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Johannes Schönberger
91 lines
3.3 KiB
Python
91 lines
3.3 KiB
Python
"""
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=======================================================
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Gabors / Primary Visual Cortex "Simple Cells" from Lena
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=======================================================
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How to build a (bio-plausible) "sparse" dictionary (or 'codebook', or
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'filterbank') for e.g. image classification without any fancy math and
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with just standard python scientific libraries?
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Please find below a short answer ;-)
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This simple example shows how to get Gabor-like filters [1]_ using just
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the famous Lena image. Gabor filters are good approximations of the
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"Simple Cells" [2]_ receptive fields [3]_ found in the mammalian primary
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visual cortex (V1) (for details, see e.g. the Nobel-prize winning work
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of Hubel & Wiesel done in the 60s [4]_ [5]_).
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Here we use McQueen's 'kmeans' algorithm [6]_, as a simple biologically
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plausible hebbian-like learning rule and we apply it (a) to patches of
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the original Lena image (retinal projection), and (b) to patches of an
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LGN-like [7]_ Lena image using a simple difference of gaussians (DoG)
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approximation.
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Enjoy ;-) And keep in mind that getting Gabors on natural image patches
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is not rocket science.
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.. [1] http://en.wikipedia.org/wiki/Gabor_filter
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.. [2] http://en.wikipedia.org/wiki/Simple_cell
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.. [3] http://en.wikipedia.org/wiki/Receptive_field
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.. [4] http://en.wikipedia.org/wiki/K-means_clustering
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.. [5] http://en.wikipedia.org/wiki/Lateral_geniculate_nucleus
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.. [6] D. H. Hubel and T. N., Wiesel Receptive Fields of Single Neurones
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in the Cat's Striate Cortex, J. Physiol. pp. 574-591 (148) 1959
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.. [7] D. H. Hubel and T. N., Wiesel Receptive Fields, Binocular
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Interaction, and Functional Architecture in the Cat's Visual Cortex,
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J. Physiol. 160 pp. 106-154 1962
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"""
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import numpy as np
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from scipy.cluster.vq import kmeans2
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from scipy import ndimage as ndi
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import matplotlib.pyplot as plt
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from skimage import data
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from skimage import color
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from skimage.util.shape import view_as_windows
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from skimage.util.montage import montage2d
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np.random.seed(42)
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patch_shape = 8, 8
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n_filters = 49
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lena = color.rgb2gray(data.lena())
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# -- filterbank1 on original Lena
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patches1 = view_as_windows(lena, patch_shape)
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patches1 = patches1.reshape(-1, patch_shape[0] * patch_shape[1])[::8]
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fb1, _ = kmeans2(patches1, n_filters, minit='points')
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fb1 = fb1.reshape((-1,) + patch_shape)
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fb1_montage = montage2d(fb1, rescale_intensity=True)
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# -- filterbank2 LGN-like Lena
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lena_dog = ndi.gaussian_filter(lena, .5) - ndi.gaussian_filter(lena, 1)
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patches2 = view_as_windows(lena_dog, patch_shape)
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patches2 = patches2.reshape(-1, patch_shape[0] * patch_shape[1])[::8]
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fb2, _ = kmeans2(patches2, n_filters, minit='points')
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fb2 = fb2.reshape((-1,) + patch_shape)
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fb2_montage = montage2d(fb2, rescale_intensity=True)
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# --
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fig, axes = plt.subplots(2, 2, figsize=(7, 6))
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ax0, ax1, ax2, ax3 = axes.ravel()
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ax0.imshow(lena, cmap=plt.cm.gray)
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ax0.set_title("Lena (original)")
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ax1.imshow(fb1_montage, cmap=plt.cm.gray, interpolation='nearest')
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ax1.set_title("K-means filterbank (codebook)\non Lena (original)")
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ax2.imshow(lena_dog, cmap=plt.cm.gray)
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ax2.set_title("Lena (LGN-like DoG)")
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ax3.imshow(fb2_montage, cmap=plt.cm.gray, interpolation='nearest')
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ax3.set_title("K-means filterbank (codebook)\non Lena (LGN-like DoG)")
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for ax in axes.ravel():
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ax.axis('off')
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fig.subplots_adjust(hspace=0.3)
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plt.show()
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