def alt_to_disp(rpc1, rpc2, x, y, alt, H1, H2, A=None):
"""
Converts an altitude into a disparity.
Args:
rpc1: an instance of the rpc_model.RPCModel class for the reference
image
rpc2: an instance of the rpc_model.RPCModel class for the secondary
image
x, y: coordinates of the point in the reference image
alt: altitude above the WGS84 ellipsoid (in meters) of the point
H1, H2: rectifying homographies
A (optional): pointing correction matrix
Returns:
the horizontal disparity of the (x, y) point of im1, assuming that the
3-space point associated has altitude alt. The disparity is made
horizontal thanks to the two rectifying homographies H1 and H2.
"""
xx, yy = find_corresponding_point(rpc1, rpc2, x, y, alt)[0:2]
p1 = np.vstack([x, y]).T
p2 = np.vstack([xx, yy]).T
if A is not None:
print "rpc_utils.alt_to_disp: applying pointing error correction"
# correct coordinates of points in im2, according to A
p2 = common.points_apply_homography(np.linalg.inv(A), p2)
p1 = common.points_apply_homography(H1, p1)
p2 = common.points_apply_homography(H2, p2)
# np.testing.assert_allclose(p1[:, 1], p2[:, 1], atol=0.1)
disp = p2[:, 0] - p1[:, 0]
return disp
def register_horizontally_shear(matches, H1, H2):
"""
Adjust rectifying homographies with a shear 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
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.
"""
# 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]
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)
# we search the (s, b) vector that minimises \sum (x1 - (x2+s*y2+b))^2
# it is a least squares minimisation problem
A = np.vstack((y2, y2 * 0 + 1)).T
B = x1 - x2
s, b = np.linalg.lstsq(A, B)[0].flatten()
# correct H2 with the estimated shear
return np.dot(np.array([[1, s, b], [0, 1, 0], [0, 0, 1]]), H2)
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 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 update_disp_range(matches, H1, H2, w, h):
"""
Update the disparity range considering the extrapolation of the affine
registration estimated from the matches. Extrapolate on the whole region
of the region of interest.
Args:
matches: list of pairs of 2D points, stored as a Nx4 numpy array
H1, H2: two rectifying homographies, stored as numpy 3x3 matrices
w, h: width and height of the region of interest
Returns:
disp_min, disp_max: horizontal disparity range
"""
# transform the matches according to the homographies
pt1 = common.points_apply_homography(H1, matches[:, 0:2])
x1 = pt1[:, 0]
pt2 = common.points_apply_homography(H2, matches[:, 2:4])
x2 = pt2[:, 0]
y2 = pt2[:, 1]
# estimate an affine transformation (tilt, shear and bias)
# that maps pt1 on pt2
A = np.vstack((x2, y2, y2*0+1)).T
B = x1
z = np.linalg.lstsq(A, B)[0]
t, s, b = z[0:3]
# corners of ROI
xx2 = np.array([0, w, 0, w])
yy2 = np.array([0, 0, h, h])
# compute the max and min disparity values according to the estimated
# model. The min/max disp values are necessarily obtained at the ROI
# corners
roi_disparities_by_the_affine_model = (xx2*t + yy2*s + b) - xx2
max_roi = np.max(roi_disparities_by_the_affine_model)
min_roi = np.min(roi_disparities_by_the_affine_model)
# min/max disparities according to the keypoints
max_kpt = np.max(x2 - x1)
min_kpt = np.min(x2 - x1)
# compute the range with the extracted min and max disparities
dispx_min = np.floor(min(min_roi, min_kpt))
dispx_max = np.floor(max(max_roi, max_kpt))
# 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
return dispx_min, dispx_max
def update_disp_range(matches, H1, H2, w, h):
"""
Update the disparity range considering the extrapolation of the affine
registration estimated from the matches. Extrapolate on the whole region
of the region of interest.
