def compute_rectification_homographies_sift(im1, im2, rpc1, rpc2, x, y, w, h):
"""
Computes rectifying homographies for a ROI in a pair of Pleiades images.
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 definig the rectangular ROI in the first
image. (x, y) is the top-left corner, and (w, h) are the dimensions
of the rectangle.
Returns:
H1, H2: Two 3x3 matrices representing the rectifying homographies to be
applied to the two images.
disp_min, disp_max: horizontal disparity range, computed on a set of
sift matches
"""
# in brief: use ransac to estimate F from a set of sift matches, then use
# loop-zhang to estimate rectifying homographies.
matches = sift.matches_on_rpc_roi(im1, im2, rpc1, rpc2, x, y, w, h)
p1 = matches[:, 0:2]
p2 = matches[:, 2:4]
# the matching points are translated to be centered in 0, in order to deal
# with coordinates ranging from -1000 to 1000, and decrease imprecision
# effects of the loop-zhang rectification. These effects may become very
# important (~ 10 pixels error) when using coordinates around 20000.
pp1, T1 = center_2d_points(p1)
pp2, T2 = center_2d_points(p2)
F = estimation.fundamental_matrix_ransac(np.hstack([pp1, pp2]))
H1, H2 = estimation.loop_zhang(F, w, h)
# compose with previous translations to get H1, H2 in the big images frame
H1 = np.dot(H1, T1)
H2 = np.dot(H2, T2)
# for debug
print "max, min, mean rectification error on sift matches ----------------"
tmp = common.points_apply_homography(H1, p1)
y1 = tmp[:, 1]
tmp = common.points_apply_homography(H2, p2)
y2 = tmp[:, 1]
err = np.abs(y1 - y2)
print np.max(err), np.min(err), np.mean(err)
# pull back top-left corner of the ROI in the origin
roi = [[x, y], [x + w, y], [x + w, y + h], [x, y + h]]
pts = common.points_apply_homography(H1, roi)
x0, y0 = common.bounding_box2D(pts)[0:2]
T = common.matrix_translation(-x0, -y0)
H1 = np.dot(T, H1)
H2 = np.dot(T, H2)
# add an horizontal translation to H2 to center the disparity range around
H2 = register_horizontally(matches, H1, H2)
disp_m, disp_M = update_disp_range(matches, H1, H2, w, h)
return H1, H2, disp_m, disp_M
def transfer_map(in_map, H, x, y, w, h, zoom, out_map):
"""
Transfer the heights computed on the rectified grid to the original
Pleiades image grid.
Args:
in_map: path to the input map, usually a height map or a mask, sampled
on the rectified grid
H: path to txt file containing a numpy 3x3 array representing the
rectifying homography
x, y, w, h: four integers defining the rectangular ROI in the original
image. (x, y) is the top-left corner, and (w, h) are the dimensions
of the rectangle.
zoom: zoom factor (usually 1, 2 or 4) used to produce the input height
map
out_map: path to the output map
"""
# write the inverse of the resampling transform matrix. In brief it is:
# homography * translation * zoom
# This matrix transports the coordinates of the original cropped and
# zoomed grid (the one desired for out_height) to the rectified cropped and
# zoomed grid (the one we have for height)
Z = np.diag([zoom, zoom, 1])
A = common.matrix_translation(x, y)
HH = np.dot(np.loadtxt(H), np.dot(A, Z))
# apply the homography
# write the 9 coefficients of the homography to a string, then call synflow
# to produce the flow, then backflow to apply it
# zero:256x256 is the iio way to create a 256x256 image filled with zeros
hij = ' '.join(['%r' % num for num in HH.flatten()])
common.run('synflow hom "%s" zero:%dx%d /dev/null - | BILINEAR=1 backflow - %s %s' % (
hij, w/zoom, h/zoom, in_map, out_map))
def compute_rectification_homographies_sift(im1, im2, rpc1, rpc2, x, y, w, h):
"""
Computes rectifying homographies for a ROI in a pair of Pleiades images.
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 definig the rectangular ROI in the first
image. (x, y) is the top-left corner, and (w, h) are the dimensions
of the rectangle.
Returns:
H1, H2: Two 3x3 matrices representing the rectifying homographies to be
applied to the two images.
disp_min, disp_max: horizontal disparity range, computed on a set of
sift matches
"""
# in brief: use ransac to estimate F from a set of sift matches, then use
# loop-zhang to estimate rectifying homographies.
matches = matches_from_sift_rpc_roi(im1, im2, rpc1, rpc2, x, y, w, h)
p1 = matches[:, 0:2]
p2 = matches[:, 2:4]
