mirror of
https://github.com/wassname/scikit-image.git
synced 2026-06-28 22:21:06 +08:00
Jostein Bø Fløystad
302 lines
11 KiB
Python
302 lines
11 KiB
Python
from __future__ import print_function
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from __future__ import division
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import numpy as np
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from numpy.testing import assert_raises
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import itertools
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from skimage.transform import radon, iradon
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from skimage.io import imread
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from skimage import data_dir
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__PHANTOM = imread(data_dir + "/phantom.png", as_grey=True)[::2, ::2]
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def _get_phantom():
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return __PHANTOM
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def _debug_plot(original, result, sinogram=None):
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from matplotlib import pyplot as plt
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imkwargs = dict(cmap='gray', interpolation='nearest')
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if sinogram is None:
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plt.figure(figsize=(15, 6))
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sp = 130
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else:
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plt.figure(figsize=(11, 11))
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sp = 221
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plt.subplot(sp + 0)
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plt.imshow(sinogram, aspect='auto', **imkwargs)
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plt.subplot(sp + 1)
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plt.imshow(original, **imkwargs)
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plt.subplot(sp + 2)
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plt.imshow(result, vmin=original.min(), vmax=original.max(), **imkwargs)
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plt.subplot(sp + 3)
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plt.imshow(result - original, **imkwargs)
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plt.colorbar()
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plt.show()
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def rescale(x):
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x = x.astype(float)
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x -= x.min()
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x /= x.max()
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return x
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def check_radon_center(shape, circle):
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# Create a test image with only a single non-zero pixel at the origin
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image = np.zeros(shape, dtype=np.float)
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image[(shape[0] // 2, shape[1] // 2)] = 1.
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# Calculate the sinogram
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theta = np.linspace(0., 180., max(shape), endpoint=False)
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sinogram = radon(image, theta=theta, circle=circle)
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# The sinogram should be a straight, horizontal line
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sinogram_max = np.argmax(sinogram, axis=0)
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print(sinogram_max)
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assert np.std(sinogram_max) < 1e-6
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def test_radon_center():
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shapes = [(16, 16), (17, 17)]
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circles = [False, True]
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for shape, circle in itertools.product(shapes, circles):
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yield check_radon_center, shape, circle
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rectangular_shapes = [(32, 16), (33, 17)]
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for shape in rectangular_shapes:
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yield check_radon_center, shape, False
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def check_iradon_center(size, theta, circle):
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debug = False
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# Create a test sinogram corresponding to a single projection
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# with a single non-zero pixel at the rotation center
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if circle:
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sinogram = np.zeros((size, 1), dtype=np.float)
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sinogram[size // 2, 0] = 1.
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else:
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diagonal = int(np.ceil(np.sqrt(2) * size))
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sinogram = np.zeros((diagonal, 1), dtype=np.float)
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sinogram[sinogram.shape[0] // 2, 0] = 1.
