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 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]
# compute the final disparity range
disp_min = np.floor(np.min(x2 - x1))
disp_max = np.ceil(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 register_horizontally_shear(matches, H1, H2):
"""
Adjust rectifying homographies with tilt, shear and translation to reduce 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 (a, b, c) vector that minimises \sum (x1 - (a*x2+b*y2+c))^2
# it is a least squares minimisation problem
A = np.vstack((x2, y2, y2 * 0 + 1)).T
a, b, c = np.linalg.lstsq(A, x1)[0].flatten()
# correct H2 with the estimated tilt, shear and translation
return np.dot(np.array([[a, b, c], [0, 1, 0], [0, 0, 1]]), H2)
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]
# compute the final disparity range
disp_min = np.floor(np.min(x2 - x1))
disp_max = np.ceil(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 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 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 range(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 range(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 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 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 rectification_homographies(matches, x, y, w, h, hmargin=0, vmargin=0):
"""
Computes rectifying homographies from point matches for a given ROI.
The affine fundamental matrix F is estimated with the gold-standard
algorithm, then two rectifying similarities (rotation, zoom, translation)
are computed directly from F.
Args:
matches: numpy array of shape (n, 4) containing a list of 2D point
correspondences between the two images.
x, y, w, h: four integers defining the rectangular ROI in the first
image. (x, y) is the top-left corner, and (w, h) are the dimensions
of the rectangle.
{h,v}margin: translations added to the rectifying similarities to extend the
horizontal and vertical footprint of the rectified images
Returns:
S1, S2, F: three numpy arrays of shape (3, 3) representing the
two rectifying similarities to be applied to the two images and the
corresponding affine fundamental matrix.
"""
# estimate the affine fundamental matrix with the Gold standard algorithm
F = estimation.affine_fundamental_matrix(matches)
# compute rectifying similarities
S1, S2 = estimation.rectifying_similarities_from_affine_fundamental_matrix(
F, cfg['debug'])
if cfg['debug']:
y1 = common.points_apply_homography(S1, matches[:, :2])[:, 1]
y2 = common.points_apply_homography(S2, matches[:, 2:])[:, 1]
err = np.abs(y1 - y2)
print("max, min, mean rectification error on point matches: ", end=' ')
print(np.max(err), np.min(err), np.mean(err))
# pull back top-left corner of the ROI to the origin (plus margin)
pts = common.points_apply_homography(
S1, [[x, y], [x + w, y], [x + w, y + h], [x, y + h]])
x0, y0 = common.bounding_box2D(pts)[:2]
T = common.matrix_translation(-x0 + hmargin, -y0 + vmargin)
return np.dot(T, S1), np.dot(T, S2), F
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 rectification_homographies(matches, x, y, w, h, hmargin=0, vmargin=0):
"""
Computes rectifying homographies from point matches for a given ROI.
The affine fundamental matrix F is estimated with the gold-standard
algorithm, then two rectifying similarities (rotation, zoom, translation)
are computed directly from F.
Args:
matches: numpy array of shape (n, 4) containing a list of 2D point
correspondences between the two images.
x, y, w, h: four integers defining the rectangular ROI in the first
image. (x, y) is the top-left corner, and (w, h) are the dimensions
of the rectangle.
{h,v}margin: translations added to the rectifying similarities to extend the
horizontal and vertical footprint of the rectified images
Returns:
S1, S2, F: three numpy arrays of shape (3, 3) representing the
two rectifying similarities to be applied to the two images and the
corresponding affine fundamental matrix.
"""
# estimate the affine fundamental matrix with the Gold standard algorithm
F = estimation.affine_fundamental_matrix(matches)
# compute rectifying similarities
S1, S2 = estimation.rectifying_similarities_from_affine_fundamental_matrix(F, cfg['debug'])
if cfg['debug']:
y1 = common.points_apply_homography(S1, matches[:, :2])[:, 1]
y2 = common.points_apply_homography(S2, matches[:, 2:])[:, 1]
err = np.abs(y1 - y2)
print("max, min, mean rectification error on point matches: ", end=' ')
print(np.max(err), np.min(err), np.mean(err))
# pull back top-left corner of the ROI to the origin (plus margin)
pts = common.points_apply_homography(S1, [[x, y], [x+w, y], [x+w, y+h], [x, y+h]])
x0, y0 = common.bounding_box2D(pts)[:2]
T = common.matrix_translation(-x0 + hmargin, -y0 + vmargin)
return np.dot(T, S1), np.dot(T, S2), F
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 plot_pointing_error_tile(im1, im2, rpc1, rpc2, x, y, w, h,
matches_sift=None, f=100, out_files_pattern=None):
"""
Args:
im1, im2: path to full images
rpc1, rcp2: path to associated rpc xml files
x, y, w, h: four integers defining the rectangular tile in the reference
image. (x, y) is the top-left corner, and (w, h) are the dimensions
of the tile.
