
corres = np.stack((rang, rang), axis=1)
corres = open3d.utility.Vector2iVector(corres)
result = open3d.pipelines.registration.registration_ransac_based_on_correspondence(
pcd,
pcd_t,
corres,
distance_threshold,
estimation_method=open3d.pipelines.registration.TransformationEstimationPointToPoint(False),
ransac_n=4,
criteria=open3d.pipelines.registration.RANSACConvergenceCriteria(4000000, num_iterations),
)
return torch.from_numpy(result.transformation).float()