Args:
matches: list of pairs of 2D points, stored as a Nx4 numpy array
H1, H2: two rectifying homographies, stored as numpy 3x3 matrices
w, h: width and height of the region of interest
Returns:
disp_min, disp_max: horizontal disparity range
"""
# transform the matches according to the homographies
pt1 = common.points_apply_homography(H1, matches[:, 0:2])
x1 = pt1[:, 0]
pt2 = common.points_apply_homography(H2, matches[:, 2:4])
x2 = pt2[:, 0]
y2 = pt2[:, 1]
# estimate an affine transformation (tilt, shear and bias)
# that maps pt1 on pt2
A = np.vstack((x2, y2, y2 * 0 + 1)).T
B = x1
z = np.linalg.lstsq(A, B)[0]
t, s, b = z[0:3]
# corners of ROI
xx2 = np.array([0, w, 0, w])
yy2 = np.array([0, 0, h, h])
# compute the max and min disparity values according to the estimated
# model. The min/max disp values are necessarily obtained at the ROI
# corners
roi_disparities_by_the_affine_model = (xx2 * t + yy2 * s + b) - xx2
max_roi = np.max(roi_disparities_by_the_affine_model)
min_roi = np.min(roi_disparities_by_the_affine_model)
# min/max disparities according to the keypoints
max_kpt = np.max(x2 - x1)
min_kpt = np.min(x2 - x1)
# compute the range with the extracted min and max disparities
dispx_min = np.floor(min(min_roi, min_kpt))
dispx_max = np.floor(max(max_roi, max_kpt))
# 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
return dispx_min, dispx_max
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 update_minmax_range_extrapolating_registration_affinity(matches, H1, H2,w_roi,h_roi):
"""
Update the disparity range considering the extrapolation of the affine registration
transformation. Extrapolate until the boundary of the region of interest
Args:
matches: list of pairs of 2D points, stored as a Nx4 numpy array
H1, H2: two homographies, stored as numpy 3x3 matrices
roi_w/h: width and height of the region of interest
Returns:
disp_min, disp_max: horizontal 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]
# estimate an affine transformation (tilt, shear and bias)
# from the matched keypoints
A = np.vstack((x2, y2, y2*0+1)).T
# A = x2[:, np.newaxis]
b = x1
z = np.linalg.lstsq(A, b)[0]
t,s,dx = z[0:3]
# corners of ROI
xx2 = np.array([0,w_roi,0,w_roi])
yy2 = np.array([0,0,h_roi,h_roi])
# compute the max and min disparity values (according to
# the estimated model) at the ROI corners
roi_disparities_by_the_affine_model = (xx2*t + yy2*s + dx) - xx2
maxb = np.max(roi_disparities_by_the_affine_model)
minb = np.min(roi_disparities_by_the_affine_model)
#print minb,maxb
# compute the rage with the extract min and max disparities
dispx_min = np.floor(minb + np.min(x2 - x1))
dispx_max = np.ceil(maxb + np.max(x2 - x1))
# add 20% security margin
if (dispx_min < 0):
dispx_min = 1.2 * dispx_min
else:
dispx_min = 0.8 * dispx_min
if (dispx_max > 0):
dispx_max = 1.2 * dispx_max
else:
dispx_max = 0.8 * dispx_max
return dispx_min, dispx_max
def test_affine_transformation():
x = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
# list of transformations to be tested
T = np.eye(3)
I = np.eye(3)
S = np.eye(3)
A = np.eye(3)
translations = []
isometries = []
similarities = []
affinities = []
for i in xrange(100):
translations.append(T)
isometries.append(I)
similarities.append(S)
affinities.append(A)
T[0:2, 2] = np.random.random(2)
I = rotation_matrix(2 * np.pi * np.random.random_sample())
I[0:2, 2] = np.random.random(2)
S = similarity_matrix(2 * np.pi * np.random.random_sample(),
np.random.random_sample())
S[0:2, 2] = 100 * np.random.random(2)
A[0:2, :] = np.random.random((2, 3))
for B in translations + isometries + similarities + affinities:
xx = common.points_apply_homography(B, x)
E = estimation.affine_transformation(x, xx)
assert_array_almost_equal(E, B)
def test_affine_transformation():
x = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
# list of transformations to be tested
T = np.eye(3)
I = np.eye(3)
S = np.eye(3)
A = np.eye(3)
translations = []
isometries = []
similarities = []
affinities = []
for i in xrange(100):
translations.append(T)
isometries.append(I)
similarities.append(S)
affinities.append(A)
T[0:2, 2] = np.random.random(2)
I = rotation_matrix(2*np.pi * np.random.random_sample())
I[0:2, 2] = np.random.random(2)
S = similarity_matrix(2*np.pi * np.random.random_sample(),
np.random.random_sample())
S[0:2, 2] = 100 * np.random.random(2)
A[0:2, :] = np.random.random((2, 3))
for B in translations + isometries + similarities + affinities:
xx = common.points_apply_homography(B, x)
E = estimation.affine_transformation(x, xx)
assert_array_almost_equal(E, B)
def matches_from_sift_rpc_roi(im1, im2, rpc1, rpc2, x, y, w, h):
"""
Computes a list of sift matches between two Pleiades images.