f (optional, default is 100): exageration factor for the error vectors
out_files_pattern (optional, default is None): pattern used to name the
two output files (plots of the pointing error)
Returns:
nothing, but opens a display
"""
# read rpcs
r1 = rpc_model.RPCModel(rpc1)
r2 = rpc_model.RPCModel(rpc2)
# compute sift matches
if not matches_sift:
matches_sift = sift.matches_on_rpc_roi(im1, im2, r1, r2, x, y, w, h)
# compute rpc matches
matches_rpc = rpc_utils.matches_from_rpc(r1, r2, x, y, w, h, 5)
# estimate affine fundamental matrix
F = estimation.affine_fundamental_matrix(matches_rpc)
# compute error vectors
e = s2plib.pointing_accuracy.error_vectors(matches_sift, F, 'ref')
A = s2plib.pointing_accuracy.local_translation(r1,r2, x,y,w,h, matches_sift)
p = matches_sift[:, 0:2]
q = matches_sift[:, 2:4]
qq = common.points_apply_homography(A, q)
ee = s2plib.pointing_accuracy.error_vectors(np.hstack((p, qq)), F, 'ref')
print(s2plib.pointing_accuracy.evaluation_from_estimated_F(im1, im2,
r1, r2, x, y, w, h, None, matches_sift))
print(s2plib.pointing_accuracy.evaluation_from_estimated_F(im1, im2,
r1, r2, x, y, w, h, A, matches_sift))
# plot the vectors: they go from the point x to the line (F.T)x'
plot_vectors(p, -e, x, y, w, h, f, out_file='%s_before.png' % out_files_pattern)
plot_vectors(p, -ee, x, y, w, h, f, out_file='%s_after.png' % out_files_pattern)
def plot_pointing_error_tile(im1, im2, rpc1, rpc2, x, y, w, h,
matches_sift=None, f=100, out_files_pattern=None):
"""
Args:
im1, im2: path to full images
rpc1, rcp2: path to associated rpc xml files
x, y, w, h: four integers defining the rectangular tile in the reference
image. (x, y) is the top-left corner, and (w, h) are the dimensions
of the tile.
f (optional, default is 100): exageration factor for the error vectors
out_files_pattern (optional, default is None): pattern used to name the
two output files (plots of the pointing error)
Returns:
nothing, but opens a display
"""
# read rpcs
r1 = rpc_model.RPCModel(rpc1)
r2 = rpc_model.RPCModel(rpc2)
# compute sift matches
if not matches_sift:
matches_sift = sift.matches_on_rpc_roi(im1, im2, r1, r2, x, y, w, h)
# compute rpc matches
matches_rpc = rpc_utils.matches_from_rpc(r1, r2, x, y, w, h, 5)
# estimate affine fundamental matrix
F = estimation.affine_fundamental_matrix(matches_rpc)
# compute error vectors
e = s2plib.pointing_accuracy.error_vectors(matches_sift, F, 'ref')
A = s2plib.pointing_accuracy.local_translation(r1,r2, x,y,w,h, matches_sift)
p = matches_sift[:, 0:2]
q = matches_sift[:, 2:4]
qq = common.points_apply_homography(A, q)
ee = s2plib.pointing_accuracy.error_vectors(np.hstack((p, qq)), F, 'ref')
print(s2plib.pointing_accuracy.evaluation_from_estimated_F(im1, im2,
r1, r2, x, y, w, h, None, matches_sift))
print(s2plib.pointing_accuracy.evaluation_from_estimated_F(im1, im2,
r1, r2, x, y, w, h, A, matches_sift))
# plot the vectors: they go from the point x to the line (F.T)x'
plot_vectors(p, -e, x, y, w, h, f, out_file='%s_before.png' % out_files_pattern)
plot_vectors(p, -ee, x, y, w, h, f, out_file='%s_after.png' % out_files_pattern)
def cost_function_linear(v, rpc1, rpc2, matches):
"""
Objective function to minimize in order to correct the pointing error.
Arguments:
v: vector of size 4, containing the 4 parameters of the euclidean
transformation we are looking for.
rpc1, rpc2: two instances of the rpc_model.RPCModel class
matches: 2D numpy array containing a list of matches. Each line
contains one pair of points, ordered as x1 y1 x2 y2.
The coordinate system is the one of the big images.
alpha: relative weight of the error terms: e + alpha*(h-h0)^2. See
paper for more explanations.
Returns:
The sum of pointing errors and altitude differences, as written in the
paper formula (1).