# the matching points are translated to be centered in 0, in order to deal
# with coordinates ranging from -1000 to 1000, and decrease imprecision
# effects of the loop-zhang rectification. These effects may become very
# important (~ 10 pixels error) when using coordinates around 20000.
pp1, T1 = center_2d_points(p1)
pp2, T2 = center_2d_points(p2)
F = estimation.fundamental_matrix_ransac(np.hstack([pp1, pp2]))
H1, H2 = estimation.loop_zhang(F, w, h)
# compose with previous translations to get H1, H2 in the big images frame
H1 = np.dot(H1, T1)
H2 = np.dot(H2, T2)
# for debug
print "max, min, mean rectification error on sift matches ----------------"
tmp = common.points_apply_homography(H1, p1)
y1 = tmp[:, 1]
tmp = common.points_apply_homography(H2, p2)
y2 = tmp[:, 1]
err = np.abs(y1 - y2)
print np.max(err), np.min(err), np.mean(err)
# pull back top-left corner of the ROI in the origin
roi = [[x, y], [x+w, y], [x+w, y+h], [x, y+h]]
pts = common.points_apply_homography(H1, roi)
x0, y0 = common.bounding_box2D(pts)[0:2]
T = common.matrix_translation(-x0, -y0)
H1 = np.dot(T, H1)
H2 = np.dot(T, H2)
# add an horizontal translation to H2 to center the disparity range around
H2 = register_horizontally(matches, H1, H2)
disp_m, disp_M = update_disp_range(matches, H1, H2, w, h)
return H1, H2, disp_m, disp_M
def transfer_map(in_map, H, x, y, w, h, zoom, out_map):
"""
Transfer the heights computed on the rectified grid to the original
Pleiades image grid.
Args:
in_map: path to the input map, usually a height map or a mask, sampled
on the rectified grid
H: path to txt file containing a numpy 3x3 array representing the
rectifying homography
x, y, w, h: four integers defining the rectangular ROI in the original
image. (x, y) is the top-left corner, and (w, h) are the dimensions
of the rectangle.
zoom: zoom factor (usually 1, 2 or 4) used to produce the input height
map
out_map: path to the output map
"""
# write the inverse of the resampling transform matrix. In brief it is:
# homography * translation * zoom
# This matrix transports the coordinates of the original cropped and
# zoomed grid (the one desired for out_height) to the rectified cropped and
# zoomed grid (the one we have for height)
Z = np.diag([zoom, zoom, 1])
A = common.matrix_translation(x, y)
HH = np.dot(np.loadtxt(H), np.dot(A, Z))
# apply the homography
# write the 9 coefficients of the homography to a string, then call synflow
# to produce the flow, then backflow to apply it
# zero:256x256 is the iio way to create a 256x256 image filled with zeros
hij = ' '.join(['%r' % num for num in HH.flatten()])
common.run(
'synflow hom "%s" zero:%dx%d /dev/null - | BILINEAR=1 backflow - %s %s'
% (hij, w / zoom, h / zoom, in_map, out_map))
def register_horizontally(matches, H1, H2, do_shear=False, flag='center'):
"""
Adjust rectifying homographies to modify the disparity range.
Args:
matches: list of pairs of 2D points, stored as a Nx4 numpy array
H1, H2: two homographies, stored as numpy 3x3 matrices
do_shear: boolean flag indicating wheter to minimize the shear on im2
or not.
flag: option needed to control how to modify the disparity range:
'center': move the barycenter of disparities of matches to zero
'positive': make all the disparities positive
'negative': make all the disparities negative. Required for
Hirshmuller stereo (java)
Returns:
H2: corrected homography H2
The matches are provided in the original images coordinate system. By
transforming these coordinates with the provided homographies, we obtain
matches whose disparity is only along the x-axis. The second homography H2
is corrected with a horizontal translation to obtain the desired property
on the disparity range.
"""
# transform the matches according to the homographies
p1 = common.points_apply_homography(H1, matches[:, 0:2])
x1 = p1[:, 0]
y1 = p1[:, 1]
p2 = common.points_apply_homography(H2, matches[:, 2:4])
x2 = p2[:, 0]
y2 = p2[:, 1]
# for debug, print the vertical disparities. Should be zero.
print "Residual vertical disparities: max, min, mean. Should be zero ------"
print np.max(y2 - y1), np.min(y2 - y1), np.mean(y2 - y1)
# shear correction
# we search the (s, b) vector that minimises \sum (x1 - (x2+s*y2+b))^2
# it is a least squares minimisation problem
if do_shear:
A = np.vstack((y2, y2*0+1)).T
B = x1 - x2
z = np.linalg.lstsq(A, B)[0]
s = z[0]
b = z[1]
H2 = np.dot(np.array([[1, s, b], [0, 1, 0], [0, 0, 1]]), H2)
x2 = x2 + s*y2 + b
# compute the disparity offset according to selected option
t = 0
if (flag == 'center'):
t = np.mean(x2 - x1)
if (flag == 'positive'):
t = np.min(x2 - x1)
if (flag == 'negative'):
t = np.max(x2 - x1)
# correct H2 with a translation
return np.dot(common.matrix_translation(-t, 0), H2)
def register_horizontally_translation(matches, H1, H2, flag="center"):
"""
Adjust rectifying homographies with a translation to modify the disparity range.
Args:
matches: list of pairs of 2D points, stored as a Nx4 numpy array
H1, H2: two homographies, stored as numpy 3x3 matrices
flag: option needed to control how to modify the disparity range:
'center': move the barycenter of disparities of matches to zero
'positive': make all the disparities positive
'negative': make all the disparities negative. Required for
Hirshmuller stereo (java)
Returns:
H2: corrected homography H2
The matches are provided in the original images coordinate system. By
transforming these coordinates with the provided homographies, we obtain
matches whose disparity is only along the x-axis. The second homography H2
is corrected with a horizontal translation to obtain the desired property
on the disparity range.
