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 rpc_model.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)
# 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,
extra_params='--thresh-dog %f' % thresh_dog)
p2 = image_keypoints(im2,
x2,
y2,
w2,
h2,
extra_params='--thresh-dog %f' % thresh_dog)
matches = keypoints_match(p1,
p2,
'relative',
cfg['sift_match_thresh'],
F,
model='fundamental',
epipolar_threshold=cfg['max_pointing_error'])
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 evaluation_from_estimated_F(im1,
im2,
rpc1,
rpc2,
x,
y,
w,
h,
A=None,
matches=None):
"""
Measures the pointing error on a Pleiades' pair of images, affine approx.
Args:
im1, im2: paths to the two Pleiades images (usually jp2 or tif)
rpc1, rpc2: two instances of the rpc_model.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.
A (optional): 3x3 numpy array containing the pointing error correction
for im2.
matches (optional): Nx4 numpy array containing a list of matches to use
to compute the pointing error
Returns:
the mean pointing error, in the direction orthogonal to the epipolar
lines. This error is measured in pixels, and computed from an
approximated fundamental matrix.
"""
if not matches:
matches = sift.matches_on_rpc_roi(im1, im2, rpc1, rpc2, x, y, w, h)
p1 = matches[:, 0:2]
p2 = matches[:, 2:4]
print('%d sift matches' % len(matches))
# apply pointing correction matrix, if available
if A is not None:
p2 = common.points_apply_homography(A, p2)
# estimate the fundamental matrix between the two views
rpc_matches = rpc_utils.matches_from_rpc(rpc1, rpc2, x, y, w, h, 5)
F = estimation.affine_fundamental_matrix(rpc_matches)
# compute the mean displacement from epipolar lines
d_sum = 0
for i in range(len(p1)):
x = np.array([p1[i, 0], p1[i, 1], 1])
xx = np.array([p2[i, 0], p2[i, 1], 1])
ll = F.dot(x)
#d = np.sign(xx.dot(ll)) * evaluation.distance_point_to_line(xx, ll)
d = evaluation.distance_point_to_line(xx, ll)
d_sum += d
return d_sum / len(p1)
def plot_pointing_error_tile(im1, im2, rpc1, rpc2, x, y, w, h,
matches_sift=None, f=100, out_files_pattern=None):
"""
Args:
im1, im2: path to full images
rpc1, rcp2: path to associated rpc xml files
x, y, w, h: four integers defining the rectangular tile in the reference
image. (x, y) is the top-left corner, and (w, h) are the dimensions
of the tile.
f (optional, default is 100): exageration factor for the error vectors
out_files_pattern (optional, default is None): pattern used to name the
two output files (plots of the pointing error)
Returns:
nothing, but opens a display
"""
# read rpcs
r1 = rpc_model.RPCModel(rpc1)
r2 = rpc_model.RPCModel(rpc2)
# compute sift matches
if not matches_sift:
matches_sift = sift.matches_on_rpc_roi(im1, im2, r1, r2, x, y, w, h)
# compute rpc matches
matches_rpc = rpc_utils.matches_from_rpc(r1, r2, x, y, w, h, 5)
# estimate affine fundamental matrix
F = estimation.affine_fundamental_matrix(matches_rpc)
# compute error vectors
e = s2plib.pointing_accuracy.error_vectors(matches_sift, F, 'ref')
A = s2plib.pointing_accuracy.local_translation(r1,r2, x,y,w,h, matches_sift)
p = matches_sift[:, 0:2]
q = matches_sift[:, 2:4]
qq = common.points_apply_homography(A, q)
ee = s2plib.pointing_accuracy.error_vectors(np.hstack((p, qq)), F, 'ref')
print(s2plib.pointing_accuracy.evaluation_from_estimated_F(im1, im2,
r1, r2, x, y, w, h, None, matches_sift))
print(s2plib.pointing_accuracy.evaluation_from_estimated_F(im1, im2,
r1, r2, x, y, w, h, A, matches_sift))
# plot the vectors: they go from the point x to the line (F.T)x'
plot_vectors(p, -e, x, y, w, h, f, out_file='%s_before.png' % out_files_pattern)
plot_vectors(p, -ee, x, y, w, h, f, out_file='%s_after.png' % out_files_pattern)
def plot_pointing_error_tile(im1, im2, rpc1, rpc2, x, y, w, h,
matches_sift=None, f=100, out_files_pattern=None):
"""
Args:
im1, im2: path to full images
rpc1, rcp2: path to associated rpc xml files
x, y, w, h: four integers defining the rectangular tile in the reference
image. (x, y) is the top-left corner, and (w, h) are the dimensions
of the tile.