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 big images.
"""
x1, y1, w1, h1 = x, y, w, h
x2, y2, w2, h2 = rpc_utils.corresponding_roi(rpc1, rpc2, x, y, w, h)
p1 = common.image_sift_keypoints(im1, x1, y1, w1, h1, max_nb=2000)
p2 = common.image_sift_keypoints(im2, x2, y2, w2, h2, max_nb=2000)
matches = common.sift_keypoints_match(p1, p2, 'relative',
cfg['sift_match_thresh'])
# Below is an alternative to ASIFT: lower the thresh_dog for the sift calls.
# Default value for thresh_dog is 0.0133
thresh_dog = 0.0133
nb_sift_tries = 1
while (matches.shape[0] < 10 and nb_sift_tries < 6):
nb_sift_tries += 1
thresh_dog /= 2.0
p1 = common.image_sift_keypoints(im1, x1, y1, w1, h1, None,
'-thresh_dog %f' % thresh_dog)
p2 = common.image_sift_keypoints(im2, x2, y2, w2, h2, None,
'-thresh_dog %f' % thresh_dog)
matches = common.sift_keypoints_match(p1, p2, 'relative',
cfg['sift_match_thresh'])
return matches
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:
return np.array([[]])
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 cost_function(v, *args):
"""
Objective function to minimize in order to correct the pointing error.
Arguments:
v: vector of size 3 or 4, containing the 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).
"""
rpc1, rpc2, matches = args[0], args[1], args[2]
if len(args) == 4:
alpha = args[3]
else:
alpha = 0.01
# 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):
print 'warning: cost_function is going too far'
print v
if (len(v) > 3):
if (np.abs(v[3]) > 20000):
print 'warning: cost_function is going too far'
print v
# compute the altitudes from the matches without correction
x1 = matches[:, 0]
y1 = matches[:, 1]
x2 = matches[:, 2]
y2 = matches[:, 3]
h0 = rpc_utils.compute_height(rpc1, rpc2, x1, y1, x2, y2)[0]
# 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])
x2 = p2[:, 0]
y2 = p2[:, 1]
# compute the cost
h, e = rpc_utils.compute_height(rpc1, rpc2, x1, y1, x2, y2)
cost = np.sum((h - h0)**2)
cost *= alpha
cost += np.sum(e)
#print cost
return cost
def matches_from_sift_rpc_roi(im1, im2, rpc1, rpc2, x, y, w, h):
"""
Computes a list of sift matches between two Pleiades images.
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 big images.