"""
# transform the matches according to the homographies
p1 = common.points_apply_homography(H1, matches[:, :2])
x1 = p1[:, 0]
y1 = p1[:, 1]
p2 = common.points_apply_homography(H2, matches[:, 2:])
x2 = p2[:, 0]
y2 = p2[:, 1]
# for debug, print the vertical disparities. Should be zero.
if cfg["debug"]:
print "Residual vertical disparities: max, min, mean. Should be zero"
print np.max(y2 - y1), np.min(y2 - y1), np.mean(y2 - y1)
# compute the disparity offset according to selected option
t = 0
if flag == "center":
t = np.mean(x2 - x1)
if flag == "positive":
t = np.min(x2 - x1)
if flag == "negative":
t = np.max(x2 - x1)
# correct H2 with a translation
return np.dot(common.matrix_translation(-t, 0), H2)
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 definig 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, True)
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: ",
print np.max(err), np.min(err), np.mean(err)
# pull back top-left corner of the ROI to the origin
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
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 definig 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, True)
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: ",
print np.max(err), np.min(err), np.mean(err)
# pull back top-left corner of the ROI to the origin
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
def compute_rectification_homographies(im1,
im2,
rpc1,
rpc2,
x,
y,
w,
h,
A=None,
m=None):
"""
Computes rectifying homographies for a ROI in a pair of Pleiades images.
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 definig 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. This matrix is usually estimated with the pointing_accuracy
module.
m (optional): Nx4 numpy array containing a list of matches.
Returns:
H1, H2: Two 3x3 matrices representing the rectifying homographies to be
applied to the two images.
disp_min, disp_max: horizontal disparity range, computed on a set of
sift matches
"""
# in brief: use 8-pts normalized algo to estimate F, then use loop-zhang to
# estimate rectifying homographies.
print "step 1: find virtual matches, and center them ----------------------"
n = cfg['n_gcp_per_axis']
rpc_matches = rpc_utils.matches_from_rpc(rpc1, rpc2, x, y, w, h, n)
p1 = rpc_matches[:, 0:2]
p2 = rpc_matches[:, 2:4]
if A is not None:
print "applying pointing error correction"
# correct coordinates of points in im2, according to A
p2 = common.points_apply_homography(np.linalg.inv(A), p2)
# the matching points are translated to be centered in 0, in order to deal
# with coordinates ranging from -1000 to 1000, and decrease imprecision
# effects of the loop-zhang rectification. These effects may become very
# important (~ 10 pixels error) when using coordinates around 20000.
pp1, T1 = center_2d_points(p1)
pp2, T2 = center_2d_points(p2)
print "step 2: estimate F (Gold standard algorithm) -----------------------"
F = estimation.affine_fundamental_matrix(np.hstack([pp1, pp2]))
print "step 3: compute rectifying homographies (loop-zhang algorithm) -----"
H1, H2 = estimation.loop_zhang(F, w, h)
S1, S2 = estimation.rectifying_similarities_from_affine_fundamental_matrix(
F, True)
print "F\n", F, "\n"
print "H1\n", H1, "\n"
print "S1\n", S1, "\n"
print "H2\n", H2, "\n"
print "S2\n", S2, "\n"
# compose with previous translations to get H1, H2 in the big images frame
H1 = np.dot(H1, T1)
H2 = np.dot(H2, T2)
# for debug
print "max, min, mean rectification error on rpc matches ------------------"
tmp = common.points_apply_homography(H1, p1)
y1 = tmp[:, 1]
tmp = common.points_apply_homography(H2, p2)
y2 = tmp[:, 1]
err = np.abs(y1 - y2)
print np.max(err), np.min(err), np.mean(err)
print "step 4: pull back top-left corner of the ROI in the origin ---------"
roi = [[x, y], [x + w, y], [x + w, y + h], [x, y + h]]
pts = common.points_apply_homography(H1, roi)
x0, y0 = common.bounding_box2D(pts)[0:2]
T = common.matrix_translation(-x0, -y0)
H1 = np.dot(T, H1)
H2 = np.dot(T, H2)
# add an horizontal translation to H2 to center the disparity range around
# the origin, if sift matches are available
if m is not None:
print "step 5: horizontal registration --------------------------------"
# filter sift matches with the known fundamental matrix
# but first convert F for big images coordinate frame
F = np.dot(T2.T, np.dot(F, T1))
print '%d sift matches before epipolar constraint filering' % len(m)
m = filter_matches_epipolar_constraint(F, m, cfg['epipolar_thresh'])
print '%d sift matches after epipolar constraint filering' % len(m)
if len(m) < 2:
# 0 or 1 sift match
print 'rectification.compute_rectification_homographies: less than'
print '2 sift matches after filtering by the epipolar constraint.'
print 'This may be due to the pointing error, or to strong'
print 'illumination changes between the input images.'
print 'No registration will be performed.'