f (optional, default is 100): exageration factor for the error vectors
out_files_pattern (optional, default is None): pattern used to name the
two output files (plots of the pointing error)
Returns:
nothing, but opens a display
"""
# read rpcs
r1 = rpc_model.RPCModel(rpc1)
r2 = rpc_model.RPCModel(rpc2)
# compute sift matches
if not matches_sift:
matches_sift = sift.matches_on_rpc_roi(im1, im2, r1, r2, x, y, w, h)
# compute rpc matches
matches_rpc = rpc_utils.matches_from_rpc(r1, r2, x, y, w, h, 5)
# estimate affine fundamental matrix
F = estimation.affine_fundamental_matrix(matches_rpc)
# compute error vectors
e = s2plib.pointing_accuracy.error_vectors(matches_sift, F, 'ref')
A = s2plib.pointing_accuracy.local_translation(r1,r2, x,y,w,h, matches_sift)
p = matches_sift[:, 0:2]
q = matches_sift[:, 2:4]
qq = common.points_apply_homography(A, q)
ee = s2plib.pointing_accuracy.error_vectors(np.hstack((p, qq)), F, 'ref')
print(s2plib.pointing_accuracy.evaluation_from_estimated_F(im1, im2,
r1, r2, x, y, w, h, None, matches_sift))
print(s2plib.pointing_accuracy.evaluation_from_estimated_F(im1, im2,
r1, r2, x, y, w, h, A, matches_sift))
# plot the vectors: they go from the point x to the line (F.T)x'
plot_vectors(p, -e, x, y, w, h, f, out_file='%s_before.png' % out_files_pattern)
plot_vectors(p, -ee, x, y, w, h, f, out_file='%s_after.png' % out_files_pattern)
def cost_function_linear(v, rpc1, rpc2, matches):
"""
Objective function to minimize in order to correct the pointing error.
Arguments:
v: vector of size 4, containing the 4 parameters of the euclidean
transformation we are looking for.
rpc1, rpc2: two instances of the rpc_model.RPCModel class
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 the one of the big images.
alpha: relative weight of the error terms: e + alpha*(h-h0)^2. See
paper for more explanations.
Returns:
The sum of pointing errors and altitude differences, as written in the
paper formula (1).
"""
print_params(v)
# verify that parameters are in the bounding box
if (np.abs(v[0]) > 200 * np.pi or np.abs(v[1]) > 10000
or np.abs(v[2]) > 10000 or np.abs(v[3]) > 20000):
print('warning: cost_function is going too far')
print(v)
x, y, w, h = common.bounding_box2D(matches[:, 0:2])
matches_rpc = rpc_utils.matches_from_rpc(rpc1, rpc2, x, y, w, h, 5)
F = estimation.fundamental_matrix(matches_rpc)
# transform the coordinates of points in the second image according to
# matrix A, built from vector v
A = euclidean_transform_matrix(v)
p2 = common.points_apply_homography(A, matches[:, 2:4])
return evaluation.fundamental_matrix_L1(F, np.hstack([matches[:, 0:2],
p2]))
def rectify_pair(im1,
im2,
rpc1,
rpc2,
x,
y,
w,
h,
out1,
out2,
A=None,
sift_matches=None,
method='rpc',
hmargin=0,
vmargin=0):
"""
Rectify a ROI in a pair of images.
Args:
im1, im2: paths to two image files
rpc1, rpc2: paths to the two xml files containing RPC data
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.
out1, out2: paths to the output rectified crops
A (optional): 3x3 numpy array containing the pointing error correction
for im2. This matrix is usually estimated with the pointing_accuracy
module.
sift_matches (optional): Nx4 numpy array containing a list of sift
matches, in the full image coordinates frame
method (default: 'rpc'): option to decide wether to use rpc of sift
matches for the fundamental matrix estimation.
