def recover_relative_pose_from_essential_matrix(
i2Ei1: np.ndarray,
verified_coordinates_i1: np.ndarray,
verified_coordinates_i2: np.ndarray,
camera_intrinsics_i1: Cal3Bundler,
camera_intrinsics_i2: Cal3Bundler,
) -> Tuple[Rot3, Unit3]:
"""Recovers the relative rotation and translation direction from essential matrix and verified correspondences
using opencv's API.
Args:
i2Ei1: essential matrix as a numpy array, of shape 3x3.
verified_coordinates_i1: coordinates of verified correspondences in image i1, of shape Nx2.
verified_coordinates_i2: coordinates of verified correspondences in image i2, of shape Nx2.
camera_intrinsics_i1: intrinsics for image i1.
camera_intrinsics_i2: intrinsics for image i2.
Returns:
relative rotation i2Ri1.
relative translation direction i2Ui1.
"""
# obtain points in normalized coordinates using intrinsics.
normalized_coordinates_i1 = feature_utils.normalize_coordinates(
verified_coordinates_i1, camera_intrinsics_i1)
normalized_coordinates_i2 = feature_utils.normalize_coordinates(
verified_coordinates_i2, camera_intrinsics_i2)
# use opencv to recover pose
_, i2Ri1, i2ti1, _ = cv.recoverPose(i2Ei1, normalized_coordinates_i1,
normalized_coordinates_i2)
return Rot3(i2Ri1), Unit3(i2ti1.squeeze())
def recover_relative_pose_from_essential_matrix(
i2Ei1: Optional[np.ndarray],
verified_coordinates_i1: np.ndarray,
verified_coordinates_i2: np.ndarray,
camera_intrinsics_i1: Cal3Bundler,
camera_intrinsics_i2: Cal3Bundler,
) -> Tuple[Optional[Rot3], Optional[Unit3]]:
"""Recovers the relative rotation and translation direction from essential matrix and verified correspondences
using opencv's API.
Args:
i2Ei1: essential matrix as a numpy array, of shape 3x3.
verified_coordinates_i1: coordinates of verified correspondences in image i1, of shape Nx2.
verified_coordinates_i2: coordinates of verified correspondences in image i2, of shape Nx2.
camera_intrinsics_i1: intrinsics for image i1.
camera_intrinsics_i2: intrinsics for image i2.
Returns:
relative rotation i2Ri1, or None if the input essential matrix is None.
relative translation direction i2Ui1, or None if the input essential matrix is None.
"""
if i2Ei1 is None:
return None, None
# obtain points in normalized coordinates using intrinsics.
normalized_coordinates_i1 = feature_utils.normalize_coordinates(
verified_coordinates_i1, camera_intrinsics_i1)
normalized_coordinates_i2 = feature_utils.normalize_coordinates(
verified_coordinates_i2, camera_intrinsics_i2)
# use opencv to recover pose
_, i2Ri1, i2ti1, _ = cv.recoverPose(i2Ei1, normalized_coordinates_i1,
normalized_coordinates_i2)
i2Ri1 = Rot3(i2Ri1)
i2Ui1 = Unit3(i2ti1.squeeze())
i2Ei1_reconstructed = EssentialMatrix(i2Ri1, i2Ui1).matrix()
# normalizing the two essential matrices
i2Ei1_normalized = i2Ei1 / np.linalg.norm(i2Ei1, axis=None)
i2Ei1_reconstructed_normalized = i2Ei1_reconstructed / np.linalg.norm(
i2Ei1_reconstructed, axis=None)
if not np.allclose(i2Ei1_normalized, i2Ei1_reconstructed_normalized):
logger.warning(
"Recovered R, t cannot create the input Essential Matrix")
return i2Ri1, i2Ui1
def test_normalize_coordinates(self):
coordinates = np.array([[10.0, 20.0], [25.0, 12.0], [30.0, 33.0]])
intrinsics = Cal3Bundler(fx=100, k1=0.0, k2=0.0, u0=20.0, v0=30.0)
normalized_coordinates = feature_utils.normalize_coordinates(coordinates, intrinsics)
expected_coordinates = np.array([[-0.1, -0.1], [0.05, -0.18], [0.1, 0.03]])
np.testing.assert_allclose(normalized_coordinates, expected_coordinates)
def count_correct_correspondences(
keypoints_i1: Keypoints,
keypoints_i2: Keypoints,
intrinsics_i1: Cal3Bundler,
intrinsics_i2: Cal3Bundler,
i2Ti1: Pose3,
epipolar_dist_threshold: float,
) -> int:
"""Checks the correspondences for epipolar distances and counts ones which are below the threshold.
Args:
keypoints_i1: keypoints in image i1.
keypoints_i2: corr. keypoints in image i2.
intrinsics_i1: intrinsics for i1.
intrinsics_i2: intrinsics for i2.
i2Ti1: relative pose
epipolar_dist_threshold: max acceptable distance for a correct correspondence.