"""
print_params(v)
# verify that parameters are in the bounding box
if (np.abs(v[0]) > 200 * np.pi or np.abs(v[1]) > 10000
or np.abs(v[2]) > 10000 or np.abs(v[3]) > 20000):
print('warning: cost_function is going too far')
print(v)
x, y, w, h = common.bounding_box2D(matches[:, 0:2])
matches_rpc = rpc_utils.matches_from_rpc(rpc1, rpc2, x, y, w, h, 5)
F = estimation.fundamental_matrix(matches_rpc)
# transform the coordinates of points in the second image according to
# matrix A, built from vector v
A = euclidean_transform_matrix(v)
p2 = common.points_apply_homography(A, matches[:, 2:4])
return evaluation.fundamental_matrix_L1(F, np.hstack([matches[:, 0:2],
p2]))
def disparity_to_ply(tile):
"""
Compute a point cloud from the disparity map of a pair of image tiles.
Args:
tile: dictionary containing the information needed to process a tile.
"""
out_dir = os.path.join(tile['dir'])
ply_file = os.path.join(out_dir, 'cloud.ply')
plyextrema = os.path.join(out_dir, 'plyextrema.txt')
x, y, w, h = tile['coordinates']
rpc1 = cfg['images'][0]['rpc']
rpc2 = cfg['images'][1]['rpc']
if os.path.exists(os.path.join(out_dir, 'stderr.log')):
print('triangulation: stderr.log exists')
print('pair_1 not processed on tile {} {}'.format(x, y))
return
if cfg['skip_existing'] and os.path.isfile(ply_file):
print('triangulation done on tile {} {}'.format(x, y))
return
print('triangulating tile {} {}...'.format(x, y))
# This function is only called when there is a single pair (pair_1)
H_ref = os.path.join(out_dir, 'pair_1', 'H_ref.txt')
H_sec = os.path.join(out_dir, 'pair_1', 'H_sec.txt')
pointing = os.path.join(cfg['out_dir'], 'global_pointing_pair_1.txt')
disp = os.path.join(out_dir, 'pair_1', 'rectified_disp.tif')
mask_rect = os.path.join(out_dir, 'pair_1', 'rectified_mask.png')
mask_orig = os.path.join(out_dir, 'cloud_water_image_domain_mask.png')
# prepare the image needed to colorize point cloud
colors = os.path.join(out_dir, 'rectified_ref.png')
if cfg['images'][0]['clr']:
hom = np.loadtxt(H_ref)
roi = [[x, y], [x + w, y], [x + w, y + h], [x, y + h]]
ww, hh = common.bounding_box2D(common.points_apply_homography(
hom, roi))[2:]
tmp = common.tmpfile('.tif')
common.image_apply_homography(tmp, cfg['images'][0]['clr'], hom,
ww + 2 * cfg['horizontal_margin'],
hh + 2 * cfg['vertical_margin'])
common.image_qauto(tmp, colors)
else:
common.image_qauto(
os.path.join(out_dir, 'pair_1', 'rectified_ref.tif'), colors)
# compute the point cloud
triangulation.disp_map_to_point_cloud(ply_file,
disp,
mask_rect,
rpc1,
rpc2,
H_ref,
H_sec,
pointing,
colors,
utm_zone=cfg['utm_zone'],
llbbx=tuple(cfg['ll_bbx']),
xybbx=(x, x + w, y, y + h),
xymsk=mask_orig)
# compute the point cloud extrema (xmin, xmax, xmin, ymax)
common.run("plyextrema %s %s" % (ply_file, plyextrema))
if cfg['clean_intermediate']:
common.remove(H_ref)
common.remove(H_sec)
common.remove(disp)
common.remove(mask_rect)
common.remove(mask_orig)
common.remove(colors)
common.remove(os.path.join(out_dir, 'pair_1', 'rectified_ref.tif'))
def local_translation_rotation(r1, r2, x, y, w, h, m):
"""
Estimates the optimal translation to minimise the relative pointing error
on a given tile.
Args:
r1, r2: two instances of the rpc_model.RPCModel class
x, y, w, h: region of interest in the reference image (r1)
m: Nx4 numpy array containing a list of matches, one per line. Each
match is given by (p1, p2, q1, q2) where (p1, p2) is a point of the
reference view and (q1, q2) is the corresponding point in the
secondary view.
Returns:
3x3 numpy array containing the homogeneous representation of the
optimal planar translation, to be applied to the secondary image in
order to correct the pointing error.