{h,v}margin (optional): horizontal and vertical margins added on the
sides of the rectified images
Returns:
H1, H2: Two 3x3 matrices representing the rectifying homographies that
have been applied to the two original (large) images.
disp_min, disp_max: horizontal disparity range
"""
# read RPC data
rpc1 = rpc_model.RPCModel(rpc1)
rpc2 = rpc_model.RPCModel(rpc2)
# compute real or virtual matches
if method == 'rpc':
# find virtual matches from RPC camera models
matches = rpc_utils.matches_from_rpc(rpc1, rpc2, x, y, w, h,
cfg['n_gcp_per_axis'])
# correct second image coordinates with the pointing correction matrix
if A is not None:
matches[:, 2:] = common.points_apply_homography(
np.linalg.inv(A), matches[:, 2:])
else:
matches = sift_matches
# compute rectifying homographies
H1, H2, F = rectification_homographies(matches, x, y, w, h, hmargin,
vmargin)
if cfg['register_with_shear']:
# compose H2 with a horizontal shear to reduce the disparity range
a = np.mean(rpc_utils.altitude_range(rpc1, x, y, w, h))
lon, lat, alt = rpc_utils.ground_control_points(
rpc1, x, y, w, h, a, a, 4)
x1, y1 = rpc1.inverse_estimate(lon, lat, alt)[:2]
x2, y2 = rpc2.inverse_estimate(lon, lat, alt)[:2]
m = np.vstack([x1, y1, x2, y2]).T
m = np.vstack({tuple(row)
for row in m}) # remove duplicates due to no alt range
H2 = register_horizontally_shear(m, H1, H2)
# compose H2 with a horizontal translation to center disp range around 0
if sift_matches is not None:
sift_matches = filter_matches_epipolar_constraint(
F, sift_matches, cfg['epipolar_thresh'])
if len(sift_matches) < 10:
print('WARNING: no registration with less than 10 matches')
else:
H2 = register_horizontally_translation(sift_matches, H1, H2)
# compute disparity range
if cfg['debug']:
out_dir = os.path.dirname(out1)
np.savetxt(os.path.join(out_dir, 'sift_matches_disp.txt'),
sift_matches,
fmt='%9.3f')
visualisation.plot_matches(
im1, im2, rpc1, rpc2, sift_matches, x, y, w, h,
os.path.join(out_dir, 'sift_matches_disp.png'))
disp_m, disp_M = disparity_range(rpc1, rpc2, x, y, w, h, H1, H2,
sift_matches, A)
# compute rectifying homographies for non-epipolar mode (rectify the secondary tile only)
if block_matching.rectify_secondary_tile_only(cfg['matching_algorithm']):
H1_inv = np.linalg.inv(H1)
H1 = np.eye(
3
) # H1 is replaced by 2-D array with ones on the diagonal and zeros elsewhere
H2 = np.dot(H1_inv, H2)
T = common.matrix_translation(-x + hmargin, -y + vmargin)
H1 = np.dot(T, H1)
H2 = np.dot(T, H2)
# compute output images size
roi = [[x, y], [x + w, y], [x + w, y + h], [x, y + h]]
pts1 = common.points_apply_homography(H1, roi)
x0, y0, w0, h0 = common.bounding_box2D(pts1)
# check that the first homography maps the ROI in the positive quadrant
np.testing.assert_allclose(np.round([x0, y0]), [hmargin, vmargin],
atol=.01)
# apply homographies and do the crops
common.image_apply_homography(out1, im1, H1, w0 + 2 * hmargin,
h0 + 2 * vmargin)
common.image_apply_homography(out2, im2, H2, w0 + 2 * hmargin,
h0 + 2 * vmargin)
if block_matching.rectify_secondary_tile_only(cfg['matching_algorithm']):
pts_in = [[0, 0], [disp_m, 0], [disp_M, 0]]
pts_out = common.points_apply_homography(H1_inv, pts_in)
disp_m = pts_out[1, :] - pts_out[0, :]
disp_M = pts_out[2, :] - pts_out[0, :]
return H1, H2, disp_m, disp_M
def rectify_pair(im1, im2, rpc1, rpc2, x, y, w, h, out1, out2, A=None,
sift_matches=None, method='rpc', hmargin=0, vmargin=0):
"""
Rectify a ROI in a pair of images.