Raises:
ValueError: when the number of keypoints do not match.
Returns:
Number of correspondences which are correct.
"""
# TODO: add unit test, with mocking.
if len(keypoints_i1) != len(keypoints_i2):
raise ValueError("Keypoints must have same counts")
if len(keypoints_i1) == 0:
return 0
normalized_coords_i1 = feature_utils.normalize_coordinates(
keypoints_i1.coordinates, intrinsics_i1)
normalized_coords_i2 = feature_utils.normalize_coordinates(
keypoints_i2.coordinates, intrinsics_i2)
i2Ei1 = EssentialMatrix(i2Ti1.rotation(), Unit3(i2Ti1.translation()))
epipolar_distances = verification_utils.compute_epipolar_distances(
normalized_coords_i1, normalized_coords_i2, i2Ei1)
return np.count_nonzero(epipolar_distances < epipolar_dist_threshold)
def verify(
self,
keypoints_i1: Keypoints,
keypoints_i2: Keypoints,
match_indices: np.ndarray,
camera_intrinsics_i1: Cal3Bundler,
camera_intrinsics_i2: Cal3Bundler,
) -> Tuple[Optional[Rot3], Optional[Unit3], np.ndarray, float]:
"""Performs verification of correspondences between two images to recover the relative pose and indices of
verified correspondences.
Args:
keypoints_i1: detected features in image #i1.
keypoints_i2: detected features in image #i2.
match_indices: matches as indices of features from both images, of shape (N3, 2), where N3 <= min(N1, N2).
camera_intrinsics_i1: intrinsics for image #i1.
camera_intrinsics_i2: intrinsics for image #i2.
Returns:
Estimated rotation i2Ri1, or None if it cannot be estimated.
Estimated unit translation i2Ui1, or None if it cannot be estimated.
Indices of verified correspondences, of shape (N, 2) with N <= N3. These are subset of match_indices.
Inlier ratio w.r.t. the estimated model, i.e. #ransac inliers / # putative matches.
"""
if match_indices.shape[0] < self._min_matches:
return self._failure_result
if self._use_intrinsics_in_verification:
uv_norm_i1 = feature_utils.normalize_coordinates(
keypoints_i1.coordinates, camera_intrinsics_i1)
uv_norm_i2 = feature_utils.normalize_coordinates(
keypoints_i2.coordinates, camera_intrinsics_i2)
# OpenCV can fail here, for some reason
if match_indices.shape[0] < 6:
return self._failure_result
if np.amax(match_indices[:, 1]) >= uv_norm_i2.shape[0]:
print("Out of bounds access w/ keypoints",
keypoints_i2.coordinates[:10])
if np.amax(match_indices[:, 0]) >= uv_norm_i1.shape[0]:
print("Out of bounds access w/ keypoints",
keypoints_i1.coordinates[:10])
# Use larger focal length, among the two choices, to yield a stricter threshold as (threshold_px / fx).
fx = max(camera_intrinsics_i1.K()[0, 0],
camera_intrinsics_i2.K()[0, 0])
i2Ei1, inlier_mask = self.estimate_E(uv_norm_i1=uv_norm_i1,
uv_norm_i2=uv_norm_i2,
match_indices=match_indices,
fx=fx)
else:
i2Fi1, inlier_mask = self.estimate_F(keypoints_i1=keypoints_i1,
keypoints_i2=keypoints_i2,
match_indices=match_indices)
i2Ei1 = verification_utils.fundamental_to_essential_matrix(
i2Fi1, camera_intrinsics_i1, camera_intrinsics_i2)
inlier_idxs = np.where(inlier_mask.ravel() == 1)[0]
v_corr_idxs = match_indices[inlier_idxs]
inlier_ratio_est_model = np.mean(inlier_mask)
(i2Ri1, i2Ui1
) = verification_utils.recover_relative_pose_from_essential_matrix(
i2Ei1,
keypoints_i1.coordinates[v_corr_idxs[:, 0]],
keypoints_i2.coordinates[v_corr_idxs[:, 1]],
camera_intrinsics_i1,
camera_intrinsics_i2,
)
return i2Ri1, i2Ui1, v_corr_idxs, inlier_ratio_est_model
def verify_with_exact_intrinsics(
self,
keypoints_i1: Keypoints,
keypoints_i2: Keypoints,
match_indices: np.ndarray,
camera_intrinsics_i1: Cal3Bundler,
camera_intrinsics_i2: Cal3Bundler,
) -> Tuple[Optional[Rot3], Optional[Unit3], np.ndarray]:
"""Estimates the essential matrix and verifies the feature matches.
Note: this function is preferred when camera intrinsics are known. The
feature coordinates are normalized and the essential matrix is directly
estimated.