"""
x1, y1, w1, h1 = x, y, w, h
x2, y2, w2, h2 = rpc_utils.corresponding_roi(rpc1, rpc2, x, y, w, h)
p1 = common.image_sift_keypoints(im1, x1, y1, w1, h1, max_nb=2000)
p2 = common.image_sift_keypoints(im2, x2, y2, w2, h2, max_nb=2000)
matches = common.sift_keypoints_match(p1, p2, 'relative',
cfg['sift_match_thresh'])
# Below is an alternative to ASIFT: lower the thresh_dog for the sift calls.
# Default value for thresh_dog is 0.0133
thresh_dog = 0.0133
nb_sift_tries = 1
while (matches.shape[0] < 10 and nb_sift_tries < 6):
nb_sift_tries += 1
thresh_dog /= 2.0
p1 = common.image_sift_keypoints(im1, x1, y1, w1, h1, None, '-thresh_dog %f' % thresh_dog)
p2 = common.image_sift_keypoints(im2, x2, y2, w2, h2, None, '-thresh_dog %f' % thresh_dog)
matches = common.sift_keypoints_match(p1, p2, 'relative',
cfg['sift_match_thresh'])
return matches
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:
return np.array([[]])
def disparity_range_from_matches(matches, H1, H2, w, h):
"""
Compute the disparity range of a ROI from a list of point matches.
The estimation is based on the extrapolation of the affine registration
estimated from the matches. The extrapolation is done on the whole region of
interest.
Args:
matches: Nx4 numpy array containing a list of matches, in the full
image coordinates frame, before rectification
w, h: width and height of the rectangular ROI in the first image.
H1, H2: two rectifying homographies, stored as numpy 3x3 matrices
Returns:
disp_min, disp_max: horizontal disparity range
"""
# transform the matches according to the homographies
p1 = common.points_apply_homography(H1, matches[:, :2])
x1 = p1[:, 0]
p2 = common.points_apply_homography(H2, matches[:, 2:])
x2 = p2[:, 0]
y2 = p2[:, 1]
# estimate an affine transformation (tilt, shear and bias) mapping p1 on p2
t, s, b = np.linalg.lstsq(np.vstack((x2, y2, y2*0+1)).T, x1)[0][:3]
# compute the disparities for the affine model. The extrema are obtained at
# the ROI corners
xx = np.array([0, w, 0, w])
yy = np.array([0, 0, h, h])
disp_affine_model = (xx*t + yy*s + b) - xx
# compute the final disparity range
disp_min = np.floor(min(np.min(disp_affine_model), np.min(x2 - x1)))
disp_max = np.ceil(max(np.max(disp_affine_model), np.max(x2 - x1)))
# add a security margin to the disparity range
disp_min *= (1 - np.sign(disp_min) * cfg['disp_range_extra_margin'])
disp_max *= (1 + np.sign(disp_max) * cfg['disp_range_extra_margin'])
return disp_min, disp_max
def disparity_range_from_matches(matches, H1, H2, w, h):
"""
Compute the disparity range of a ROI from a list of point matches.
The estimation is based on the extrapolation of the affine registration
estimated from the matches. The extrapolation is done on the whole region of
interest.
Args:
matches: Nx4 numpy array containing a list of matches, in the full
image coordinates frame, before rectification
w, h: width and height of the rectangular ROI in the first image.
H1, H2: two rectifying homographies, stored as numpy 3x3 matrices
Returns:
disp_min, disp_max: horizontal disparity range
"""
# transform the matches according to the homographies
p1 = common.points_apply_homography(H1, matches[:, :2])
x1 = p1[:, 0]
p2 = common.points_apply_homography(H2, matches[:, 2:])
x2 = p2[:, 0]
y2 = p2[:, 1]
# estimate an affine transformation (tilt, shear and bias) mapping p1 on p2
t, s, b = np.linalg.lstsq(np.vstack((x2, y2, y2 * 0 + 1)).T, x1)[0][:3]
# compute the disparities for the affine model. The extrema are obtained at
# the ROI corners
xx = np.array([0, w, 0, w])
yy = np.array([0, 0, h, h])
disp_affine_model = (xx * t + yy * s + b) - xx
# compute the final disparity range
disp_min = np.floor(min(np.min(disp_affine_model), np.min(x2 - x1)))
disp_max = np.ceil(max(np.max(disp_affine_model), np.max(x2 - x1)))
# add a security margin to the disparity range
disp_min *= 1 - np.sign(disp_min) * cfg["disp_range_extra_margin"]
disp_max *= 1 + np.sign(disp_max) * cfg["disp_range_extra_margin"]
return disp_min, disp_max
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 evaluation_iterative(im1,
im2,
rpc1,
rpc2,
x,
y,
w,
h,
A=None,
matches=None):
"""
Measures the maximal pointing error on a Pleiades' pair of 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 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.
