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Michael Sarahan
86 lines
2.4 KiB
Python
86 lines
2.4 KiB
Python
"""
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=====================================
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Cross-Correlation (Phase Correlation)
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=====================================
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In this example, we use phase correlation to identify the relative shift
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between two similar-sized images.
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The ``register_translation`` function uses cross-correlation in Fourier space,
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optionally employing an upsampled matrix-multiplication DFT to achieve
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arbitrary subpixel precision. [1]_
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.. [1] Manuel Guizar-Sicairos, Samuel T. Thurman, and James R. Fienup,
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"Efficient subpixel image registration algorithms," Optics Letters 33,
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156-158 (2008).
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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from skimage import data
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from skimage.feature import register_translation
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from skimage.feature.register_translation import _upsampled_dft
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from scipy.ndimage.fourier import fourier_shift
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image = data.camera()
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shift = (-2.4, 1.32)
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# (-2.4, 1.32) pixel offset relative to reference coin
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offset_image = fourier_shift(np.fft.fftn(image), shift)
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offset_image = np.fft.ifftn(offset_image)
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print("Known offset (y, x):")
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print(shift)
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# pixel precision first
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shift, error, diffphase = register_translation(image, offset_image)
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fig, (ax1, ax2, ax3) = plt.subplots(ncols=3, figsize=(8, 3))
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ax1.imshow(image)
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ax1.set_axis_off()
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ax1.set_title('Reference image')
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ax2.imshow(offset_image.real)
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ax2.set_axis_off()
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ax2.set_title('Offset image')
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# View the output of a cross-correlation to show what the algorithm is
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# doing behind the scenes
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image_product = np.fft.fft2(image) * np.fft.fft2(offset_image).conj()
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cc_image = np.fft.fftshift(np.fft.ifft2(image_product))
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ax3.imshow(cc_image.real)
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ax3.set_axis_off()
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ax3.set_title("Cross-correlation")
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plt.show()
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print("Detected pixel offset (y, x):")
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print(shift)
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# subpixel precision
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shift, error, diffphase = register_translation(image, offset_image, 100)
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fig, (ax1, ax2, ax3) = plt.subplots(ncols=3, figsize=(8, 3))
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ax1.imshow(image)
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ax1.set_axis_off()
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ax1.set_title('Reference image')
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ax2.imshow(offset_image.real)
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ax2.set_axis_off()
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ax2.set_title('Offset image')
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# Calculate the upsampled DFT, again to show what the algorithm is doing
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# behind the scenes. Constants correspond to calculated values in routine.
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# See source code for details.
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cc_image = _upsampled_dft(image_product, 150, 100, (shift*100)+75).conj()
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ax3.imshow(cc_image.real)
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ax3.set_axis_off()
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ax3.set_title("Supersampled XC sub-area")
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plt.show()
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print("Detected subpixel offset (y, x):")
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print(shift)
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