else:
H2 = register_horizontally(m, H1, H2)
disp_m, disp_M = update_disp_range(m, H1, H2, w, h)
print "SIFT disparity range: [%f,%f]" % (disp_m, disp_M)
# expand disparity range with srtm according to cfg params
print cfg['disp_range_method']
if (cfg['disp_range_method'] == "srtm") or (m is None) or (len(m) < 2):
disp_m, disp_M = rpc_utils.srtm_disp_range_estimation(
rpc1, rpc2, x, y, w, h, H1, H2, A,
cfg['disp_range_srtm_high_margin'],
cfg['disp_range_srtm_low_margin'])
print "SRTM disparity range: [%f,%f]" % (disp_m, disp_M)
if ((cfg['disp_range_method'] == "wider_sift_srtm") and (m is not None)
and (len(m) >= 2)):
d_m, d_M = rpc_utils.srtm_disp_range_estimation(
rpc1, rpc2, x, y, w, h, H1, H2, A,
cfg['disp_range_srtm_high_margin'],
cfg['disp_range_srtm_low_margin'])
print "SRTM disparity range: [%f,%f]" % (d_m, d_M)
disp_m = min(disp_m, d_m)
disp_M = max(disp_M, d_M)
print "Final disparity range: [%s, %s]" % (disp_m, disp_M)
return H1, H2, disp_m, disp_M
def matches_from_projection_matrices_roi(im1, im2, rpc1, rpc2, x, y, w, h):
"""
Computes a list of sift matches between two Pleiades images.
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 definig the rectangular ROI in the first image.
(x, y) is the top-left corner, and (w, h) are the dimensions of the
rectangle.
This function uses the parameter subsampling_factor_registration
from the config module. If factor > 1 then the registration
is performed over subsampled images, but the resulting keypoints
are then scaled back to conceal the subsampling
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 big images.
If no sift matches are found, then an exception is raised.
"""
#m, M = rpc_utils.altitude_range(rpc1, x, y, w, h)
m=5
M=20
# build an array with vertices of the 3D ROI, obtained as {2D ROI} x [m, M]
# also include the midpoints because the 8 corners of the frustum alone don't seem to work
a = np.array([x, x, x, x, x+w, x+w, x+w, x+w,x+w/2,x+w/2,x+w/2,x+w/2,x+w/2,x+w/2,x ,x ,x+w ,x+w ])
b = np.array([y, y, y+h, y+h, y, y, y+h, y+h,y ,y ,y+h/2,y+h/2,y+h ,y+h ,y+h/2,y+h/2,y+h/2,y+h/2])
c = np.array([m, M, m, M, m, M, m, M,m ,M ,m ,M ,m ,M ,m ,M ,m ,M ])
xx = np.zeros(len(a))
yy = np.zeros(len(a))
# corresponding points in im2
P1 = np.loadtxt(rpc1)
P2 = np.loadtxt(rpc2)
M = P1[:,:3]
p4 = P1[:,3]
m3 = M[2,:]
inv_M = np.linalg.inv(M)
v = np.vstack((a,b,c*0+1))
for i in range(len(a)):
v = np.array([a[i],b[i],1])
mu = c[i] / np.sign ( np.linalg.det(M) )
X3D = inv_M.dot (mu * v - p4 )
# backproject
newpoints = P2.dot(np.hstack([X3D,1]))
xx[i] = newpoints[0] / newpoints[2]
yy[i] = newpoints[1] / newpoints[2]
print xx
print yy
matches = np.vstack([a, b,xx,yy]).T
return matches
##### xx, yy = rpc_utils.find_corresponding_point(rpc1, rpc2, a, b, c)[0:2]
# bounding box in im2
x2, y2, w2, h2 = common.bounding_box2D(np.vstack([xx, yy]).T) ## GF NOT USED
x1, y1, w1, h1 = x, y, w, h
x2, y2, w2, h2 = x, y, w, h
# do crops, to apply sift on reasonably sized images
crop1 = common.image_crop_LARGE(im1, x1, y1, w1, h1)
crop2 = common.image_crop_LARGE(im2, x2, y2, w2, h2)
T1 = common.matrix_translation(x1, y1)
T2 = common.matrix_translation(x2, y2)
# call sift matches for the images
matches = matches_from_sift(crop1, crop2)
if matches.size:
# compensate coordinates for the crop and the zoom
pts1 = common.points_apply_homography(T1, matches[:, 0:2])
pts2 = common.points_apply_homography(T2, matches[:, 2:4])
return np.hstack([pts1, pts2])
else:
raise Exception("no sift matches")
def compute_rectification_homographies(im1, im2, rpc1, rpc2, x, y, w, h, A=None):
"""
Computes rectifying homographies for a ROI in a pair of Pleiades images.
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 definig 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. This matrix is usually estimated with the pointing_accuracy
module.
Returns:
H1, H2: Two 3x3 matrices representing the rectifying homographies to be applied
to the two images.
disp_min, disp_max: horizontal disparity range, computed on a set of
sift matches
"""
# in brief: use 8-pts normalized algo to estimate F, then use loop-zhang to
# estimate rectifying homographies.
print "step 1: find matches, and center them ------------------------------"
sift_matches = matches_from_projection_matrices_roi(im1, im2, rpc1, rpc2, x+w/4, y+h/4, w*2/4, h*2/4)
#sift_matches2 = matches_from_sift(im1, im2)
#sift_matches = sift_matches2
# import visualisation
# print visualisation.plot_matches(im1,im2,sift_matches)
p1 = sift_matches[:, 0:2]
p2 = sift_matches[:, 2:4]