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maxpoint = np.unravel_index(np.argmax(sinogram), sinogram.shape)
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print('shape of generated sinogram', sinogram.shape)
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print('maximum in generated sinogram', maxpoint)
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# Compare reconstructions for theta=angle and theta=angle + 180;
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# these should be exactly equal
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reconstruction = iradon(sinogram, theta=[theta], circle=circle)
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reconstruction_opposite = iradon(sinogram, theta=[theta + 180],
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circle=circle)
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print('rms deviance:',
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np.sqrt(np.mean((reconstruction_opposite - reconstruction)**2)))
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if debug:
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import matplotlib.pyplot as plt
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imkwargs = dict(cmap='gray', interpolation='nearest')
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plt.figure()
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plt.subplot(221)
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plt.imshow(sinogram, **imkwargs)
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plt.subplot(222)
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plt.imshow(reconstruction_opposite - reconstruction, **imkwargs)
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plt.subplot(223)
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plt.imshow(reconstruction, **imkwargs)
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plt.subplot(224)
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plt.imshow(reconstruction_opposite, **imkwargs)
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plt.show()
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assert np.allclose(reconstruction, reconstruction_opposite)
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def test_iradon_center():
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sizes = [16, 17]
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thetas = [0, 90]
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circles = [False, True]
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for size, theta, circle in itertools.product(sizes, thetas, circles):
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yield check_iradon_center, size, theta, circle
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def check_radon_iradon(interpolation_type, filter_type):
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debug = False
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image = _get_phantom()
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reconstructed = iradon(radon(image), filter=filter_type,
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interpolation=interpolation_type)
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delta = np.mean(np.abs(image - reconstructed))
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print('\n\tmean error:', delta)
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if debug:
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_debug_plot(image, reconstructed)
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if filter_type == 'ramp':
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if interpolation_type == 'linear':
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allowed_delta = 0.02
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else:
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allowed_delta = 0.03
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else:
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allowed_delta = 0.05
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assert delta < allowed_delta
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def test_radon_iradon():
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filter_types = ["ramp", "shepp-logan", "cosine", "hamming", "hann"]
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interpolation_types = ["linear", "nearest"]
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for interpolation_type, filter_type in \
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itertools.product(interpolation_types, filter_types):
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yield check_radon_iradon, interpolation_type, filter_type
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def test_iradon_angles():
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"""
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Test with different number of projections
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"""
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size = 100
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# Synthetic data
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image = np.tri(size) + np.tri(size)[::-1]
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# Large number of projections: a good quality is expected
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nb_angles = 200
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radon_image_200 = radon(image, theta=np.linspace(0, 180, nb_angles,
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endpoint=False))
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reconstructed = iradon(radon_image_200)
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delta_200 = np.mean(abs(rescale(image) - rescale(reconstructed)))
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assert delta_200 < 0.03
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# Lower number of projections
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nb_angles = 80
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radon_image_80 = radon(image, theta=np.linspace(0, 180, nb_angles,
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endpoint=False))
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# Test whether the sum of all projections is approximately the same
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s = radon_image_80.sum(axis=0)
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assert np.allclose(s, s[0], rtol=0.01)
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reconstructed = iradon(radon_image_80)
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delta_80 = np.mean(abs(image / np.max(image) -
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reconstructed / np.max(reconstructed)))
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# Loss of quality when the number of projections is reduced
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assert delta_80 > delta_200
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def check_radon_iradon_minimal(shape, slices):
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debug = False
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theta = np.arange(180)
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image = np.zeros(shape, dtype=np.float)
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image[slices] = 1.
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sinogram = radon(image, theta)
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reconstructed = iradon(sinogram, theta)
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print('\n\tMaximum deviation:', np.max(np.abs(image - reconstructed)))
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if debug:
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_debug_plot(image, reconstructed, sinogram)
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if image.sum() == 1:
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assert (np.unravel_index(np.argmax(reconstructed), image.shape)
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== np.unravel_index(np.argmax(image), image.shape))
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def test_radon_iradon_minimal():
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shapes = [(3, 3), (4, 4), (5, 5)]
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for shape in shapes:
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c0, c1 = shape[0] // 2, shape[1] // 2
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coordinates = itertools.product((c0 - 1, c0, c0 + 1),
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(c1 - 1, c1, c1 + 1))
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for coordinate in coordinates:
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yield check_radon_iradon_minimal, shape, coordinate
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def test_reconstruct_with_wrong_angles():
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a = np.zeros((3, 3))
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p = radon(a, theta=[0, 1, 2])
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iradon(p, theta=[0, 1, 2])
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assert_raises(ValueError, iradon, p, theta=[0, 1, 2, 3])
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def _random_circle(shape):
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# Synthetic random data, zero outside reconstruction circle
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np.random.seed(98312871)
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image = np.random.rand(*shape)
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c0, c1 = np.ogrid[0:shape[0], 0:shape[1]]
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r = np.sqrt((c0 - shape[0] // 2)**2 + (c1 - shape[1] // 2)**2)
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radius = min(shape) // 2
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image[r >= radius] = 0.