Args:
im1, im2: paths to two image files
rpc1, rpc2: paths to the two xml files containing RPC data
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.
out1, out2: paths to the output rectified crops
A (optional): 3x3 numpy array containing the pointing error correction
for im2. This matrix is usually estimated with the pointing_accuracy
module.
sift_matches (optional): Nx4 numpy array containing a list of sift
matches, in the full image coordinates frame
method (default: 'rpc'): option to decide wether to use rpc of sift
matches for the fundamental matrix estimation.
{h,v}margin (optional): horizontal and vertical margins added on the
sides of the rectified images
This function uses the parameter subsampling_factor from the
config module. If the factor z > 1 then the output images will
be subsampled by a factor z. The output matrices H1, H2, and the
ranges are also updated accordingly:
Hi = Z * Hi with Z = diag(1/z, 1/z, 1) and
disp_min = disp_min / z (resp _max)
Returns:
H1, H2: Two 3x3 matrices representing the rectifying homographies that
have been applied to the two original (large) images.
disp_min, disp_max: horizontal disparity range
"""
# read RPC data
rpc1 = rpc_model.RPCModel(rpc1)
rpc2 = rpc_model.RPCModel(rpc2)
# compute real or virtual matches
if method == 'rpc':
# find virtual matches from RPC camera models
matches = rpc_utils.matches_from_rpc(rpc1, rpc2, x, y, w, h,
cfg['n_gcp_per_axis'])
# correct second image coordinates with the pointing correction matrix
if A is not None:
matches[:, 2:] = common.points_apply_homography(np.linalg.inv(A),
matches[:, 2:])
else:
matches = sift_matches
# compute rectifying homographies
H1, H2, F = rectification_homographies(matches, x, y, w, h, hmargin, vmargin)
if cfg['register_with_shear']:
# compose H2 with a horizontal shear to reduce the disparity range
a = np.mean(rpc_utils.altitude_range(rpc1, x, y, w, h))
lon, lat, alt = rpc_utils.ground_control_points(rpc1, x, y, w, h, a, a, 4)
x1, y1 = rpc1.inverse_estimate(lon, lat, alt)[:2]
x2, y2 = rpc2.inverse_estimate(lon, lat, alt)[:2]
m = np.vstack([x1, y1, x2, y2]).T
m = np.vstack({tuple(row) for row in m}) # remove duplicates due to no alt range
H2 = register_horizontally_shear(m, H1, H2)
# compose H2 with a horizontal translation to center disp range around 0
if sift_matches is not None:
sift_matches = filter_matches_epipolar_constraint(F, sift_matches,
cfg['epipolar_thresh'])
if len(sift_matches) < 10:
print('WARNING: no registration with less than 10 matches')
else:
H2 = register_horizontally_translation(sift_matches, H1, H2)
# compute disparity range
if cfg['debug']:
out_dir = os.path.dirname(out1)
np.savetxt(os.path.join(out_dir, 'sift_matches_disp.txt'),
sift_matches, fmt='%9.3f')
visualisation.plot_matches(im1, im2, rpc1, rpc2, sift_matches, x, y, w, h,
os.path.join(out_dir, 'sift_matches_disp.png'))
disp_m, disp_M = disparity_range(rpc1, rpc2, x, y, w, h, H1, H2,
sift_matches, A)
# impose a minimal disparity range (TODO this is valid only with the
# 'center' flag for register_horizontally_translation)
disp_m = min(-3, disp_m)
disp_M = max(3, disp_M)
# compute rectifying homographies for non-epipolar mode (rectify the secondary tile only)
if block_matching.rectify_secondary_tile_only(cfg['matching_algorithm']):
H1_inv = np.linalg.inv(H1)
H1 = np.eye(3) # H1 is replaced by 2-D array with ones on the diagonal and zeros elsewhere
H2 = np.dot(H1_inv,H2)
T = common.matrix_translation(-x + hmargin, -y + vmargin)
H1 = np.dot(T, H1)