"""
# estimate the affine fundamental matrix between the two views
n = cfg['n_gcp_per_axis']
rpc_matches = rpc_utils.matches_from_rpc(r1, r2, x, y, w, h, n)
F = estimation.affine_fundamental_matrix(rpc_matches)
# Compute rectification homographies
# S1, S2 = estimation.rectifying_similarities_from_affine_fundamental_matrix(F, cfg['debug'])
hmargin = cfg['horizontal_margin']
vmargin = cfg['vertical_margin']
S1, S2, F_rect = rectification.rectification_homographies(rpc_matches, x, y, w, h, hmargin, vmargin)
N = len(m)
# Apply rectification on image 1
S1p1 = common.points_apply_homography(S1, m[:,0:2])
S1p1 = np.column_stack((S1p1,np.ones((N,1))))
print("Points 1 rectied")
print(S1p1[:10])
# Apply rectification on image 2
S2p2 = common.points_apply_homography(S1, m[:,2:4])
S2p2 = np.column_stack((S2p2, np.ones((N,1))))
print("Points 2 rectied")
print(S2p2[:10])
# Compute F in the rectified space
rect_matches = np.column_stack((S1p1[:,0:2], S2p2[:, 0:2]))
F_rect2 = estimation.affine_fundamental_matrix(rect_matches)
# Compute epipolar lines
FS1p1 = np.dot(F_rect2, S1p1.T).T
print(FS1p1[:10])
# Normalize epipolar lines
c1 = -FS1p1[:, 1]
FS1p1_norm = FS1p1/c1[:, np.newaxis]
print(FS1p1_norm[:10])
# Variable of optimization problem
A_ = np.ones((N,1))
# A_ = np.column_stack((S2p2[:,0].reshape(N, 1),np.ones((N,1))))
# b_ = S2p2[:, 1] - FS1p1_norm[:, 2]
b_ = S2p2[:, 1] - S1p1[:, 1]
t_med = np.median(b_)
print(t_med)
t_med2 = np.sort(b_)[int(N/2)]
print("t_med2", t_med2)
# min ||Ax + b||^2 => x = - (A^T A )^-1 A^T b
# X_ = - np.dot(np.linalg.inv(np.dot(A_.T, A_)), np.dot(A_.T, b_))
# [theta, t] = X_
# print(t, theta)
# t = X_[0]
# Compute epipolar lines witout recitifcation
p1 = np.column_stack((m[:,0:2],np.ones((N,1))))
Fp1 = np.dot(F, p1.T).T
# Compute normal vector to epipolar liness
ab = np.array([Fp1[0][0], Fp1[0][1]])
ab = ab/np.linalg.norm(ab)
tx = t_med*ab[0]
ty = t_med*ab[1]
print(tx, ty)
# Get translation in not rectified image
T = common.matrix_translation(0, -t_med)
T = np.linalg.inv(S2).dot(T).dot(S2)
# T = np.dot(S2_inv, T)
print(T)
theta = 0
cos_theta = np.cos(theta)
sin_theta = np.sin(theta)
A = np.array([[cos_theta, -sin_theta, tx],
[sin_theta, cos_theta, ty],
[0, 0, 1]])
return A, F
def local_translation_rectified(r1, r2, x, y, w, h, m):
"""
Estimates the optimal translation to minimise the relative pointing error
on a given tile.
Args:
r1, r2: two instances of the rpc_model.RPCModel class
x, y, w, h: region of interest in the reference image (r1)
m: Nx4 numpy array containing a list of matches, one per line. Each
match is given by (p1, p2, q1, q2) where (p1, p2) is a point of the
reference view and (q1, q2) is the corresponding point in the
secondary view.
Returns:
3x3 numpy array containing the homogeneous representation of the
optimal planar translation, to be applied to the secondary image in
order to correct the pointing error.
"""
# estimate the affine fundamental matrix between the two views
n = cfg['n_gcp_per_axis']
rpc_matches = rpc_utils.matches_from_rpc(r1, r2, x, y, w, h, n)
F = estimation.affine_fundamental_matrix(rpc_matches)
# Apply rectification on image 1
S1p1 = common.points_apply_homography(S1, m[:,0:2])
S1p1 = np.column_stack((S1p1,np.ones((N,1))))
print("Points 1 rectied")
print(S1p1[:10])
# Apply rectification on image 2
S2p2 = common.points_apply_homography(S1, m[:,2:4])
S2p2 = np.column_stack((S2p2, np.ones((N,1))))
print("Points 2 rectied")
print(S2p2[:10])
# Compute F in the rectified space
rect_matches = np.column_stack((S1p1[:,0:2], S2p2[:, 0:2]))
F_rect2 = estimation.affine_fundamental_matrix(rect_matches)
# Compute epipolar lines
FS1p1 = np.dot(F_rect2, S1p1.T).T
print(FS1p1[:10])
# Normalize epipolar lines
c1 = -FS1p1[:, 1]
FS1p1_norm = FS1p1/c1[:, np.newaxis]
print(FS1p1_norm[:10])
b_ = np.abs(S2p2[:, 1] - S1p1[:, 1])
t_med = np.median(b_)
print(t_med)
t_med2 = np.sort(b_)[int(N/2)]
print("t_med2", t_med2)
# Compute epipolar lines witout recitifcation
p1 = np.column_stack((m[:,0:2],np.ones((N,1))))
Fp1 = np.dot(F, p1.T).T
# Compute normal vector to epipolar liness
ab = np.array([Fp1[0][0], Fp1[0][1]])
ab = ab/np.linalg.norm(ab)
tx = t_med*ab[0]
ty = t_med*ab[1]
print(tx, ty)
# Get translation in not rectified image
T = common.matrix_translation(0, -t_med)
T = np.linalg.inv(S2).dot(T).dot(S2)
# T = np.dot(S2_inv, T)
print(T)
# the correction to be applied to the second view is the opposite
A = np.array([[1, 0, -out_x],
[0, 1, -out_y],
[0, 0, 1]])
return A, F
def rectify_pair(im1,
im2,
rpc1,
rpc2,
x,
y,
w,
h,
out1,
out2,
A=None,
sift_matches=None,
method='rpc',
hmargin=0,
vmargin=0):
"""
Rectify a ROI in a pair of images.
