71 lines
2.2 KiB
Python
71 lines
2.2 KiB
Python
"""
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=========================
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Different perimeters
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=========================
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In this example we show the uncertainty on calculating perimeters, comparing
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classic and Crofton ones. For that, we evaluate the perimeters of a square and
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its rotated version.
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"""
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from skimage.measure import perimeter
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from skimage.measure import perimeter_crofton
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from skimage.transform import rotate
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import matplotlib.pyplot as plt
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import numpy as np
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# scale parameter can be used to increase the grid size. The resulting curves
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# should be smoothed with higer scales
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scale = 10
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# Construct 2 figures, square and disks
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square = np.zeros((100*scale, 100*scale))
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square[40*scale:60*scale, 40*scale:60*scale] = 1
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[X, Y] = np.meshgrid(np.linspace(0, 100*scale), np.linspace(0, 100*scale))
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R = 20 * scale
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disk = (X-50*scale)**2+(Y-50*scale)**2 <= R**2
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fig, axes = plt.subplots(1, 2, figsize=(8, 5))
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ax = axes.flatten()
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dX = X[0, 1] - X[0, 0]
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true_perimeters = [80 * scale, 2 * np.pi * R / dX]
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# for each type of objects, the different perimeters are evaluated
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for index, obj in enumerate([square, disk]):
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# 2 neighbourhoud configurations for measure.perimeter
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for n in [4, 6]:
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p = []
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angles = range(90)
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for i in angles:
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# rotation and perimeter evaluation
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rotated = rotate(obj, i, order=0)
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p.append(perimeter(rotated, n))
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ax[index].plot(angles, p)
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# 2 or 4 directions can be used by measure.perimeter_crofton
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for d in [2, 4]:
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p = []
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angles = np.arange(0, 90, 2)
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for i in angles:
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# rotation and perimeter evaluation
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rotated = rotate(obj, i, order=0)
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p.append(perimeter_crofton(rotated, d))
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ax[index].plot(angles, p)
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ax[index].axhline(true_perimeters[index], linestyle='--', color='k')
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ax[index].set_xlabel('Rotation angle')
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ax[index].legend(['N4 perimeter', 'N8 perimeter',
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'Crofton 2 directions', 'Crofton 4 directions',
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'Ground truth'],
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loc='best')
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ax[index].set_ylabel('Perimeter of the rotated object')
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ax[0].set_title('Square')
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ax[1].set_title('Disk')
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plt.tight_layout()
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plt.show()
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