"""
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)
# compute the pointing error for each match
x1 = p1[:, 0]
y1 = p1[:, 1]
x2 = p2[:, 0]
y2 = p2[:, 1]
e = rpc_utils.compute_height(rpc1, rpc2, x1, y1, x2, y2)[1]
# matches = matches[e < 0.1, :]
# visualisation.plot_matches_pleiades(im1, im2, matches)
print "max, mean, min pointing error, from %d points:" % (len(matches))
print np.max(e), np.mean(e), np.min(e)
# return the mean error
return np.mean(np.abs(e))
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 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 pleiades 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 matches_sift is None:
matches_sift = pointing_accuracy.filtered_sift_matches_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 = pointing_accuracy.error_vectors(matches_sift, F, 'ref')
A = 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 = pointing_accuracy.error_vectors(np.hstack((p, qq)), F, 'ref')
print pointing_accuracy.evaluation_from_estimated_F(im1, im2, r1, r2, x, y, w, h, None, matches_sift)
print 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 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 matches is None:
matches = filtered_sift_matches_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 evaluation_iterative(im1, im2, rpc1, rpc2, x, y, w, h, A=None,
matches=None):
"""
Measures the maximal pointing error on a Pleiades' pair of 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 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.
"""
if matches is None:
matches = filtered_sift_matches_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)
# compute the pointing error for each match
x1 = p1[:, 0]
y1 = p1[:, 1]
x2 = p2[:, 0]
y2 = p2[:, 1]
e = rpc_utils.compute_height(rpc1, rpc2, x1, y1, x2, y2)[1]
# matches = matches[e < 0.1, :]
# visualisation.plot_matches_pleiades(im1, im2, matches)
print "max, mean, min pointing error, from %d points:" % (len(matches))
print np.max(e), np.mean(e), np.min(e)
# return the mean error
return np.mean(np.abs(e))
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 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 rectify_pair(im1, im2, rpc1, rpc2, x, y, w, h, out1, out2, A=None):
"""
Rectify a ROI in a pair of Pleiades images.
Args:
im1, im2: paths to the two Pleiades images (usually jp2 or tif)
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 crops
A (optional): 3x3 numpy array containing the pointing error correction
for im2. This matrix is usually estimated with the pointing_accuracy
module.
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 (big) images.
disp_min, disp_max: horizontal disparity range
"""
# compute rectifying homographies
H1, H2, disp_min, disp_max = compute_rectification_homographies(im1, im2,
rpc1, rpc2, x, y, w, h, A)
## 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)
#x0,y0,w0,h0 = x,y,w,h
# check that the first homography maps the ROI in the positive quadrant
assert (round(x0) == 0)
assert (round(y0) == 0)
z = cfg['subsampling_factor']
# apply homographies and do the crops
# THIS STEP IS HERE TO PRODUCE THE MASKS WHERE THE IMAGE IS KNOWN
# SURE THIS IS A CRAPPY WAY TO DO THIS, WE SHOULD DEFINITIVELY DO IT
# SIMULTANEOUSLY WITH THE HOMOGRAPHIC TRANSFORMATION
msk1 = common.tmpfile('.png')
msk2 = common.tmpfile('.png')
common.run('plambda %s "x 255" -o %s' % (im1, msk1))