Args:
im1, im2: paths to two image files
rpc1, rpc2: paths to the two xml files containing RPC data
x, y, w, h: four integers defining the rectangular ROI in the first
image. (x, y) is the top-left corner, and (w, h) are the dimensions
of the rectangle.
out1, out2: paths to the output rectified crops
A (optional): 3x3 numpy array containing the pointing error correction
for im2. This matrix is usually estimated with the pointing_accuracy
module.
sift_matches (optional): Nx4 numpy array containing a list of sift
matches, in the full image coordinates frame
method (default: 'rpc'): option to decide wether to use rpc of sift
matches for the fundamental matrix estimation.
{h,v}margin (optional): horizontal and vertical margins added on the
sides of the rectified images
Returns:
H1, H2: Two 3x3 matrices representing the rectifying homographies that
have been applied to the two original (large) images.
disp_min, disp_max: horizontal disparity range
"""
# read RPC data
rpc1 = rpc_model.RPCModel(rpc1)
rpc2 = rpc_model.RPCModel(rpc2)
# compute real or virtual matches
if method == 'rpc':
# find virtual matches from RPC camera models
matches = rpc_utils.matches_from_rpc(rpc1, rpc2, x, y, w, h,
cfg['n_gcp_per_axis'])
# correct second image coordinates with the pointing correction matrix
if A is not None:
matches[:, 2:] = common.points_apply_homography(
np.linalg.inv(A), matches[:, 2:])
else:
matches = sift_matches
# compute rectifying homographies
H1, H2, F = rectification_homographies(matches, x, y, w, h, hmargin,
vmargin)
if cfg['register_with_shear']:
# compose H2 with a horizontal shear to reduce the disparity range
a = np.mean(rpc_utils.altitude_range(rpc1, x, y, w, h))
lon, lat, alt = rpc_utils.ground_control_points(
rpc1, x, y, w, h, a, a, 4)
x1, y1 = rpc1.inverse_estimate(lon, lat, alt)[:2]
x2, y2 = rpc2.inverse_estimate(lon, lat, alt)[:2]
m = np.vstack([x1, y1, x2, y2]).T
m = np.vstack({tuple(row)
for row in m}) # remove duplicates due to no alt range
H2 = register_horizontally_shear(m, H1, H2)
# compose H2 with a horizontal translation to center disp range around 0
if sift_matches is not None:
sift_matches = filter_matches_epipolar_constraint(
F, sift_matches, cfg['epipolar_thresh'])
if len(sift_matches) < 10:
print('WARNING: no registration with less than 10 matches')
else:
H2 = register_horizontally_translation(sift_matches, H1, H2)
# compute disparity range
if cfg['debug']:
out_dir = os.path.dirname(out1)
np.savetxt(os.path.join(out_dir, 'sift_matches_disp.txt'),
sift_matches,
fmt='%9.3f')
visualisation.plot_matches(
im1, im2, rpc1, rpc2, sift_matches, x, y, w, h,
os.path.join(out_dir, 'sift_matches_disp.png'))
disp_m, disp_M = disparity_range(rpc1, rpc2, x, y, w, h, H1, H2,
sift_matches, A)
# compute rectifying homographies for non-epipolar mode (rectify the secondary tile only)
if block_matching.rectify_secondary_tile_only(cfg['matching_algorithm']):
H1_inv = np.linalg.inv(H1)
H1 = np.eye(
3
) # H1 is replaced by 2-D array with ones on the diagonal and zeros elsewhere
H2 = np.dot(H1_inv, H2)
T = common.matrix_translation(-x + hmargin, -y + vmargin)
H1 = np.dot(T, H1)
H2 = np.dot(T, H2)
# compute output images size
roi = [[x, y], [x + w, y], [x + w, y + h], [x, y + h]]
pts1 = common.points_apply_homography(H1, roi)
x0, y0, w0, h0 = common.bounding_box2D(pts1)
# check that the first homography maps the ROI in the positive quadrant
np.testing.assert_allclose(np.round([x0, y0]), [hmargin, vmargin],
atol=.01)
# apply homographies and do the crops
common.image_apply_homography(out1, im1, H1, w0 + 2 * hmargin,
h0 + 2 * vmargin)
common.image_apply_homography(out2, im2, H2, w0 + 2 * hmargin,
h0 + 2 * vmargin)
if block_matching.rectify_secondary_tile_only(cfg['matching_algorithm']):
pts_in = [[0, 0], [disp_m, 0], [disp_M, 0]]
pts_out = common.points_apply_homography(H1_inv, pts_in)
disp_m = pts_out[1, :] - pts_out[0, :]
disp_M = pts_out[2, :] - pts_out[0, :]
return H1, H2, disp_m, disp_M
def rectify_pair(im1,
im2,
rpc1,
rpc2,
x,
y,
w,
h,
out1,
out2,
A=None,
sift_matches=None,
method='rpc',
hmargin=0,
vmargin=0):
"""
Rectify a ROI in a pair of images.