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return image
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def test_radon_circle():
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a = np.ones((10, 10))
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assert_raises(ValueError, radon, a, circle=True)
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# Synthetic data, circular symmetry
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shape = (61, 79)
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c0, c1 = np.ogrid[0:shape[0], 0:shape[1]]
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r = np.sqrt((c0 - shape[0] // 2)**2 + (c1 - shape[1] // 2)**2)
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radius = min(shape) // 2
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image = np.clip(radius - r, 0, np.inf)
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image = rescale(image)
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angles = np.linspace(0, 180, min(shape), endpoint=False)
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sinogram = radon(image, theta=angles, circle=True)
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assert np.all(sinogram.std(axis=1) < 1e-2)
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# Synthetic data, random
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image = _random_circle(shape)
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sinogram = radon(image, theta=angles, circle=True)
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mass = sinogram.sum(axis=0)
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average_mass = mass.mean()
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relative_error = np.abs(mass - average_mass) / average_mass
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print(relative_error.max(), relative_error.mean())
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assert np.all(relative_error < 3e-3)
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def check_sinogram_circle_to_square(size):
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from skimage.transform.radon_transform import _sinogram_circle_to_square
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image = _random_circle((size, size))
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theta = np.linspace(0., 180., size, False)
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sinogram_circle = radon(image, theta, circle=True)
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argmax_shape = lambda a: np.unravel_index(np.argmax(a), a.shape)
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print('\n\targmax of circle:', argmax_shape(sinogram_circle))
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sinogram_square = radon(image, theta, circle=False)
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print('\targmax of square:', argmax_shape(sinogram_square))
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sinogram_circle_to_square = _sinogram_circle_to_square(sinogram_circle)
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print('\targmax of circle to square:',
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argmax_shape(sinogram_circle_to_square))
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error = abs(sinogram_square - sinogram_circle_to_square)
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print(np.mean(error), np.max(error))
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assert (argmax_shape(sinogram_square)
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== argmax_shape(sinogram_circle_to_square))
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def test_sinogram_circle_to_square():
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for size in (50, 51):
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yield check_sinogram_circle_to_square, size
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def check_radon_iradon_circle(interpolation, shape, output_size):
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# Forward and inverse radon on synthetic data
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image = _random_circle(shape)
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radius = min(shape) // 2
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sinogram_rectangle = radon(image, circle=False)
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reconstruction_rectangle = iradon(sinogram_rectangle,
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output_size=output_size,
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interpolation=interpolation,
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circle=False)
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sinogram_circle = radon(image, circle=True)
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reconstruction_circle = iradon(sinogram_circle,
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output_size=output_size,
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interpolation=interpolation,
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circle=True)
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# Crop rectangular reconstruction to match circle=True reconstruction
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width = reconstruction_circle.shape[0]
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excess = int(np.ceil((reconstruction_rectangle.shape[0] - width) / 2))
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s = np.s_[excess:width + excess, excess:width + excess]
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reconstruction_rectangle = reconstruction_rectangle[s]
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# Find the reconstruction circle, set reconstruction to zero outside
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c0, c1 = np.ogrid[0:width, 0:width]
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r = np.sqrt((c0 - width // 2)**2 + (c1 - width // 2)**2)
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reconstruction_rectangle[r >= radius] = 0.
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print(reconstruction_circle.shape)
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print(reconstruction_rectangle.shape)
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np.allclose(reconstruction_rectangle, reconstruction_circle)
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def test_radon_iradon_circle():
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shape = (61, 79)
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interpolations = ('nearest', 'linear')
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output_sizes = (None, min(shape), max(shape), 97)
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for interpolation, output_size in itertools.product(interpolations,
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output_sizes):
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yield check_radon_iradon_circle, interpolation, shape, output_size
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if __name__ == "__main__":
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from numpy.testing import run_module_suite
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run_module_suite()
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