common.run('plambda %s "x 255" -o %s' % (im2, msk2))
homography_cropper.crop_and_apply_homography(msk1, msk1, H1, w0, h0, z)
homography_cropper.crop_and_apply_homography(msk2, msk2, H2, w0, h0, z)
# FINALLY : apply homographies and do the crops of the images
homography_cropper.crop_and_apply_homography(out1, im1, H1, w0, h0, z)
homography_cropper.crop_and_apply_homography(out2, im2, H2, w0, h0, z)
# COMBINE THE MASK TO REMOVE THE POINTS THAT FALL OUTSIDE THE IMAGE
common.run('plambda %s %s "x 200 > y nan if" -o %s' % (msk1, out1, out1))
common.run('plambda %s %s "x 200 > y nan if" -o %s' % (msk2, out2, out2))
# This also does the job but when z != 1 it fails (segfault: homography)
# TODO: FIX homography, maybe code a new one
# common.image_apply_homography(out1, im1, H1, w0, h0)
# common.image_apply_homography(out2, im2, H2, w0, h0)
# If subsampling_factor the homographies are altered to reflect the zoom
if z != 1:
from math import floor, ceil
# update the H1 and H2 to reflect the zoom
Z = np.eye(3);
Z[0,0] = Z[1,1] = 1.0 / z
H1 = np.dot(Z, H1)
H2 = np.dot(Z, H2)
disp_min = floor(disp_min / z)
disp_max = ceil(disp_max / z)
w0 = w0 / subsampling_factor
h0 = h0 / subsampling_factor
return H1, H2, disp_min, disp_max
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 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 rectify_pair(im1,
im2,
rpc1,
rpc2,
x,
y,
w,
h,
out1,
out2,
A=None,
m=None,
flag='rpc'):
"""
Rectify a ROI in a pair of Pleiades images.
Args:
im1, im2: paths to the two Pleiades images (usually jp2 or tif)
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 crops
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 sift matches, in the
full image coordinates frame
flag (default: 'rpc'): option to decide wether to use rpc of sift
matches for the fundamental matrix estimation.
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 (big) images.
disp_min, disp_max: horizontal disparity range
"""
# read RPC data
rpc1 = rpc_model.RPCModel(rpc1)
rpc2 = rpc_model.RPCModel(rpc2)
# compute rectifying homographies
if flag == 'rpc':
H1, H2, disp_min, disp_max = compute_rectification_homographies(
im1, im2, rpc1, rpc2, x, y, w, h, A, m)
else:
H1, H2, disp_min, disp_max = compute_rectification_homographies_sift(
im1, im2, rpc1, rpc2, x, y, w, h)
# 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]), 0, atol=.01)
# apply homographies and do the crops TODO XXX FIXME cleanup here
#homography_cropper.crop_and_apply_homography(out1, im1, H1, w0, h0, cfg['subsampling_factor'], True)
#homography_cropper.crop_and_apply_homography(out2, im2, H2, w0, h0, cfg['subsampling_factor'], True)
common.image_apply_homography(out1, im1, H1, w0, h0)
common.image_apply_homography(out2, im2, H2, w0, h0)
# If subsampling_factor'] the homographies are altered to reflect the zoom
if cfg['subsampling_factor'] != 1:
from math import floor, ceil
# update the H1 and H2 to reflect the zoom
Z = np.eye(3)
Z[0, 0] = Z[1, 1] = 1.0 / cfg['subsampling_factor']
H1 = np.dot(Z, H1)
H2 = np.dot(Z, H2)
disp_min = floor(disp_min / cfg['subsampling_factor'])
disp_max = ceil(disp_max / cfg['subsampling_factor'])
return H1, H2, disp_min, disp_max
def rectify_pair(im1, im2, rpc1, rpc2, x, y, w, h, out1, out2, A=None, sift_matches=None, method="rpc"):
"""
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.