H2 = np.dot(T, H2)
# if subsampling_factor'] the homographies are altered to reflect the zoom
z = cfg['subsampling_factor']
if z != 1:
Z = np.diag((1/z, 1/z, 1))
H1 = np.dot(Z, H1)
H2 = np.dot(Z, H2)
disp_m = np.floor(disp_m / z)
disp_M = np.ceil(disp_M / z)
hmargin = int(np.floor(hmargin / z))
vmargin = int(np.floor(vmargin / z))
# compute output images size
roi = [[x, y], [x+w, y], [x+w, y+h], [x, y+h]]
pts1 = common.points_apply_homography(H1, roi)
x0, y0, w0, h0 = common.bounding_box2D(pts1)
# check that the first homography maps the ROI in the positive quadrant
np.testing.assert_allclose(np.round([x0, y0]), [hmargin, vmargin], atol=.01)
# apply homographies and do the crops
common.image_apply_homography(out1, im1, H1, w0 + 2*hmargin, h0 + 2*vmargin)
common.image_apply_homography(out2, im2, H2, w0 + 2*hmargin, h0 + 2*vmargin)
if cfg['disp_min'] is not None: disp_m = cfg['disp_min']
if cfg['disp_max'] is not None: disp_M = cfg['disp_max']
if block_matching.rectify_secondary_tile_only(cfg['matching_algorithm']):
pts_in = [[0, 0], [disp_m, 0], [disp_M, 0]]
pts_out = common.points_apply_homography(H1_inv,
pts_in)
disp_m = pts_out[1,:] - pts_out[0,:]
disp_M = pts_out[2,:] - pts_out[0,:]
return H1, H2, disp_m, disp_M
def local_translation_rectified(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)
# Apply rectification on image 1
S1p1 = common.points_apply_homography(S1, m[:,0:2])
S1p1 = np.column_stack((S1p1,np.ones((N,1))))
print("Points 1 rectied")
print(S1p1[:10])
# Apply rectification on image 2
S2p2 = common.points_apply_homography(S1, m[:,2:4])
S2p2 = np.column_stack((S2p2, np.ones((N,1))))
print("Points 2 rectied")
print(S2p2[:10])
# Compute F in the rectified space
rect_matches = np.column_stack((S1p1[:,0:2], S2p2[:, 0:2]))
F_rect2 = estimation.affine_fundamental_matrix(rect_matches)
# Compute epipolar lines
FS1p1 = np.dot(F_rect2, S1p1.T).T
print(FS1p1[:10])
# Normalize epipolar lines
c1 = -FS1p1[:, 1]
FS1p1_norm = FS1p1/c1[:, np.newaxis]
print(FS1p1_norm[:10])
b_ = np.abs(S2p2[:, 1] - S1p1[:, 1])
t_med = np.median(b_)
print(t_med)
t_med2 = np.sort(b_)[int(N/2)]
print("t_med2", t_med2)
# Compute epipolar lines witout recitifcation
p1 = np.column_stack((m[:,0:2],np.ones((N,1))))
Fp1 = np.dot(F, p1.T).T
# Compute normal vector to epipolar liness
ab = np.array([Fp1[0][0], Fp1[0][1]])
ab = ab/np.linalg.norm(ab)
tx = t_med*ab[0]
ty = t_med*ab[1]
print(tx, ty)
# Get translation in not rectified image
T = common.matrix_translation(0, -t_med)
T = np.linalg.inv(S2).dot(T).dot(S2)
# T = np.dot(S2_inv, T)
print(T)
# 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, F
def local_translation_rotation(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 rectification homographies
# S1, S2 = estimation.rectifying_similarities_from_affine_fundamental_matrix(F, cfg['debug'])
hmargin = cfg['horizontal_margin']
vmargin = cfg['vertical_margin']
S1, S2, F_rect = rectification.rectification_homographies(rpc_matches, x, y, w, h, hmargin, vmargin)
N = len(m)
# Apply rectification on image 1
S1p1 = common.points_apply_homography(S1, m[:,0:2])
S1p1 = np.column_stack((S1p1,np.ones((N,1))))
print("Points 1 rectied")
print(S1p1[:10])
# Apply rectification on image 2
S2p2 = common.points_apply_homography(S1, m[:,2:4])
S2p2 = np.column_stack((S2p2, np.ones((N,1))))
print("Points 2 rectied")
print(S2p2[:10])
# Compute F in the rectified space
rect_matches = np.column_stack((S1p1[:,0:2], S2p2[:, 0:2]))
F_rect2 = estimation.affine_fundamental_matrix(rect_matches)