Args:
im1, im2: paths to two image files
rpc1, rpc2: paths to the two xml files containing RPC data
x, y, w, h: four integers defining the rectangular ROI in the first
image. (x, y) is the top-left corner, and (w, h) are the dimensions
of the rectangle.
out1, out2: paths to the output rectified crops
A (optional): 3x3 numpy array containing the pointing error correction
for im2. This matrix is usually estimated with the pointing_accuracy
module.
sift_matches (optional): Nx4 numpy array containing a list of sift
matches, in the full image coordinates frame
method (default: 'rpc'): option to decide wether to use rpc of sift
matches for the fundamental matrix estimation.
{h,v}margin (optional): horizontal and vertical margins added on the
sides of the rectified images
This function uses the parameter subsampling_factor from the
config module. If the factor z > 1 then the output images will
be subsampled by a factor z. The output matrices H1, H2, and the
ranges are also updated accordingly:
Hi = Z * Hi with Z = diag(1/z, 1/z, 1) and
disp_min = disp_min / z (resp _max)
Returns:
H1, H2: Two 3x3 matrices representing the rectifying homographies that
have been applied to the two original (large) images.
disp_min, disp_max: horizontal disparity range
"""
# read RPC data
rpc1 = rpc_model.RPCModel(rpc1)
rpc2 = rpc_model.RPCModel(rpc2)
# compute real or virtual matches
if method == 'rpc':
# find virtual matches from RPC camera models
matches = rpc_utils.matches_from_rpc(rpc1, rpc2, x, y, w, h,
cfg['n_gcp_per_axis'])
# correct second image coordinates with the pointing correction matrix
if A is not None:
matches[:, 2:] = common.points_apply_homography(
np.linalg.inv(A), matches[:, 2:])
else:
matches = sift_matches
# compute rectifying homographies
H1, H2, F = rectification_homographies(matches, x, y, w, h, hmargin,
vmargin)
if cfg['register_with_shear']:
# compose H2 with a horizontal shear to reduce the disparity range
a = np.mean(rpc_utils.altitude_range(rpc1, x, y, w, h))
lon, lat, alt = rpc_utils.ground_control_points(
rpc1, x, y, w, h, a, a, 4)
x1, y1 = rpc1.inverse_estimate(lon, lat, alt)[:2]
x2, y2 = rpc2.inverse_estimate(lon, lat, alt)[:2]
m = np.vstack([x1, y1, x2, y2]).T
m = np.vstack({tuple(row)
for row in m}) # remove duplicates due to no alt range
H2 = register_horizontally_shear(m, H1, H2)
# compose H2 with a horizontal translation to center disp range around 0
if sift_matches is not None:
sift_matches = filter_matches_epipolar_constraint(
F, sift_matches, cfg['epipolar_thresh'])
if len(sift_matches) < 10:
print('WARNING: no registration with less than 10 matches')
else:
H2 = register_horizontally_translation(sift_matches, H1, H2)
# compute disparity range
if cfg['debug']:
out_dir = os.path.dirname(out1)
np.savetxt(os.path.join(out_dir, 'sift_matches_disp.txt'),
sift_matches,
fmt='%9.3f')
visualisation.plot_matches(
im1, im2, rpc1, rpc2, sift_matches, x, y, w, h,
os.path.join(out_dir, 'sift_matches_disp.png'))
disp_m, disp_M = disparity_range(rpc1, rpc2, x, y, w, h, H1, H2,
sift_matches, A)
# impose a minimal disparity range (TODO this is valid only with the
# 'center' flag for register_horizontally_translation)
disp_m = min(-3, disp_m)
disp_M = max(3, disp_M)
# if subsampling_factor'] the homographies are altered to reflect the zoom
z = cfg['subsampling_factor']
if z != 1:
Z = np.diag((1 / z, 1 / z, 1))
H1 = np.dot(Z, H1)
H2 = np.dot(Z, H2)
disp_m = np.floor(disp_m / z)
disp_M = np.ceil(disp_M / z)
hmargin = int(np.floor(hmargin / z))
vmargin = int(np.floor(vmargin / z))
# compute output images size
roi = [[x, y], [x + w, y], [x + w, y + h], [x, y + h]]
pts1 = common.points_apply_homography(H1, roi)
x0, y0, w0, h0 = common.bounding_box2D(pts1)
# check that the first homography maps the ROI in the positive quadrant
np.testing.assert_allclose(np.round([x0, y0]), [hmargin, vmargin],
atol=.01)
# apply homographies and do the crops
common.image_apply_homography(out1, im1, H1, w0 + 2 * hmargin,
h0 + 2 * vmargin)
common.image_apply_homography(out2, im2, H2, w0 + 2 * hmargin,
h0 + 2 * vmargin)
return H1, H2, disp_m, disp_M
def disparity_to_ply(tile):
"""
Compute a point cloud from the disparity map of a pair of image tiles.