# the matching points are translated to be centered in 0, in order to deal
# with coordinates ranging from -1000 to 1000, and decrease imprecision
# effects of the loop-zhang rectification. These effects may become very
# important (~ 10 pixels error) when using coordinates around 20000.
pp1, T1 = center_2d_points(p1)
pp2, T2 = center_2d_points(p2)
print "step 2: estimate F (8-points algorithm) ----------------------------"
F = estimation.fundamental_matrix(np.hstack([pp1, pp2]))
F = np.dot(T2.T, np.dot(F, T1)) # convert F for big images coordinate frame
print "step 3: compute rectifying homographies (loop-zhang algorithm) -----"
H1, H2 = estimation.loop_zhang(F, w, h)
#### ATTENTION: LOOP-ZHANG IMPLICITLY ASSUMES THAT F IS IN THE FINAL (CROPPED)
# IMAGE GEOMETRY. THUS 0,0 IS THE UPPER LEFT CORNER OF THE IMAGE AND W,H ARE
# USED TO ESTIMATE THE DISTORTION WITHIN THE REGION. BY CENTERING THE COORDINATES
# OF THE PIXELS WE ARE CONSTRUCTING A RECTIFICATION DOES NOT TAKE INTO ACCOUNT THE
# CORRECT IMAGE PORTION.
# compose with previous translations to get H1, H2 in the big images frame
#H1 = np.dot(H1, T1)
#H2 = np.dot(H2, T2)
# for debug
print "min, max, mean rectification error on rpc matches ------------------"
tmp = common.points_apply_homography(H1, p1)
y1 = tmp[:, 1]
tmp = common.points_apply_homography(H2, p2)
y2 = tmp[:, 1]
err = np.abs(y1 - y2)
print np.min(err), np.max(err), np.mean(err)
# print "step 4: pull back top-left corner of the ROI in the origin ---------"
roi = [[x, y], [x+w, y], [x+w, y+h], [x, y+h]]
pts = common.points_apply_homography(H1, roi)
x0, y0 = common.bounding_box2D(pts)[0:2]
T = common.matrix_translation(-x0, -y0)
H1 = np.dot(T, H1)
H2 = np.dot(T, H2)
# add an horizontal translation to H2 to center the disparity range around
# the origin, if sift matches are available
print "step 5: horizontal registration ------------------------------------"
sift_matches2 = matches_from_sift(im1, im2)
# filter sift matches with the known fundamental matrix
sift_matches2 = filter_matches_epipolar_constraint(F, sift_matches2,
cfg['epipolar_thresh'])
if not len(sift_matches2):
print """all the sift matches have been discarded by the epipolar
constraint. This is probably due to the pointing error. Try with a
bigger value for epipolar_thresh."""
sys.exit()
H2, disp_m, disp_M = register_horizontally(sift_matches2, H1, H2, do_scale_horizontally=True)
disp_m, disp_M = update_minmax_range_extrapolating_registration_affinity(sift_matches2,
H1, H2, w, h)
return H1, H2, disp_m, disp_M
def register_horizontally(matches, H1, H2, do_shear=True,
do_scale_horizontally=False , flag='center'):
"""
Adjust rectifying homographies to modify the disparity range.
Args:
matches: list of pairs of 2D points, stored as a Nx4 numpy array
H1, H2: two homographies, stored as numpy 3x3 matrices
do_shear: boolean flag indicating wheter to minimize the shear on im2
or not.
do_scale_horizontally: boolean flag indicating wheter to minimize
with respect to the horizontal scaling on im2 or not.
flag: option needed to control how to modify the disparity range:
'center': move the barycenter of disparities of matches to zero
'positive': make all the disparities positive
'negative': make all the disparities negative. Required for
Hirshmuller stereo (java)
Returns:
H2: corrected homography H2
disp_min, disp_max: horizontal disparity range
The matches are provided in the original images coordinate system. By
transforming these coordinates with the provided homographies, we obtain
matches whose disparity is only along the x-axis. The second homography H2
is corrected with a horizontal translation to obtain the desired property
on the disparity range. The minimum and maximal disparities over the set
of matches are extracted, with a security margin of 20 percent.
"""
# transform the matches according to the homographies
pt1 = common.points_apply_homography(H1, matches[:, 0:2])
x1 = pt1[:, 0]
y1 = pt1[:, 1]
pt2 = common.points_apply_homography(H2, matches[:, 2:4])
x2 = pt2[:, 0]
y2 = pt2[:, 1]
# shear correction
# we search the (s, b) vector that minimises \sum (x1 - (x2+s*y2+b))^2
# it is a least squares minimisation problem
if do_shear:
# horizontal scale correction
if do_scale_horizontally: # | x1 - (s*x2 + t*y2 +d) |^2
A = np.vstack((x2, y2, y2*0+1)).T
b = x1
z = np.linalg.lstsq(A, b)[0]
s = z[0]
t = z[1]
d = z[2]
H2 = np.dot(np.array([[s, t, d], [0, 1, 0], [0, 0, 1]]), H2)
x2 = s*x2 + t*y2 + d
else:
A = np.vstack((y2, y2*0+1)).T
b = x1 - x2
z = np.linalg.lstsq(A, b)[0]
s = z[0]
b = z[1]
H2 = np.dot(np.array([[1, s, b], [0, 1, 0], [0, 0, 1]]), H2)
x2 = x2 + s*y2 + b
# compute the disparity offset according to selected option
if (flag == 'center'):
t = np.mean(x2 - x1)
if (flag == 'positive'):
t = np.min(x2 - x1)
if (flag == 'negative'):
t = np.max(x2 - x1)
if (flag == 'none'):
t = 0
# correct H2 with a translation
H2 = np.dot(common.matrix_translation(-t, 0), H2)
x2 = x2 - t
# extract min and max disparities
dispx_min = np.floor((np.min(x2 - x1)))
dispx_max = np.ceil((np.max(x2 - x1)))
# add a security margin to the disp range
d = cfg['disp_range_extra_margin']
if (dispx_min < 0):
dispx_min = (1+d) * dispx_min
else:
dispx_min = (1-d) * dispx_min
if (dispx_max > 0):
dispx_max = (1+d) * dispx_max
else:
dispx_max = (1-d) * dispx_max
# for debug, print the vertical disparities. Should be zero.
print "Residual vertical disparities: min, max, mean. Should be zero ------"
print np.min(y2 - y1), np.max(y2 - y1), np.mean(y1 - y2)
return H2, dispx_min, dispx_max
def crop_and_apply_homography(im_out, im_in, H, w, h, subsampling_factor=1,
convert_to_gray=False):
"""
Warps a piece of a Pleiades (panchro or ms) image with a homography.
Args:
im_out: path to the output image
im_in: path to the input (tif) full Pleiades image
H: numpy array containing the 3x3 homography matrix
w, h: size of the output image
subsampling_factor (optional, default=1): when set to z>1,
will result in the application of the homography Z*H where Z =
diag(1/z, 1/z, 1), so the output will be zoomed out by a factor z.
The output image will be (w/z, h/z)
convert_to_gray (optional, default False): it set to True, and if the
input image has 4 channels, it is converted to gray before applying
zoom and homographies.
Returns:
nothing
The homography has to be used as: coord_out = H coord_in. The produced
output image corresponds to coord_out in [0, w] x [0, h]. The warp is made
by Pascal Monasse's binary named 'homography'.
"""
# crop a piece of the big input image, to which the homography will be
# applied
# warning: as the crop uses integer coordinates, be careful to round off
# (x0, y0) before modifying the homograpy. You want the crop and the
# translation representing it do exactly the same thing.
pts = [[0, 0], [w, 0], [w, h], [0, h]]
inv_H_pts = common.points_apply_homography(np.linalg.inv(H), pts)
x0, y0, w0, h0 = common.bounding_box2D(inv_H_pts)
x0, y0 = np.floor([x0, y0])
w0, h0 = np.ceil([w0, h0])
crop_fullres = common.image_crop_LARGE(im_in, x0, y0, w0, h0)
# This filter is needed (for panchro images) because the original PLEAIDES
# SENSOR PERFECT images are aliased
if (common.image_pix_dim(crop_fullres) == 1 and subsampling_factor == 1 and
cfg['use_pleiades_unsharpening']):
tmp = image_apply_pleiades_unsharpening_filter(crop_fullres)
common.run('rm -f %s' % crop_fullres)
crop_fullres = tmp
# convert to gray
if common.image_pix_dim(crop_fullres) == 4:
if convert_to_gray:
crop_fullres = common.pansharpened_to_panchro(crop_fullres)
# compensate the homography with the translation induced by the preliminary
# crop, then apply the homography and crop.
H = np.dot(H, common.matrix_translation(x0, y0))
# Since the objective is to compute a zoomed out homographic transformation
# of the input image, to save computations we zoom out the image before
# applying the homography. If Z is the matrix representing the zoom out and
# H the homography matrix, this trick consists in applying Z*H*Z^{-1} to
# the zoomed image Z*Im instead of applying Z*H to the original image Im.
if subsampling_factor == 1:
common.image_apply_homography(im_out, crop_fullres, H, w, h)
return
else:
assert(subsampling_factor >= 1)
# H becomes Z*H*Z^{-1}
Z = np.eye(3);
Z[0,0] = Z[1,1] = 1 / float(subsampling_factor)
H = np.dot(Z, H)
H = np.dot(H, np.linalg.inv(Z))
# w, and h are updated accordingly
w = int(w / subsampling_factor)
h = int(h / subsampling_factor)
# the DCT zoom is NOT SAFE when the input image size is not a multiple
# of the zoom factor
tmpw, tmph = common.image_size(crop_fullres)
tmpw, tmph = int(tmpw / subsampling_factor), int(tmph / subsampling_factor)
crop_fullres_safe = common.image_crop_tif(crop_fullres, 0, 0, tmpw *
subsampling_factor, tmph * subsampling_factor)
common.run('rm -f %s' % crop_fullres)
# zoom out the input image (crop_fullres)
crop_zoom_out = common.image_safe_zoom_fft(crop_fullres_safe,
subsampling_factor)
common.run('rm -f %s' % crop_fullres_safe)
# apply the homography to the zoomed out crop
common.image_apply_homography(im_out, crop_zoom_out, H, w, h)
return
def crop_and_apply_homography(im_out,
im_in,
H,
w,
h,
subsampling_factor=1,
convert_to_gray=False):
"""
Warps a piece of a Pleiades (panchro or ms) image with a homography.
Args:
im_out: path to the output image
im_in: path to the input (tif) full Pleiades image
H: numpy array containing the 3x3 homography matrix
w, h: size of the output image
subsampling_factor (optional, default=1): when set to z>1,
will result in the application of the homography Z*H where Z =
diag(1/z, 1/z, 1), so the output will be zoomed out by a factor z.