# Compute epipolar lines
FS1p1 = np.dot(F_rect2, S1p1.T).T
print(FS1p1[:10])
# Normalize epipolar lines
c1 = -FS1p1[:, 1]
FS1p1_norm = FS1p1/c1[:, np.newaxis]
print(FS1p1_norm[:10])
# Variable of optimization problem
A_ = np.ones((N,1))
# A_ = np.column_stack((S2p2[:,0].reshape(N, 1),np.ones((N,1))))
# b_ = S2p2[:, 1] - FS1p1_norm[:, 2]
b_ = S2p2[:, 1] - S1p1[:, 1]
t_med = np.median(b_)
print(t_med)
t_med2 = np.sort(b_)[int(N/2)]
print("t_med2", t_med2)
# min ||Ax + b||^2 => x = - (A^T A )^-1 A^T b
# X_ = - np.dot(np.linalg.inv(np.dot(A_.T, A_)), np.dot(A_.T, b_))
# [theta, t] = X_
# print(t, theta)
# t = X_[0]
# Compute epipolar lines witout recitifcation
p1 = np.column_stack((m[:,0:2],np.ones((N,1))))
Fp1 = np.dot(F, p1.T).T
# Compute normal vector to epipolar liness
ab = np.array([Fp1[0][0], Fp1[0][1]])
ab = ab/np.linalg.norm(ab)
tx = t_med*ab[0]
ty = t_med*ab[1]
print(tx, ty)
# Get translation in not rectified image
T = common.matrix_translation(0, -t_med)
T = np.linalg.inv(S2).dot(T).dot(S2)
# T = np.dot(S2_inv, T)
print(T)
theta = 0
cos_theta = np.cos(theta)
sin_theta = np.sin(theta)
A = np.array([[cos_theta, -sin_theta, tx],
[sin_theta, cos_theta, ty],
[0, 0, 1]])
return A, F
def local_transformation(r1, r2, x, y, w, h, m,
pointing_error_correction_method='analytic', apply_rectification=True):
"""
Estimates the optimal rotation following a 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 rotation composed with 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)
args_opti = (F, m, apply_rectification)
# Solve the resulting optimization problem
from scipy.optimize import fmin_l_bfgs_b
number_variables = pointing_error_correction_method
if (not apply_rectification):
number_variables += 1
v0 = np.zeros(number_variables)
v, min_val, debug = fmin_l_bfgs_b(
cost_function,
v0,
args=args_opti,
approx_grad=True,
factr=1,
#bounds=[(-150, 150), (-100, 100), (-100, 100)])
#maxiter=50,
callback=print_params)
#iprint=0,
#disp=0)
# compute epipolar lines
p1 = np.column_stack((m[:,0:2],np.ones((len(m),1))))
Fp1 = np.dot(F, np.transpose(p1)).T
if (apply_rectification):
# Compute normal vector to epipolar liness
ab = np.array([Fp1[0][0], Fp1[0][1]])
ab = ab/np.linalg.norm(ab)
# Compute translation
t = v[0]
tx = t*ab[0]
ty = t*ab[1]
# theta
if (pointing_error_correction_method > 1):
theta = v[1]
theta /= 10
else:
theta = 0
else:
ab = []
tx = v[0]
ty = v[1]
# theta
if (pointing_error_correction_method > 1):
theta = v[2]
theta /= 10
else:
theta = 0
print('tx: %f' % tx)
print('ty: %f' % ty)
print('theta: %f' % theta)
if (len(v) > 3):
print('cx: %f' % v[3])
print('cy: %f' % v[4])
print('min cost: %f' % min_val)
print(debug)
A = rigid_transform_matrix(v, ab)
print('A:', A)
return A, F
def rectify_pair(im1,
im2,
rpc1,
rpc2,
x,
y,
w,
h,
out1,
out2,
A=None,
sift_matches=None,
method='rpc',
hmargin=0,
vmargin=0):
"""
Rectify a ROI in a pair of images.
Args:
im1, im2: paths to two image files
rpc1, rpc2: paths to the two xml files containing RPC data
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.
out1, out2: paths to the output rectified crops
A (optional): 3x3 numpy array containing the pointing error correction
for im2. This matrix is usually estimated with the pointing_accuracy
module.
sift_matches (optional): Nx4 numpy array containing a list of sift
matches, in the full image coordinates frame
method (default: 'rpc'): option to decide wether to use rpc of sift
matches for the fundamental matrix estimation.
