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import cv2 as cv
import open3d as o3d
def backproject_3d(uv, depth, K):
'''
Backprojects 2d points given by uv coordinates into 3D using their depth values and intrinsic K
:param uv: array [N,2]
:param depth: array [N]
:param K: array [3,3]
:return: xyz: array [N,3]
'''
uv1 = np.concatenate([uv, np.ones((uv.shape[0], 1))], axis=1)
xyz = depth.reshape(-1, 1) * (np.linalg.inv(K) @ uv1.T).T
return xyz
class EssentialMatrixSolver:
'''Obtain relative pose (up to scale) given a set of 2D-2D correspondences'''
def __init__(self, ransac_pix_threshold=0.5, ransac_confidence=0.99999):
# EMat RANSAC parameters
self.ransac_pix_threshold = ransac_pix_threshold
self.ransac_confidence = ransac_confidence
def estimate_pose(self, kpts0, kpts1, data):
R = np.full((3, 3), np.nan)
t = np.full((3), np.nan)
if len(kpts0) < 5:
return R, t, 0
K0 = data['K_color0'].numpy()
K1 = data['K_color1'].numpy()
# normalize keypoints
kpts0 = (kpts0 - K0[[0, 1], [2, 2]][None]) / K0[[0, 1], [0, 1]][None]
kpts1 = (kpts1 - K1[[0, 1], [2, 2]][None]) / K1[[0, 1], [0, 1]][None]
# normalize ransac threshold
ransac_thr = self.ransac_pix_threshold / np.mean([K0[0, 0], K1[1, 1], K0[1, 1], K1[0, 0]])
# compute pose with OpenCV
E, mask = cv.findEssentialMat(
kpts0, kpts1, np.eye(3),
threshold=ransac_thr, prob=self.ransac_confidence, method=cv.RANSAC)
self.mask = mask
if E is None:
return R, t, 0
# recover pose from E
best_num_inliers = 0
ret = R, t, 0
for _E in np.split(E, len(E) / 3):
n, R, t, _ = cv.recoverPose(_E, kpts0, kpts1, np.eye(3), 1e9, mask=mask)
if n > best_num_inliers:
best_num_inliers = n
ret = (R, t[:, 0], n)
return ret
class EssentialMatrixMetricSolverMEAN(EssentialMatrixSolver):
'''Obtains relative pose with scale using E-Mat decomposition and depth values at inlier correspondences'''
def __init__(self, cfg):
super().__init__(cfg)
def estimate_pose(self, kpts0, kpts1, data):
'''Estimates metric translation vector using by back-projecting E-mat inliers to 3D using depthmaps.
The metric translation vector can be obtained by looking at the residual vector (projected to the translation vector direction).
In this version, each 3D-3D correspondence gives an optimal scale for the translation vector.
We simply aggregate them by averaging them.
'''
# get pose up to scale
R, t, inliers = super().estimate_pose(kpts0, kpts1, data)
if inliers == 0:
return R, t, inliers
# backproject E-mat inliers at each camera
K0 = data['K_color0']
K1 = data['K_color1']
mask = self.mask.ravel() == 1 # get E-mat inlier mask from super class
inliers_kpts0 = np.int32(kpts0[mask])
inliers_kpts1 = np.int32(kpts1[mask])
depth_inliers_0 = data['depth0'][inliers_kpts0[:, 1], inliers_kpts0[:, 0]].numpy()
depth_inliers_1 = data['depth1'][inliers_kpts1[:, 1], inliers_kpts1[:, 0]].numpy()
# check for valid depth
valid = (depth_inliers_0 > 0) * (depth_inliers_1 > 0)
if valid.sum() < 1:
R = np.full((3, 3), np.nan)
t = np.full((3, 1), np.nan)
inliers = 0
return R, t, inliers
xyz0 = backproject_3d(inliers_kpts0[valid], depth_inliers_0[valid], K0)
xyz1 = backproject_3d(inliers_kpts1[valid], depth_inliers_1[valid], K1)
# rotate xyz0 to xyz1 CS (so that axes are parallel)
xyz0 = (R @ xyz0.T).T
# get average point for each camera
pmean0 = np.mean(xyz0, axis=0)
pmean1 = np.mean(xyz1, axis=0)
# find scale as the 'length' of the translation vector that minimises the 3D distance between projected points from 0 and the corresponding points in 1
scale = np.dot(pmean1 - pmean0, t)
t_metric = scale * t
t_metric = t_metric.reshape(3, 1)
return R, t_metric[:, 0], inliers
class EssentialMatrixMetricSolver(EssentialMatrixSolver):
'''
Obtains relative pose with scale using E-Mat decomposition and RANSAC for scale based on depth values at inlier correspondences.
