def test_slow_warp_nonint_oshape():
image = np.random.rand(5, 5)
with pytest.raises(ValueError):
warp(image, lambda xy: xy, output_shape=(13.1, 19.5))
warp(image, lambda xy: xy, output_shape=(13.0001, 19.9999))
def test_warp_tform():
x = np.zeros((5, 5), dtype=np.double)
x[2, 2] = 1
theta = -np.pi / 2
tform = SimilarityTransform(scale=1, rotation=theta, translation=(0, 4))
x90 = warp(x, tform, order=1)
assert_array_almost_equal(x90, np.rot90(x))
x90 = warp(x, tform.inverse, order=1)
assert_array_almost_equal(x90, np.rot90(x))
def test_bool_nonzero_order_errors(order):
img = np.zeros((10, 10), dtype=bool)
with pytest.raises(ValueError):
rescale(img, 0.5, order=order)
with pytest.raises(ValueError):
resize(img, (5, 5), order=order)
with pytest.raises(ValueError):
warp(img, np.eye(3), order=order)
def test_warp_identity():
img = img_as_float(rgb2gray(astronaut()))
assert len(img.shape) == 2
assert np.allclose(img, warp(img, AffineTransform(rotation=0)))
assert not np.allclose(img, warp(img, AffineTransform(rotation=0.1)))
rgb_img = np.transpose(np.asarray([img, np.zeros_like(img), img]),
(1, 2, 0))
warped_rgb_img = warp(rgb_img, AffineTransform(rotation=0.1))
assert np.allclose(rgb_img, warp(rgb_img, AffineTransform(rotation=0)))
assert not np.allclose(rgb_img, warped_rgb_img)
# assert no cross-talk between bands
assert np.all(0 == warped_rgb_img[:, :, 1])
def test_warp_matrix():
x = np.zeros((5, 5), dtype=np.double)
x[2, 2] = 1
refx = np.zeros((5, 5), dtype=np.double)
refx[1, 1] = 1
matrix = np.array([[1, 0, 1], [0, 1, 1], [0, 0, 1]])
# _warp_fast
outx = warp(x, matrix, order=1)
assert_array_almost_equal(outx, refx)
# check for ndimage.map_coordinates
outx = warp(x, matrix, order=5)
def test_zero_image_size():
with pytest.raises(ValueError):
warp(np.zeros(0), SimilarityTransform())
with pytest.raises(ValueError):
warp(np.zeros((0, 10)), SimilarityTransform())
with pytest.raises(ValueError):
warp(np.zeros((10, 0)), SimilarityTransform())
with pytest.raises(ValueError):
warp(np.zeros((10, 10, 0)), SimilarityTransform())
def test_bool_array_warnings():
img = np.zeros((10, 10), dtype=bool)
with expected_warnings(['Input image dtype is bool']):
rescale(img, 0.5, anti_aliasing=True)
with expected_warnings(['Input image dtype is bool']):
resize(img, (5, 5), anti_aliasing=True)
with expected_warnings(['Input image dtype is bool']):
rescale(img, 0.5, order=1)
with expected_warnings(['Input image dtype is bool']):
resize(img, (5, 5), order=1)
with expected_warnings(['Input image dtype is bool']):
warp(img, np.eye(3), order=1)
def test_homography():
x = np.zeros((5, 5), dtype=np.double)
x[1, 1] = 1
theta = -np.pi / 2
M = np.array([[np.cos(theta), -np.sin(theta), 0],
[np.sin(theta), np.cos(theta), 4], [0, 0, 1]])
x90 = warp(x, inverse_map=ProjectiveTransform(M).inverse, order=1)
assert_array_almost_equal(x90, np.rot90(x))
def applyTransformationOnIma(self, ima2):
if not self.transfMat:
self._findTransformationMatrix()
alignedIma = warp(ima2,
ProjectiveTransform(matrix=self.transfMat),
output_shape=ima2.shape,
order=3,
mode='constant',
cval=np.median(ima2.data))
return CCDData(alignedIma, unit=ima2.unit)
def test_warp_callable():
x = np.zeros((5, 5), dtype=np.double)
x[2, 2] = 1
refx = np.zeros((5, 5), dtype=np.double)
refx[1, 1] = 1
def shift(xy):
return xy + 1
outx = warp(x, shift, order=1)
assert_array_almost_equal(outx, refx)
def test_warp_nd():
for dim in range(2, 8):
shape = dim * (5, )
x = np.zeros(shape, dtype=np.double)
x_c = dim * (2, )
x[x_c] = 1
refx = np.zeros(shape, dtype=np.double)
refx_c = dim * (1, )
refx[refx_c] = 1
coord_grid = dim * (slice(0, 5, 1), )
coords = np.array(np.mgrid[coord_grid]) + 1
outx = warp(x, coords, order=0, cval=0)
assert_array_almost_equal(outx, refx)
def test_warp_clip_cval_not_used(order):
# Test that clipping does not consider cval part of the input range if it
# is not used in the output image
x = np.ones((15, 15), dtype=np.float64)
x[5:-5, 5:-5] = 2
# Transform the image by stretching it out by one pixel on each side so
# that cval will not actually be used
transform = AffineTransform(scale=15/(15+2), translation=(1, 1))
with expected_warnings(['Bi-quadratic.*bug'] if order == 2 else None):
outx = warp(x, transform, mode='constant', order=order, cval=0,
clip=True)
