def filter_matches_epipolar_constraint(F, matches, thresh):
"""
Discards matches that are not consistent with the epipolar constraint.
Args:
F: fundamental matrix
matches: list of pairs of 2D points, stored as a Nx4 numpy array
thresh: maximum accepted distance between a point and its matched
epipolar line
Returns:
the list of matches that satisfy the constraint. It is a sub-list of
the input list.
"""
out = []
mask = np.zeros((len(matches), 1)) # for debug only
for i in range(len(matches)):
x = np.array([matches[i, 0], matches[i, 1], 1])
xx = np.array([matches[i, 2], matches[i, 3], 1])
l = np.dot(F.T, xx)
ll = np.dot(F, x)
d1 = evaluation.distance_point_to_line(x, l)
d2 = evaluation.distance_point_to_line(xx, ll)
d = max(d1, d2)
if (d < thresh):
out.append(matches[i, :])
mask[i] = 1 # for debug only
# for debug only
np.savetxt('%s/sift_F_msk' % cfg['temporary_dir'], mask, '%d')
return np.array(out)
def filter_matches_epipolar_constraint(F, matches, thresh):
"""
Discards matches that are not consistent with the epipolar constraint.
Args:
F: fundamental matrix
matches: list of pairs of 2D points, stored as a Nx4 numpy array
thresh: maximum accepted distance between a point and its matched
epipolar line
Returns:
the list of matches that satisfy the constraint. It is a sub-list of
the input list.
"""
out = []
if not matches.size:
return np.array(out)
for i in range(len(matches)):
x = np.array([matches[i, 0], matches[i, 1], 1])
xx = np.array([matches[i, 2], matches[i, 3], 1])
l = np.dot(F.T, xx)
ll = np.dot(F, x)
d1 = evaluation.distance_point_to_line(x, l)
d2 = evaluation.distance_point_to_line(xx, ll)
d = max(d1, d2)
if (d < thresh):
out.append(matches[i, :])
return np.array(out)
def test_infinite_distances():
x = np.array([1, 1, 0])
l = np.array([0, 1, 0])
assert_equals(evaluation.distance_point_to_line(x, l), np.finfo(float).max)
x = np.array([1, 1, -7])
l = np.array([0, 0, 2.3])
assert_equals(evaluation.distance_point_to_line(x, l), np.finfo(float).max)
def test_infinite_distances():
x = np.array([1, 1, 0])
l = np.array([0, 1, 0])
assert_equals(evaluation.distance_point_to_line(x, l), np.finfo(float).max)
x = np.array([1, 1, -7])
l = np.array([0, 0, 2.3])
assert_equals(evaluation.distance_point_to_line(x, l), np.finfo(float).max)
def filter_matches_epipolar_constraint(F, matches, thresh):
"""
Discards matches that are not consistent with the epipolar constraint.
Args:
F: fundamental matrix
matches: list of pairs of 2D points, stored as a Nx4 numpy array
thresh: maximum accepted distance between a point and its matched
epipolar line
Returns:
the list of matches that satisfy the constraint. It is a sub-list of
the input list.
"""
out = []
if not matches.size:
return np.array(out)
for i in range(len(matches)):
x = np.array([matches[i, 0], matches[i, 1], 1])
xx = np.array([matches[i, 2], matches[i, 3], 1])
l = np.dot(F.T, xx)
ll = np.dot(F, x)
d1 = evaluation.distance_point_to_line(x, l)
d2 = evaluation.distance_point_to_line(xx, ll)
d = max(d1, d2)
if (d < thresh):
out.append(matches[i, :])
return np.array(out)
def test_finite_distances():
x = np.array([1, 1, 1])
l = np.array([0, 1, 0])
assert_equals(evaluation.distance_point_to_line(x, l), 1)
x = np.array([-1, -1, -1])
l = np.array([0, 1, 0])
assert_equals(evaluation.distance_point_to_line(x, l), 1)
x = np.array([1, 1, 1])
l = np.array([3, 2, -1])
assert_equals(evaluation.distance_point_to_line(x, l), 4 / np.sqrt(13))
def test_finite_distances():
x = np.array([1, 1, 1])
l = np.array([0, 1, 0])
assert_equals(evaluation.distance_point_to_line(x, l), 1)
x = np.array([-1, -1, -1])
l = np.array([0, 1, 0])
assert_equals(evaluation.distance_point_to_line(x, l), 1)
x = np.array([1, 1, 1])
l = np.array([3, 2, -1])
assert_equals(evaluation.distance_point_to_line(x, l), 4/np.sqrt(13))
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 filter_matches_epipolar_constraint(F, matches, thresh):
"""
Discards matches that are not consistent with the epipolar constraint.
Args:
F: fundamental matrix
matches: list of pairs of 2D points, stored as a Nx4 numpy array
thresh: maximum accepted distance between a point and its matched
epipolar line
Returns:
the list of matches that satisfy the constraint. It is a sub-list of
the input list.
"""
out = []
for match in matches:
x = np.array([match[0], match[1], 1])
xx = np.array([match[2], match[3], 1])
d1 = evaluation.distance_point_to_line(x, np.dot(F.T, xx))
d2 = evaluation.distance_point_to_line(xx, np.dot(F, x))
if max(d1, d2) < thresh:
out.append(match)
return np.array(out)
def filter_matches_epipolar_constraint(F, matches, thresh):
"""
Discards matches that are not consistent with the epipolar constraint.
Args:
F: fundamental matrix
matches: list of pairs of 2D points, stored as a Nx4 numpy array
thresh: maximum accepted distance between a point and its matched
epipolar line
Returns:
the list of matches that satisfy the constraint. It is a sub-list of
the input list.
"""
out = []
for match in matches:
x = np.array([match[0], match[1], 1])
xx = np.array([match[2], match[3], 1])
d1 = evaluation.distance_point_to_line(x, np.dot(F.T, xx))
d2 = evaluation.distance_point_to_line(xx, np.dot(F, x))
if max(d1, d2) < thresh:
out.append(match)
return np.array(out)
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)
