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fixe index errors and improve setup of some matrices

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This commit is contained in:
Johannes Schönberger
2012-07-15 15:47:11 +02:00
committed by Johannes Schönberger
parent 33a7ddec0e
commit fdf1b6dac1
1 changed files with 38 additions and 51 deletions
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skimage/transform/geometric.py
+38 -51
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@@ -35,8 +35,8 @@ def _make_similarity(src, dst):
X = a0*x - b0*y + a1
Y = b0*x + a0*y + a2
where the homogeneous transformation matrix is:
[[a1 -b1 a0]
[b1 a1 b0]
[[a0 -b0 a1]
[b0 a0 b1]
[0 0 1]]
"""
xs = src[:,0]
@@ -45,32 +45,27 @@ def _make_similarity(src, dst):
yd = dst[:,1]
rows = src.shape[0]
#: params: a0, a1, b0, b1
A = np.zeros((rows*2, 4))
b = np.zeros((rows*2,))
A[:rows,0] = xs
A[:rows,2] = - ys
A[:rows,1] = 1
A[rows:,2] = xs
A[rows:,0] = ys
A[rows:,3] = 1
b[:rows] = xd
b[rows:] = yd
b = np.hstack([xd, yd])
a0, a1, b0, b1 = np.linalg.lstsq(A, b)[0]
matrix = np.eye(3)
matrix[0,0] = a0
matrix[0,1] = - b0
matrix[0,2] = a1
matrix[1,0] = b0
matrix[1,1] = a0
matrix[1,2] = b1
matrix = np.array([[a0, -b0, a1],
[b0, a0, b1],
[ 0, 0, 1]])
return matrix
def _make_affine(src, dst):
"""Determine parameters of the 2D affine transformation:
X = a0*x + a1*y + a3
Y = b0*x + b1*y + b3
X = a0*x + a1*y + a2
Y = b0*x + b1*y + b2
where the homogeneous transformation matrix is:
[[a0 a1 a2]
[b0 b1 b2]
@@ -82,9 +77,8 @@ def _make_affine(src, dst):
yd = dst[:,1]
rows = src.shape[0]
#: params: a0, a1, a2, b0, b1, b2
A = np.zeros((rows*2, 6))
b = np.zeros((rows*2,))
A[:rows,0] = xs
A[:rows,1] = ys
A[:rows,2] = 1
@@ -92,22 +86,22 @@ def _make_affine(src, dst):
A[rows:,4] = ys
A[rows:,5] = 1
b[:rows] = xd
b[rows:] = yd
b = np.hstack([xd, yd])
params = np.linalg.lstsq(A, b)[0]
matrix = np.eye(3)
matrix[:2,:] = params.reshape((2, 3))
a0, a1, a2, b0, b1, b2 = np.linalg.lstsq(A, b)[0]
matrix = np.array([[a0, a1, a2],
[b0, b1, b2],
[0, 0, 1]])
return matrix
def _make_projective(src, dst):
"""Determine transformation matrix of the 2D projective transformation:
X = (a0 + a1*x + a2*y) / (c0*x + c1*y + c3)
Y = (b0 + b1*x + b2*y) / (c0*x + c1*y + c3)
X = (a0 + a1*x + a2*y) / (c0*x + c1*y + 1)
Y = (b0 + b1*x + b2*y) / (c0*x + c1*y + 1)
where the homogeneous transformation matrix is:
[[a0 a1 a2]
[b0 b1 b2]
[c0 c1 c3]]
[c0 c1 1]]
"""
xs = src[:,0]
ys = src[:,1]
@@ -115,10 +109,8 @@ def _make_projective(src, dst):
yd = dst[:,1]
rows = src.shape[0]
#: params: a0, a1, a2, b0, b1, b2, c0, c1
A = np.zeros((rows*2, 8))
b = np.zeros((rows*2,))
A[:rows,0] = xs
A[:rows,1] = ys
A[:rows,2] = 1
@@ -129,12 +121,14 @@ def _make_projective(src, dst):
A[rows:,5] = 1
A[rows:,6] = - yd * xs
A[rows:,7] = - yd * ys
b[:rows] = dst[:,0]
b[rows:] = dst[:,1]
matrix = np.eye(3).flatten()
matrix[:8] = np.linalg.lstsq(A, b)[0]
return matrix.reshape((3, 3))
b = np.hstack([xd, yd])
a0, a1, a2, b0, b1, b2, c0, c1 = np.linalg.lstsq(A, b)[0]
matrix = np.array([[a0, a1, a2],
[b0, b1, b2],
[c0, c1, 1]])
return matrix
def _make_polynomial(src, dst, order):
"""Determine parameters of 2D polynomial transformation of order n:
@@ -149,17 +143,16 @@ def _make_polynomial(src, dst, order):
# number of unknown polynomial coefficients
u = (order + 1) * (order + 2)
A = np.zeros((rows*2, u))
b = np.zeros((rows*2,))
A = np.zeros((rows*2, u))
pidx = 0
for j in xrange(order+1):
for i in xrange(j+1):
A[:rows,pidx] = xs ** (j - i) * ys ** i
A[rows:,pidx+u/2] = xs ** (j - i) * ys ** i
pidx += 1
b[:rows] = xd
b[rows:] = yd
b = np.hstack([xd, yd])
return np.linalg.lstsq(A, b)[0]
@@ -171,8 +164,8 @@ def _make_rotation(angle):
"""
R = [
[math.cos(angle), -math.sin(angle), 0],
[math.sin(angle), math.cos(angle), 0],
[0, 0, 1],
[math.sin(angle), math.cos(angle), 0],
[0, 0, 1],
]
return np.array(R)
@@ -180,8 +173,9 @@ def _transform(coords, matrix):
src = np.vstack((coords[:,0], coords[:,1], np.ones((coords.shape[0],))))
dst = np.dot(src.transpose(), matrix.transpose())
# rescale to homogeneous coordinates
dst[:,0] *= 1 / dst[:,2]
dst[:,1] *= 1 / dst[:,2]
dst[:,0] /= dst[:,2]
dst[:,1] /= dst[:,2]
# values close to zero because of limited numerical precision
dst[np.abs(dst) < EPS] = 0
return dst[:,:2]
@@ -334,10 +328,6 @@ def warp(image, reverse_map=None, map_args={}, tform=None,
coordinates in the *source image*. Also see examples below.
map_args : dict, optional
Keyword arguments passed to `reverse_map`.
tform : :class:`Transformation` object
The inverse transformation will be used to transform coordinates in the
*output image* into their corresponding coordinates in the
*source image*.
output_shape : tuple (rows, cols)
Shape of the output image generated.
order : int
@@ -385,10 +375,7 @@ def warp(image, reverse_map=None, map_args={}, tform=None,
# Map each (x, y) pair to the source image according to
# the user-provided mapping
if callable(reverse_map):
tf_coords = reverse_map(tf_coords, **map_args)
else:
tf_coords = tform.inv(tf_coords)
tf_coords = reverse_map(tf_coords, **map_args)
# Reshape back to a (2, M, N) coordinate grid
tf_coords = tf_coords.T.reshape((-1, cols, rows)).swapaxes(1, 2)
@@ -564,5 +551,5 @@ def homography(image, H, output_shape=None, order=1,
category=DeprecationWarning)
tform = make_tform('projective', matrix=H)
return warp(image, tform=tform, output_shape=output_shape, order=order,
mode=mode, cval=cval)
return warp(image, reverse_map=tform.inv, output_shape=output_shape,
order=order, mode=mode, cval=cval)