# At higher orders of interpolation, the transformed image has overshoots
# beyond the input range that should be clipped to the range 1 to 2. Even
# though cval=0, the minimum value of the clipped output image should be
# 1 and not affected by the unused cval.
assert_array_almost_equal(outx.min(), 1)
def test_inverse():
tform = SimilarityTransform(scale=0.5, rotation=0.1)
inverse_tform = SimilarityTransform(matrix=np.linalg.inv(tform.params))
image = np.arange(10 * 10).reshape(10, 10).astype(np.double)
assert_array_equal(warp(image, inverse_tform), warp(image, tform.inverse))
def test_invalid():
with pytest.raises(ValueError):
warp(np.ones((4, 3, 3, 3)), SimilarityTransform())
def test_const_cval_out_of_range():
img = np.random.randn(100, 100)
cval = -10
warped = warp(img, AffineTransform(translation=(10, 10)), cval=cval)
assert np.sum(warped == cval) == (2 * 100 * 10 - 10 * 10)
def radon(image, theta=None):
"""
Calculates the radon transform of an image given specified
projection angles.
Parameters
----------
image : array_like
Input image. The rotation axis will be located in the pixel with
indices ``(image.shape[0] // 2, image.shape[1] // 2)``.
theta : array_like, optional
Projection angles (in degrees). If `None`, the value is set to
np.arange(180).
circle : boolean, optional
Assume image is zero outside the inscribed circle, making the
width of each projection (the first dimension of the sinogram)
equal to ``min(image.shape)``.
preserve_range : bool, optional
Whether to keep the original range of values. Otherwise, the input
image is converted according to the conventions of `img_as_float`.
Also see https://scikit-image.org/docs/dev/user_guide/data_types.html
Returns
-------
radon_image : ndarray
Radon transform (sinogram). The tomography rotation axis will lie
at the pixel index ``radon_image.shape[0] // 2`` along the 0th
dimension of ``radon_image``.
References
----------
.. [1] AC Kak, M Slaney, "Principles of Computerized Tomographic
Imaging", IEEE Press 1988.
.. [2] B.R. Ramesh, N. Srinivasa, K. Rajgopal, "An Algorithm for Computing
the Discrete Radon Transform With Some Applications", Proceedings of
the Fourth IEEE Region 10 International Conference, TENCON '89, 1989
Notes
-----
Based on code of Justin K. Romberg
(https://www.clear.rice.edu/elec431/projects96/DSP/bpanalysis.html)
"""
image = convert_to_float(image, None)
theta = np.linspace(0., 180., max(image.shape), endpoint=False)
with tf.compat.v1.Session() as sess:
diagonal = tf.sqrt(2.0) * max(image.shape)
pad = [tf.dtypes.cast(tf.math.ceil(diagonal - s), tf.int32) for s in image.shape]
new_center = [(s + p) // 2 for s, p in zip(image.shape, pad)]
old_center = [s // 2 for s in image.shape]
pad_before = [nc - oc for oc, nc in zip(old_center, new_center)]
pad_width = [(pb, p - pb) for pb, p in zip(pad_before, pad)]
padded_image = tf.pad(image, pad_width, mode='constant', constant_values=0)
# padded_image is always square
if padded_image.shape[0] != padded_image.shape[1]:
raise ValueError('padded_image must be a square')
center = padded_image.shape[0] // 2
radon_image = np.zeros((padded_image.shape[0], len(theta)))
# convert degree to radian
for i, angle in enumerate(np.deg2rad(theta)):
cos_a, sin_a = tf.math.cos(angle), tf.math.sin(angle)
R = tf.Variable(list([[cos_a, sin_a, -center * (cos_a + sin_a - 1)],
[-sin_a, cos_a, -center * (cos_a - sin_a - 1)],
[0, 0, 1]]))
init_op = tf.compat.v1.global_variables_initializer()
sess.run(init_op)
rotated = wp.warp(padded_image.eval(), R.eval(), clip=False)
# update transformed image
radon_image[:, i] = rotated.sum(0)
return radon_image