The output image will be (w/z, h/z)
convert_to_gray (optional, default False): it set to True, and if the
input image has 4 channels, it is converted to gray before applying
zoom and homographies.
Returns:
nothing
The homography has to be used as: coord_out = H coord_in. The produced
output image corresponds to coord_out in [0, w] x [0, h]. The warp is made
by Pascal Monasse's binary named 'homography'.
"""
# crop a piece of the big input image, to which the homography will be
# applied
# warning: as the crop uses integer coordinates, be careful to round off
# (x0, y0) before modifying the homograpy. You want the crop and the
# translation representing it do exactly the same thing.
pts = [[0, 0], [w, 0], [w, h], [0, h]]
inv_H_pts = common.points_apply_homography(np.linalg.inv(H), pts)
x0, y0, w0, h0 = common.bounding_box2D(inv_H_pts)
x0, y0 = np.floor([x0, y0])
w0, h0 = np.ceil([w0, h0])
crop_fullres = common.image_crop_LARGE(im_in, x0, y0, w0, h0)
# This filter is needed (for panchro images) because the original PLEAIDES
# SENSOR PERFECT images are aliased
if (common.image_pix_dim(crop_fullres) == 1 and subsampling_factor == 1
and cfg['use_pleiades_unsharpening']):
tmp = image_apply_pleiades_unsharpening_filter(crop_fullres)
common.run('rm -f %s' % crop_fullres)
crop_fullres = tmp
# convert to gray
if common.image_pix_dim(crop_fullres) == 4:
if convert_to_gray:
crop_fullres = common.pansharpened_to_panchro(crop_fullres)
# compensate the homography with the translation induced by the preliminary
# crop, then apply the homography and crop.
H = np.dot(H, common.matrix_translation(x0, y0))
# Since the objective is to compute a zoomed out homographic transformation
# of the input image, to save computations we zoom out the image before
# applying the homography. If Z is the matrix representing the zoom out and
# H the homography matrix, this trick consists in applying Z*H*Z^{-1} to
# the zoomed image Z*Im instead of applying Z*H to the original image Im.
if subsampling_factor == 1:
common.image_apply_homography(im_out, crop_fullres, H, w, h)
return
else:
assert (subsampling_factor >= 1)
# H becomes Z*H*Z^{-1}
Z = np.eye(3)
Z[0, 0] = Z[1, 1] = 1 / float(subsampling_factor)
H = np.dot(Z, H)
H = np.dot(H, np.linalg.inv(Z))
# w, and h are updated accordingly
w = int(w / subsampling_factor)
h = int(h / subsampling_factor)
# the DCT zoom is NOT SAFE when the input image size is not a multiple
# of the zoom factor
tmpw, tmph = common.image_size(crop_fullres)
tmpw, tmph = int(tmpw / subsampling_factor), int(tmph /
subsampling_factor)
crop_fullres_safe = common.image_crop_tif(crop_fullres, 0, 0,
tmpw * subsampling_factor,
tmph * subsampling_factor)
common.run('rm -f %s' % crop_fullres)
# zoom out the input image (crop_fullres)
crop_zoom_out = common.image_safe_zoom_fft(crop_fullres_safe,
subsampling_factor)
common.run('rm -f %s' % crop_fullres_safe)
# apply the homography to the zoomed out crop
common.image_apply_homography(im_out, crop_zoom_out, H, w, h)
return
def compute_rectification_homographies(im1, im2, rpc1, rpc2, x, y, w, h, A=None,
m=None):
"""
Computes rectifying homographies for a ROI in a pair of Pleiades images.
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 definig 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. This matrix is usually estimated with the pointing_accuracy
module.
m (optional): Nx4 numpy array containing a list of matches.
Returns:
H1, H2: Two 3x3 matrices representing the rectifying homographies to be
applied to the two images.
disp_min, disp_max: horizontal disparity range, computed on a set of
sift matches
"""
# in brief: use 8-pts normalized algo to estimate F, then use loop-zhang to
# estimate rectifying homographies.
print "step 1: find virtual matches, and center them ----------------------"
n = cfg['n_gcp_per_axis']
rpc_matches = rpc_utils.matches_from_rpc(rpc1, rpc2, x, y, w, h, n)
p1 = rpc_matches[:, 0:2]
p2 = rpc_matches[:, 2:4]
if A is not None:
print "applying pointing error correction"
# correct coordinates of points in im2, according to A
p2 = common.points_apply_homography(np.linalg.inv(A), p2)
