def test_radon_dtype():
img = convert_to_float(PHANTOM, False)
img32 = img.astype(np.float32)
assert radon(img).dtype == img.dtype
assert radon(img32).dtype == img32.dtype
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