def local_translation(r1, r2, x, y, w, h, m):
"""
Estimates the optimal translation to minimise the relative pointing error
on a given tile.
Args:
r1, r2: two instances of the rpc_model.RPCModel class
x, y, w, h: region of interest in the reference image (r1)
m: Nx4 numpy array containing a list of matches, one per line. Each
match is given by (p1, p2, q1, q2) where (p1, p2) is a point of the
reference view and (q1, q2) is the corresponding point in the
secondary view.
Returns:
3x3 numpy array containing the homogeneous representation of the
optimal planar translation, to be applied to the secondary image in
order to correct the pointing error.
"""
# estimate the affine fundamental matrix between the two views
n = cfg['n_gcp_per_axis']
rpc_matches = rpc_utils.matches_from_rpc(r1, r2, x, y, w, h, n)
F = estimation.affine_fundamental_matrix(rpc_matches)
# compute the error vectors
e = error_vectors(m, F, 'sec')
# compute the median: as the vectors are collinear (because F is affine)
# computing the median of each component independently is correct
N = len(e)
out_x = np.sort(e[:, 0])[int(N / 2)]
out_y = np.sort(e[:, 1])[int(N / 2)]
# the correction to be applied to the second view is the opposite
A = np.array([[1, 0, -out_x], [0, 1, -out_y], [0, 0, 1]])
return A
def matches_on_rpc_roi(im1, im2, rpc1, rpc2, x, y, w, h):
"""
Compute a list of SIFT matches between two images on a given roi.
The corresponding roi in the second image is determined using the rpc
functions.
Args:
im1, im2: paths to two large tif images
rpc1, rpc2: two instances of the rpcm.RPCModel class
x, y, w, h: four integers defining the rectangular ROI in the first
image. (x, y) is the top-left corner, and (w, h) are the dimensions
of the rectangle.
Returns:
matches: 2D numpy array containing a list of matches. Each line
contains one pair of points, ordered as x1 y1 x2 y2.
The coordinate system is that of the full images.
"""
x2, y2, w2, h2 = rpc_utils.corresponding_roi(rpc1, rpc2, x, y, w, h)
# estimate an approximate affine fundamental matrix from the rpcs
rpc_matches = rpc_utils.matches_from_rpc(rpc1, rpc2, x, y, w, h, 5)
F = estimation.affine_fundamental_matrix(rpc_matches)
# sift matching method:
method = 'relative' if cfg[
'relative_sift_match_thresh'] is True else 'absolute'
# if less than 10 matches, lower thresh_dog. An alternative would be ASIFT
thresh_dog = 0.0133
for i in range(2):
p1 = image_keypoints(im1, x, y, w, h, thresh_dog=thresh_dog)
p2 = image_keypoints(im2, x2, y2, w2, h2, thresh_dog=thresh_dog)
matches = keypoints_match(p1,
p2,
method,
cfg['sift_match_thresh'],
F,
epipolar_threshold=cfg['max_pointing_error'],
model='fundamental')
if matches is not None and matches.ndim == 2 and matches.shape[0] > 10:
break
thresh_dog /= 2.0
else:
print("WARNING: sift.matches_on_rpc_roi: found no matches.")
return None
return matches
def rectification_homographies(matches, x, y, w, h):
"""
Computes rectifying homographies from point matches for a given ROI.
The affine fundamental matrix F is estimated with the gold-standard
algorithm, then two rectifying similarities (rotation, zoom, translation)
are computed directly from F.
Args:
matches: numpy array of shape (n, 4) containing a list of 2D point
correspondences between the two images.
x, y, w, h: four integers defining the rectangular ROI in the first
image. (x, y) is the top-left corner, and (w, h) are the dimensions
of the rectangle.
Returns:
S1, S2, F: three numpy arrays of shape (3, 3) representing the
two rectifying similarities to be applied to the two images and the
corresponding affine fundamental matrix.
"""
# estimate the affine fundamental matrix with the Gold standard algorithm
F = estimation.affine_fundamental_matrix(matches)
# compute rectifying similarities
S1, S2 = estimation.rectifying_similarities_from_affine_fundamental_matrix(
F, cfg['debug'])
if cfg['debug']:
y1 = common.points_apply_homography(S1, matches[:, :2])[:, 1]
y2 = common.points_apply_homography(S2, matches[:, 2:])[:, 1]
err = np.abs(y1 - y2)
print("max, min, mean rectification error on point matches: ", end=' ')
print(np.max(err), np.min(err), np.mean(err))
# pull back top-left corner of the ROI to the origin (plus margin)
pts = common.points_apply_homography(
S1, [[x, y], [x + w, y], [x + w, y + h], [x, y + h]])
x0, y0 = common.bounding_box2D(pts)[:2]
T = common.matrix_translation(-x0, -y0)
return np.dot(T, S1), np.dot(T, S2), F