The scale of the translation vector is obtained using RANSAC over the possible scales recovered from 3D-3D correspondences.
'''
def __init__(self, ransac_pix_threshold=0.5, ransac_confidence=0.99999, ransac_scale_threshold=0.1):
super().__init__(ransac_pix_threshold, ransac_confidence)
self.ransac_scale_threshold = ransac_scale_threshold
def estimate_pose(self, kpts0, kpts1, data):
'''Estimates metric translation vector using by back-projecting E-mat inliers to 3D using depthmaps.
'''
# get pose up to scale
R, t, inliers = super().estimate_pose(kpts0, kpts1, data)
if inliers == 0:
return R, t, inliers
# backproject E-mat inliers at each camera
K0 = data['K_color0']
K1 = data['K_color1']
mask = self.mask.ravel() == 1 # get E-mat inlier mask from super class
inliers_kpts0 = np.int32(kpts0[mask])
inliers_kpts1 = np.int32(kpts1[mask])
depth_inliers_0 = data['depth0'][inliers_kpts0[:, 1], inliers_kpts0[:, 0]].numpy()
depth_inliers_1 = data['depth1'][inliers_kpts1[:, 1], inliers_kpts1[:, 0]].numpy()
# check for valid depth
valid = (depth_inliers_0 > 0) * (depth_inliers_1 > 0)
if valid.sum() < 1:
R = np.full((3, 3), np.nan)
t = np.full((3, ), np.nan)
inliers = 0
return R, t, inliers
xyz0 = backproject_3d(inliers_kpts0[valid], depth_inliers_0[valid], K0)
xyz1 = backproject_3d(inliers_kpts1[valid], depth_inliers_1[valid], K1)
# rotate xyz0 to xyz1 CS (so that axes are parallel)
xyz0 = (R @ xyz0.T).T
# get individual scales (for each 3D-3D correspondence)
scale = np.dot(xyz1 - xyz0, t.reshape(3, 1)) # [N, 1]
# RANSAC loop
best_inliers = 0
best_scale = None
for scale_hyp in scale:
inliers_hyp = (np.abs(scale - scale_hyp) < self.ransac_scale_threshold).sum().item()
if inliers_hyp > best_inliers:
best_scale = scale_hyp
best_inliers = inliers_hyp
# Output results
t_metric = best_scale * t
t_metric = t_metric.reshape(3, 1)
return R, t_metric[:, 0], best_inliers
class PnPSolver:
'''Estimate relative pose (metric) using Perspective-n-Point algorithm (2D-3D) correspondences'''
def __init__(self, ransac_iterations=1000, reprojection_inlier_threshold=3, confidence=0.99999):
# PnP RANSAC parameters
self.ransac_iterations = ransac_iterations
self.reprojection_inlier_threshold = reprojection_inlier_threshold
self.confidence = confidence
def estimate_pose(self, pts0, pts1, data):
# uses nearest neighbour
pts0 = np.int32(pts0)
if len(pts0) < 4:
return np.full((3, 3), np.nan), np.full((3, 1), np.nan), 0
# get depth at correspondence points
depth_0 = data['depth0']
depth_pts0 = depth_0[pts0[:, 1], pts0[:, 0]]
# remove invalid pts (depth == 0)
valid = depth_pts0 > depth_0.min()
if valid.sum() < 4:
return np.full((3, 3), np.nan), np.full((3, 1), np.nan), 0
pts0 = pts0[valid]
pts1 = pts1[valid]
depth_pts0 = depth_pts0[valid]
# backproject points to 3D in each sensors' local coordinates
K0 = data['K_color0']
K1 = data['K_color1']
xyz_0 = backproject_3d(pts0, depth_pts0, K0).numpy()
# get relative pose using PnP + RANSAC
succ, rvec, tvec, inliers = cv.solvePnPRansac(
xyz_0, pts1, K1.numpy(),
None, iterationsCount=self.ransac_iterations,
reprojectionError=self.reprojection_inlier_threshold, confidence=self.confidence,
flags=cv.SOLVEPNP_P3P)
# refine with iterative PnP using inliers only
if succ and len(inliers) >= 6:
succ, rvec, tvec, _ = cv.solvePnPGeneric(xyz_0[inliers], pts1[inliers], K1.numpy(
), None, useExtrinsicGuess=True, rvec=rvec, tvec=tvec, flags=cv.SOLVEPNP_ITERATIVE)
rvec = rvec[0]
tvec = tvec[0]
# avoid degenerate solutions
if succ:
if np.linalg.norm(tvec) > 1000:
succ = False
if succ:
R, _ = cv.Rodrigues(rvec)
t = tvec.reshape(3, 1)
else:
R = np.full((3, 3), np.nan)
t = np.full((3, 1), np.nan)
inliers = []
return R, t[:, 0], inliers
class ProcrustesSolver:
'''Estimate relative pose (metric) using 3D-3D correspondences'''
def __init__(self, ransac_max_corr_distance=0.5, refine=False):
# Procrustes RANSAC parameters
self.ransac_max_corr_distance = ransac_max_corr_distance
self.refine = refine
def estimate_pose(self, pts0, pts1, data):
# uses nearest neighbour
pts0 = np.int32(pts0)
pts1 = np.int32(pts1)
if len(pts0) < 3:
return np.full((3, 3), np.nan), np.full((3), np.nan), 0
# get depth at correspondence points
depth_0, depth_1 = data['depth0'], data['depth1']
depth_pts0 = depth_0[pts0[:, 1], pts0[:, 0]]
depth_pts1 = depth_1[pts1[:, 1], pts1[:, 0]]
# remove invalid pts (depth == 0)
valid = (depth_pts0 > depth_0.min()) * (depth_pts1 > depth_1.min())
if valid.sum() < 3:
return np.full((3, 3), np.nan), np.full((3), np.nan), 0
pts0 = pts0[valid]
pts1 = pts1[valid]
depth_pts0 = depth_pts0[valid]
depth_pts1 = depth_pts1[valid]
# backproject points to 3D in each sensors' local coordinates
K0 = data['K_color0']
K1 = data['K_color1']
xyz_0 = backproject_3d(pts0, depth_pts0, K0)
xyz_1 = backproject_3d(pts1, depth_pts1, K1)
# create open3d point cloud objects and correspondences idxs
pcl_0 = o3d.geometry.PointCloud()
pcl_0.points = o3d.utility.Vector3dVector(xyz_0)
pcl_1 = o3d.geometry.PointCloud()
pcl_1.points = o3d.utility.Vector3dVector(xyz_1)
corr_idx = np.arange(pts0.shape[0])
corr_idx = np.tile(corr_idx.reshape(-1, 1), (1, 2))
corr_idx = o3d.utility.Vector2iVector(corr_idx)
# obtain relative pose using procrustes
ransac_criteria = o3d.pipelines.registration.RANSACConvergenceCriteria()
res = o3d.pipelines.registration.registration_ransac_based_on_correspondence(
pcl_0, pcl_1, corr_idx, self.ransac_max_corr_distance, criteria=ransac_criteria)
inliers = int(res.fitness * np.asarray(pcl_1.points).shape[0])
# refine with ICP
if self.refine:
# first, backproject both (whole) point clouds
vv, uu = np.mgrid[0:depth_0.shape[0], 0:depth_1.shape[1]]
uv_coords = np.concatenate([uu.reshape(-1, 1), vv.reshape(-1, 1)], axis=1)
valid = depth_0.reshape(-1) > 0
xyz_0 = backproject_3d(uv_coords[valid], depth_0.reshape(-1)[valid], K0)
valid = depth_1.reshape(-1) > 0
xyz_1 = backproject_3d(uv_coords[valid], depth_1.reshape(-1)[valid], K1)
pcl_0 = o3d.geometry.PointCloud()
pcl_0.points = o3d.utility.Vector3dVector(xyz_0)
pcl_1 = o3d.geometry.PointCloud()
pcl_1.points = o3d.utility.Vector3dVector(xyz_1)
icp_criteria = o3d.pipelines.registration.ICPConvergenceCriteria(relative_fitness=1e-4,
relative_rmse=1e-4,
max_iteration=30)
res = o3d.pipelines.registration.registration_icp(pcl_0,
pcl_1,
self.ransac_max_corr_distance,
init=res.transformation,
criteria=icp_criteria)
R = res.transformation[:3, :3]
t = res.transformation[:3, -1]
inliers = int(res.fitness * np.asarray(pcl_1.points).shape[0])
return R, t, inliers
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