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)
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
disp_m, disp_M = disparity_range(rpc1, rpc2, x, y, w, h, H1, H2, sift_matches, A)
# 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]), 0, atol=0.01)
# apply homographies and do the crops TODO XXX FIXME cleanup here
# homography_cropper.crop_and_apply_homography(out1, im1, H1, w0, h0, cfg['subsampling_factor'], True)
# homography_cropper.crop_and_apply_homography(out2, im2, H2, w0, h0, cfg['subsampling_factor'], True)
common.image_apply_homography(out1, im1, H1, w0, h0)
common.image_apply_homography(out2, im2, H2, w0, h0)
# if subsampling_factor'] the homographies are altered to reflect the zoom
if cfg["subsampling_factor"] != 1:
Z = np.eye(3)
Z[0, 0] = Z[1, 1] = 1.0 / cfg["subsampling_factor"]
H1 = np.dot(Z, H1)
H2 = np.dot(Z, H2)
disp_m = np.floor(disp_m / cfg["subsampling_factor"])
disp_M = np.ceil(disp_M / cfg["subsampling_factor"])
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
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 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 rectify_pair(im1, im2, rpc1, rpc2, x, y, w, h, out1, out2, A=None,
sift_matches=None, method='rpc'):
"""
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.
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)
# 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(sift_matches, H1, H2)
# compute disparity range
disp_m, disp_M = disparity_range(rpc1, rpc2, x, y, w, h, H1, H2,
sift_matches, A)
# 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]), 0, atol=.01)
# apply homographies and do the crops TODO XXX FIXME cleanup here
#homography_cropper.crop_and_apply_homography(out1, im1, H1, w0, h0, cfg['subsampling_factor'], True)
#homography_cropper.crop_and_apply_homography(out2, im2, H2, w0, h0, cfg['subsampling_factor'], True)
common.image_apply_homography(out1, im1, H1, w0, h0)
common.image_apply_homography(out2, im2, H2, w0, h0)
# if subsampling_factor'] the homographies are altered to reflect the zoom
if cfg['subsampling_factor'] != 1:
Z = np.eye(3)
Z[0, 0] = Z[1, 1] = 1.0 / cfg['subsampling_factor']
H1 = np.dot(Z, H1)
H2 = np.dot(Z, H2)
disp_m = np.floor(disp_m / cfg['subsampling_factor'])
disp_M = np.ceil(disp_M / cfg['subsampling_factor'])
return H1, H2, disp_m, disp_M
def rectify_pair(im1, im2, rpc1, rpc2, x, y, w, h, out1, out2, A=None, m=None,
flag='rpc'):
"""
Rectify a ROI in a pair of Pleiades images.
Args:
im1, im2: paths to the two Pleiades images (usually jp2 or tif)
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 crops
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 sift matches, in the
full image coordinates frame
flag (default: 'rpc'): option to decide wether to use rpc of sift
matches for the fundamental matrix estimation.
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 (big) images.
disp_min, disp_max: horizontal disparity range
"""
# read RPC data
rpc1 = rpc_model.RPCModel(rpc1)
rpc2 = rpc_model.RPCModel(rpc2)
# compute rectifying homographies
if flag == 'rpc':
H1, H2, disp_min, disp_max = compute_rectification_homographies(
im1, im2, rpc1, rpc2, x, y, w, h, A, m)
else:
H1, H2, disp_min, disp_max = compute_rectification_homographies_sift(
im1, im2, rpc1, rpc2, x, y, w, h)
# 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]), 0, atol=.01)
# apply homographies and do the crops
homography_cropper.crop_and_apply_homography(out1, im1, H1, w0, h0,
cfg['subsampling_factor'],
True)
homography_cropper.crop_and_apply_homography(out2, im2, H2, w0, h0,
cfg['subsampling_factor'],
True)
# If subsampling_factor'] the homographies are altered to reflect the zoom
if cfg['subsampling_factor'] != 1:
from math import floor, ceil
# update the H1 and H2 to reflect the zoom
Z = np.eye(3)
Z[0, 0] = Z[1, 1] = 1.0 / cfg['subsampling_factor']
H1 = np.dot(Z, H1)
H2 = np.dot(Z, H2)
disp_min = floor(disp_min / cfg['subsampling_factor'])
disp_max = ceil(disp_max / cfg['subsampling_factor'])
return H1, H2, disp_min, disp_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 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