Args:
tile: dictionary containing the information needed to process a tile.
"""
out_dir = os.path.join(tile['dir'])
ply_file = os.path.join(out_dir, 'cloud.ply')
plyextrema = os.path.join(out_dir, 'plyextrema.txt')
x, y, w, h = tile['coordinates']
rpc1 = cfg['images'][0]['rpc']
rpc2 = cfg['images'][1]['rpc']
if os.path.exists(os.path.join(out_dir, 'stderr.log')):
print('triangulation: stderr.log exists')
print('pair_1 not processed on tile {} {}'.format(x, y))
return
if cfg['skip_existing'] and os.path.isfile(ply_file):
print('triangulation done on tile {} {}'.format(x, y))
return
print('triangulating tile {} {}...'.format(x, y))
# This function is only called when there is a single pair (pair_1)
H_ref = os.path.join(out_dir, 'pair_1', 'H_ref.txt')
H_sec = os.path.join(out_dir, 'pair_1', 'H_sec.txt')
pointing = os.path.join(cfg['out_dir'], 'global_pointing_pair_1.txt')
disp = os.path.join(out_dir, 'pair_1', 'rectified_disp.tif')
mask_rect = os.path.join(out_dir, 'pair_1', 'rectified_mask.png')
mask_orig = os.path.join(out_dir, 'cloud_water_image_domain_mask.png')
# prepare the image needed to colorize point cloud
colors = os.path.join(out_dir, 'rectified_ref.png')
if cfg['images'][0]['clr']:
hom = np.loadtxt(H_ref)
roi = [[x, y], [x+w, y], [x+w, y+h], [x, y+h]]
ww, hh = common.bounding_box2D(common.points_apply_homography(hom, roi))[2:]
tmp = common.tmpfile('.tif')
common.image_apply_homography(tmp, cfg['images'][0]['clr'], hom,
ww + 2*cfg['horizontal_margin'],
hh + 2*cfg['vertical_margin'])
common.image_qauto(tmp, colors)
else:
common.image_qauto(os.path.join(out_dir, 'pair_1', 'rectified_ref.tif'), colors)
# compute the point cloud
triangulation.disp_map_to_point_cloud(ply_file, disp, mask_rect, rpc1, rpc2,
H_ref, H_sec, pointing, colors,
utm_zone=cfg['utm_zone'],
llbbx=tuple(cfg['ll_bbx']),
xybbx=(x, x+w, y, y+h),
xymsk=mask_orig)
# compute the point cloud extrema (xmin, xmax, xmin, ymax)
common.run("plyextrema %s %s" % (ply_file, plyextrema))
if cfg['clean_intermediate']:
common.remove(H_ref)
common.remove(H_sec)
common.remove(disp)
common.remove(mask_rect)
common.remove(mask_orig)
common.remove(colors)
common.remove(os.path.join(out_dir, 'pair_1', 'rectified_ref.tif'))
def rectify_pair(im1, im2, rpc1, rpc2, x, y, w, h, out1, out2, A=None,
sift_matches=None, method='rpc', hmargin=0, vmargin=0):
"""
Rectify a ROI in a pair of images.
Args:
im1, im2: paths to two image files
rpc1, rpc2: paths to the two xml files containing RPC data
x, y, w, h: four integers defining the rectangular ROI in the first
image. (x, y) is the top-left corner, and (w, h) are the dimensions
of the rectangle.
out1, out2: paths to the output rectified crops
A (optional): 3x3 numpy array containing the pointing error correction
for im2. This matrix is usually estimated with the pointing_accuracy
module.
sift_matches (optional): Nx4 numpy array containing a list of sift
matches, in the full image coordinates frame
method (default: 'rpc'): option to decide wether to use rpc of sift
matches for the fundamental matrix estimation.