# the matching points are translated to be centered in 0, in order to deal
# with coordinates ranging from -1000 to 1000, and decrease imprecision
# effects of the loop-zhang rectification. These effects may become very
# important (~ 10 pixels error) when using coordinates around 20000.
pp1, T1 = center_2d_points(p1)
pp2, T2 = center_2d_points(p2)
print "step 2: estimate F (Gold standard algorithm) -----------------------"
F = estimation.affine_fundamental_matrix(np.hstack([pp1, pp2]))
print "step 3: compute rectifying homographies (loop-zhang algorithm) -----"
H1, H2 = estimation.loop_zhang(F, w, h)
S1, S2 = estimation.rectifying_similarities_from_affine_fundamental_matrix(
F, True)
print "F\n", F, "\n"
print "H1\n", H1, "\n"
print "S1\n", S1, "\n"
print "H2\n", H2, "\n"
print "S2\n", S2, "\n"
# compose with previous translations to get H1, H2 in the big images frame
H1 = np.dot(H1, T1)
H2 = np.dot(H2, T2)
# for debug
print "max, min, mean rectification error on rpc matches ------------------"
tmp = common.points_apply_homography(H1, p1)
y1 = tmp[:, 1]
tmp = common.points_apply_homography(H2, p2)
y2 = tmp[:, 1]
err = np.abs(y1 - y2)
print np.max(err), np.min(err), np.mean(err)
print "step 4: pull back top-left corner of the ROI in the origin ---------"
roi = [[x, y], [x+w, y], [x+w, y+h], [x, y+h]]
pts = common.points_apply_homography(H1, roi)
x0, y0 = common.bounding_box2D(pts)[0:2]
T = common.matrix_translation(-x0, -y0)
H1 = np.dot(T, H1)
H2 = np.dot(T, H2)
# add an horizontal translation to H2 to center the disparity range around
# the origin, if sift matches are available
if m is not None:
print "step 5: horizontal registration --------------------------------"
# filter sift matches with the known fundamental matrix
# but first convert F for big images coordinate frame
F = np.dot(T2.T, np.dot(F, T1))
print '%d sift matches before epipolar constraint filering' % len(m)
m = filter_matches_epipolar_constraint(F, m, cfg['epipolar_thresh'])
print '%d sift matches after epipolar constraint filering' % len(m)
if len(m) < 2:
# 0 or 1 sift match
print 'rectification.compute_rectification_homographies: less than'
print '2 sift matches after filtering by the epipolar constraint.'
print 'This may be due to the pointing error, or to strong'
print 'illumination changes between the input images.'
print 'No registration will be performed.'
else:
H2 = register_horizontally(m, H1, H2)
disp_m, disp_M = update_disp_range(m, H1, H2, w, h)
print "SIFT disparity range: [%f,%f]"%(disp_m,disp_M)
# expand disparity range with srtm according to cfg params
print cfg['disp_range_method']
if (cfg['disp_range_method'] == "srtm") or (m is None) or (len(m) < 2):
disp_m, disp_M = rpc_utils.srtm_disp_range_estimation(
rpc1, rpc2, x, y, w, h, H1, H2, A,
cfg['disp_range_srtm_high_margin'],
cfg['disp_range_srtm_low_margin'])
print "SRTM disparity range: [%f,%f]"%(disp_m,disp_M)
if ((cfg['disp_range_method'] == "wider_sift_srtm") and (m is not None) and
(len(m) >= 2)):
d_m, d_M = rpc_utils.srtm_disp_range_estimation(
rpc1, rpc2, x, y, w, h, H1, H2, A,
cfg['disp_range_srtm_high_margin'],
cfg['disp_range_srtm_low_margin'])
print "SRTM disparity range: [%f,%f]"%(d_m,d_M)
disp_m = min(disp_m, d_m)
disp_M = max(disp_M, d_M)
print "Final disparity range: [%s, %s]" % (disp_m, disp_M)
return H1, H2, disp_m, disp_M
def register_horizontally(matches, H1, H2, do_shear=False, flag='center'):
"""
Adjust rectifying homographies to modify the disparity range.
Args:
matches: list of pairs of 2D points, stored as a Nx4 numpy array
H1, H2: two homographies, stored as numpy 3x3 matrices
do_shear: boolean flag indicating wheter to minimize the shear on im2
or not.
flag: option needed to control how to modify the disparity range:
'center': move the barycenter of disparities of matches to zero
'positive': make all the disparities positive
'negative': make all the disparities negative. Required for
Hirshmuller stereo (java)
Returns:
H2: corrected homography H2
The matches are provided in the original images coordinate system. By
transforming these coordinates with the provided homographies, we obtain
matches whose disparity is only along the x-axis. The second homography H2
is corrected with a horizontal translation to obtain the desired property
on the disparity range.
"""
# transform the matches according to the homographies
pt1 = common.points_apply_homography(H1, matches[:, 0:2])
x1 = pt1[:, 0]
y1 = pt1[:, 1]
pt2 = common.points_apply_homography(H2, matches[:, 2:4])
x2 = pt2[:, 0]
y2 = pt2[:, 1]
# for debug, print the vertical disparities. Should be zero.
print "Residual vertical disparities: max, min, mean. Should be zero ------"
print np.max(y2 - y1), np.min(y2 - y1), np.mean(y2 - y1)
# shear correction
# we search the (s, b) vector that minimises \sum (x1 - (x2+s*y2+b))^2
# it is a least squares minimisation problem
if do_shear:
A = np.vstack((y2, y2*0+1)).T
B = x1 - x2
z = np.linalg.lstsq(A, B)[0]
s = z[0]
b = z[1]
H2 = np.dot(np.array([[1, s, b], [0, 1, 0], [0, 0, 1]]), H2)
x2 = x2 + s*y2 + b
# compute the disparity offset according to selected option
if (flag == 'center'):
t = np.mean(x2 - x1)
if (flag == 'positive'):
t = np.min(x2 - x1)
if (flag == 'negative'):
t = np.max(x2 - x1)
if (flag == 'none'):
t = 0
# correct H2 with a translation
H2 = np.dot(common.matrix_translation(-t, 0), H2)
return H2