Args:
keypoints_i1: detected features in image #i1.
keypoints_i2: detected features in image #i2.
match_indices: matches as indices of features from both images, of
shape (N3, 2), where N3 <= min(N1, N2).
camera_intrinsics_i1: intrinsics for image #i1.
camera_intrinsics_i2: intrinsics for image #i2.
Returns:
Estimated rotation i2Ri1, or None if it cannot be estimated.
Estimated unit translation i2Ui1, or None if it cannot be estimated.
Indices of verified correspondences, of shape (N, 2) with N <= N3.
These indices are subset of match_indices.
"""
verified_indices = np.array([], dtype=np.uint32)
# check if we don't have the minimum number of points
if match_indices.shape[0] < self.min_pts:
logger.info(
"No match indices were provided to the verifier, returning early with None output"
)
return None, None, verified_indices
uv_norm_i1 = feature_utils.normalize_coordinates(
keypoints_i1.coordinates, camera_intrinsics_i1)
uv_norm_i2 = feature_utils.normalize_coordinates(
keypoints_i2.coordinates, camera_intrinsics_i2)
K = np.eye(3)
i2Ei1, inlier_mask = cv2.findEssentialMat(
uv_norm_i1[match_indices[:, 0]],
uv_norm_i2[match_indices[:, 1]],
K,
method=cv2.RANSAC,
threshold=NORMALIZED_COORD_RANSAC_THRESH,
prob=DEFAULT_RANSAC_SUCCESS_PROB,
)
inlier_idxs = np.where(inlier_mask.ravel() == 1)[0]
(
i2Ri1,
i2Ui1,
) = verification_utils.recover_relative_pose_from_essential_matrix(
i2Ei1,
keypoints_i1.coordinates[match_indices[inlier_idxs, 0]],
keypoints_i2.coordinates[match_indices[inlier_idxs, 1]],
camera_intrinsics_i1,
camera_intrinsics_i2,
)
return i2Ri1, i2Ui1, match_indices[inlier_idxs]
def verify(
self,
keypoints_i1: Keypoints,
keypoints_i2: Keypoints,
match_indices: np.ndarray,
camera_intrinsics_i1: Cal3Bundler,
camera_intrinsics_i2: Cal3Bundler,
) -> Tuple[Optional[Rot3], Optional[Unit3], np.ndarray]:
"""Performs verification of correspondences between two images to recover the relative pose and indices of
verified correspondences.
Args:
keypoints_i1: detected features in image #i1.
keypoints_i2: detected features in image #i2.
match_indices: matches as indices of features from both images, of shape (N3, 2), where N3 <= min(N1, N2).
camera_intrinsics_i1: intrinsics for image #i1.
camera_intrinsics_i2: intrinsics for image #i2.
Returns:
Estimated rotation i2Ri1, or None if it cannot be estimated.
Estimated unit translation i2Ui1, or None if it cannot be estimated.
Indices of verified correspondences, of shape (N, 2) with N <= N3. These are subset of match_indices.
"""
if match_indices.shape[0] < self._min_matches:
return self._failure_result
if self._use_intrinsics_in_verification:
uv_norm_i1 = feature_utils.normalize_coordinates(keypoints_i1.coordinates, camera_intrinsics_i1)
uv_norm_i2 = feature_utils.normalize_coordinates(keypoints_i2.coordinates, camera_intrinsics_i2)
K = np.eye(3)
i2Ei1, inlier_mask = cv2.findEssentialMat(
uv_norm_i1[match_indices[:, 0]],
uv_norm_i2[match_indices[:, 1]],
K,
method=cv2.RANSAC,
threshold=NORMALIZED_COORD_RANSAC_THRESH,
prob=DEFAULT_RANSAC_SUCCESS_PROB,
)
else:
i2Fi1, inlier_mask = cv2.findFundamentalMat(
keypoints_i1.extract_indices(match_indices[:, 0]).coordinates,
keypoints_i2.extract_indices(match_indices[:, 1]).coordinates,
method=cv2.FM_RANSAC,
ransacReprojThreshold=PIXEL_COORD_RANSAC_THRESH,
confidence=DEFAULT_RANSAC_SUCCESS_PROB,
maxIters=10000,
)
i2Ei1 = verification_utils.fundamental_to_essential_matrix(
i2Fi1, camera_intrinsics_i1, camera_intrinsics_i2
)
inlier_idxs = np.where(inlier_mask.ravel() == 1)[0]
(i2Ri1, i2Ui1) = verification_utils.recover_relative_pose_from_essential_matrix(
i2Ei1,
keypoints_i1.coordinates[match_indices[inlier_idxs, 0]],
keypoints_i2.coordinates[match_indices[inlier_idxs, 1]],
camera_intrinsics_i1,
camera_intrinsics_i2,
)
return i2Ri1, i2Ui1, match_indices[inlier_idxs]