{h,v}margin (optional): horizontal and vertical margins added on the
sides of the rectified images
This function uses the parameter subsampling_factor from the
config module. If the factor z > 1 then the output images will
be subsampled by a factor z. The output matrices H1, H2, and the
ranges are also updated accordingly:
Hi = Z * Hi with Z = diag(1/z, 1/z, 1) and
disp_min = disp_min / z (resp _max)
Returns:
H1, H2: Two 3x3 matrices representing the rectifying homographies that
have been applied to the two original (large) images.
disp_min, disp_max: horizontal disparity range
"""
# read RPC data
rpc1 = rpc_model.RPCModel(rpc1)
rpc2 = rpc_model.RPCModel(rpc2)
# compute real or virtual matches
if method == 'rpc':
# find virtual matches from RPC camera models
matches = rpc_utils.matches_from_rpc(rpc1, rpc2, x, y, w, h,
cfg['n_gcp_per_axis'])
# correct second image coordinates with the pointing correction matrix
if A is not None:
matches[:, 2:] = common.points_apply_homography(np.linalg.inv(A),
matches[:, 2:])
else:
matches = sift_matches
# compute rectifying homographies
H1, H2, F = rectification_homographies(matches, x, y, w, h, hmargin, vmargin)
if cfg['register_with_shear']:
# compose H2 with a horizontal shear to reduce the disparity range
a = np.mean(rpc_utils.altitude_range(rpc1, x, y, w, h))
lon, lat, alt = rpc_utils.ground_control_points(rpc1, x, y, w, h, a, a, 4)
x1, y1 = rpc1.inverse_estimate(lon, lat, alt)[:2]
x2, y2 = rpc2.inverse_estimate(lon, lat, alt)[:2]
m = np.vstack([x1, y1, x2, y2]).T
m = np.vstack({tuple(row) for row in m}) # remove duplicates due to no alt range
H2 = register_horizontally_shear(m, H1, H2)
# compose H2 with a horizontal translation to center disp range around 0
if sift_matches is not None:
sift_matches = filter_matches_epipolar_constraint(F, sift_matches,
cfg['epipolar_thresh'])
if len(sift_matches) < 10:
print('WARNING: no registration with less than 10 matches')
else:
H2 = register_horizontally_translation(sift_matches, H1, H2)
# compute disparity range
if cfg['debug']:
out_dir = os.path.dirname(out1)
np.savetxt(os.path.join(out_dir, 'sift_matches_disp.txt'),
sift_matches, fmt='%9.3f')
visualisation.plot_matches(im1, im2, rpc1, rpc2, sift_matches, x, y, w, h,
os.path.join(out_dir, 'sift_matches_disp.png'))
disp_m, disp_M = disparity_range(rpc1, rpc2, x, y, w, h, H1, H2,
sift_matches, A)
# impose a minimal disparity range (TODO this is valid only with the
# 'center' flag for register_horizontally_translation)
disp_m = min(-3, disp_m)
disp_M = max(3, disp_M)
# compute rectifying homographies for non-epipolar mode (rectify the secondary tile only)
if block_matching.rectify_secondary_tile_only(cfg['matching_algorithm']):
H1_inv = np.linalg.inv(H1)
H1 = np.eye(3) # H1 is replaced by 2-D array with ones on the diagonal and zeros elsewhere
H2 = np.dot(H1_inv,H2)
T = common.matrix_translation(-x + hmargin, -y + vmargin)
H1 = np.dot(T, H1)
H2 = np.dot(T, H2)
# if subsampling_factor'] the homographies are altered to reflect the zoom
z = cfg['subsampling_factor']
if z != 1:
Z = np.diag((1/z, 1/z, 1))
H1 = np.dot(Z, H1)
H2 = np.dot(Z, H2)
disp_m = np.floor(disp_m / z)
disp_M = np.ceil(disp_M / z)
hmargin = int(np.floor(hmargin / z))
vmargin = int(np.floor(vmargin / z))
# compute output images size
roi = [[x, y], [x+w, y], [x+w, y+h], [x, y+h]]
pts1 = common.points_apply_homography(H1, roi)
x0, y0, w0, h0 = common.bounding_box2D(pts1)
# check that the first homography maps the ROI in the positive quadrant
np.testing.assert_allclose(np.round([x0, y0]), [hmargin, vmargin], atol=.01)
# apply homographies and do the crops
common.image_apply_homography(out1, im1, H1, w0 + 2*hmargin, h0 + 2*vmargin)
common.image_apply_homography(out2, im2, H2, w0 + 2*hmargin, h0 + 2*vmargin)
if cfg['disp_min'] is not None: disp_m = cfg['disp_min']
if cfg['disp_max'] is not None: disp_M = cfg['disp_max']
if block_matching.rectify_secondary_tile_only(cfg['matching_algorithm']):
pts_in = [[0, 0], [disp_m, 0], [disp_M, 0]]
pts_out = common.points_apply_homography(H1_inv,
pts_in)
disp_m = pts_out[1,:] - pts_out[0,:]
disp_M = pts_out[2,:] - pts_out[0,:]
return H1, H2, disp_m, disp_M