{h,v}margin (optional): horizontal and vertical margins added on the
sides of the rectified images
This function uses the parameter subsampling_factor from the
config module. If the factor z > 1 then the output images will
be subsampled by a factor z. The output matrices H1, H2, and the
ranges are also updated accordingly:
Hi = Z * Hi with Z = diag(1/z, 1/z, 1) and
disp_min = disp_min / z (resp _max)
Returns:
H1, H2: Two 3x3 matrices representing the rectifying homographies that
have been applied to the two original (large) images.
disp_min, disp_max: horizontal disparity range
"""
# read RPC data
rpc1 = rpc_model.RPCModel(rpc1)
rpc2 = rpc_model.RPCModel(rpc2)
# compute real or virtual matches
if method == 'rpc':
# find virtual matches from RPC camera models
matches = rpc_utils.matches_from_rpc(rpc1, rpc2, x, y, w, h,
cfg['n_gcp_per_axis'])
# correct second image coordinates with the pointing correction matrix
if A is not None:
matches[:, 2:] = common.points_apply_homography(
np.linalg.inv(A), matches[:, 2:])
else:
matches = sift_matches
# compute rectifying homographies
H1, H2, F = rectification_homographies(matches, x, y, w, h, hmargin,
vmargin)
if cfg['register_with_shear']:
# compose H2 with a horizontal shear to reduce the disparity range
a = np.mean(rpc_utils.altitude_range(rpc1, x, y, w, h))
lon, lat, alt = rpc_utils.ground_control_points(
rpc1, x, y, w, h, a, a, 4)
x1, y1 = rpc1.inverse_estimate(lon, lat, alt)[:2]
x2, y2 = rpc2.inverse_estimate(lon, lat, alt)[:2]
m = np.vstack([x1, y1, x2, y2]).T
m = np.vstack({tuple(row)
for row in m}) # remove duplicates due to no alt range
H2 = register_horizontally_shear(m, H1, H2)
# compose H2 with a horizontal translation to center disp range around 0
if sift_matches is not None:
sift_matches = filter_matches_epipolar_constraint(
F, sift_matches, cfg['epipolar_thresh'])
if len(sift_matches) < 10:
print('WARNING: no registration with less than 10 matches')
else:
H2 = register_horizontally_translation(sift_matches, H1, H2)
# compute disparity range
if cfg['debug']:
out_dir = os.path.dirname(out1)
np.savetxt(os.path.join(out_dir, 'sift_matches_disp.txt'),
sift_matches,
fmt='%9.3f')
visualisation.plot_matches(
im1, im2, rpc1, rpc2, sift_matches, x, y, w, h,
os.path.join(out_dir, 'sift_matches_disp.png'))
disp_m, disp_M = disparity_range(rpc1, rpc2, x, y, w, h, H1, H2,
sift_matches, A)
# impose a minimal disparity range (TODO this is valid only with the
# 'center' flag for register_horizontally_translation)
disp_m = min(-3, disp_m)
disp_M = max(3, disp_M)
# if subsampling_factor'] the homographies are altered to reflect the zoom
z = cfg['subsampling_factor']
if z != 1:
Z = np.diag((1 / z, 1 / z, 1))
H1 = np.dot(Z, H1)
H2 = np.dot(Z, H2)
disp_m = np.floor(disp_m / z)
disp_M = np.ceil(disp_M / z)
hmargin = int(np.floor(hmargin / z))
vmargin = int(np.floor(vmargin / z))
# compute output images size
roi = [[x, y], [x + w, y], [x + w, y + h], [x, y + h]]
pts1 = common.points_apply_homography(H1, roi)
x0, y0, w0, h0 = common.bounding_box2D(pts1)
# check that the first homography maps the ROI in the positive quadrant
np.testing.assert_allclose(np.round([x0, y0]), [hmargin, vmargin],
atol=.01)
# apply homographies and do the crops
common.image_apply_homography(out1, im1, H1, w0 + 2 * hmargin,
h0 + 2 * vmargin)
common.image_apply_homography(out2, im2, H2, w0 + 2 * hmargin,
h0 + 2 * vmargin)
return H1, H2, disp_m, disp_M
