plot_gabors_from_astronaut.py

"""
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Gabors / Primary Visual Cortex "Simple Cells" from an Image
============================================================

How to build a (bio-plausible) *sparse* dictionary (or 'codebook', or
'filterbank') for e.g. image classification without any fancy math and
with just standard python scientific libraries?

Please find below a short answer ;-)

This simple example shows how to get Gabor-like filters [1]_ using just
a simple image. In our example, we use a photograph of the astronaut Eileen
Collins. Gabor filters are good approximations of the "Simple Cells" [2]_
receptive fields [3]_ found in the mammalian primary visual cortex (V1)
(for details, see e.g. the Nobel-prize winning work of Hubel & Wiesel done
in the 60s [4]_ [5]_).

Here we use McQueen's 'kmeans' algorithm [6]_, as a simple biologically
plausible hebbian-like learning rule and we apply it (a) to patches of
the original image (retinal projection), and (b) to patches of an
LGN-like [7]_ image using a simple difference of gaussians (DoG)
approximation.

Enjoy ;-) And keep in mind that getting Gabors on natural image patches
is not rocket science.

.. [1] https://en.wikipedia.org/wiki/Gabor_filter
.. [2] https://en.wikipedia.org/wiki/Simple_cell
.. [3] https://en.wikipedia.org/wiki/Receptive_field
.. [4] D. H. Hubel and T. N., Wiesel Receptive Fields of Single Neurones
       in the Cat's Striate Cortex, J. Physiol. pp. 574-591 (148) 1959
.. [5] D. H. Hubel and T. N., Wiesel Receptive Fields, Binocular
       Interaction, and Functional Architecture in the Cat's Visual Cortex,
       J. Physiol. 160 pp.  106-154 1962
.. [6] https://en.wikipedia.org/wiki/K-means_clustering
.. [7] https://en.wikipedia.org/wiki/Lateral_geniculate_nucleus
"""
import numpy as np
from scipy.cluster.vq import kmeans2
from scipy import ndimage as ndi
import matplotlib.pyplot as plt

from skimage import data
from skimage import color
from skimage.util.shape import view_as_windows
from skimage.util import montage

np.random.seed(42)

patch_shape = 8, 8
n_filters = 49

astro = color.rgb2gray(data.astronaut())

# -- filterbank1 on original image
patches1 = view_as_windows(astro, patch_shape)
patches1 = patches1.reshape(-1, patch_shape[0] * patch_shape[1])[::8]
fb1, _ = kmeans2(patches1, n_filters, minit='points')
fb1 = fb1.reshape((-1,) + patch_shape)
fb1_montage = montage(fb1, rescale_intensity=True)

# -- filterbank2 LGN-like image
astro_dog = ndi.gaussian_filter(astro, .5) - ndi.gaussian_filter(astro, 1)
patches2 = view_as_windows(astro_dog, patch_shape)
patches2 = patches2.reshape(-1, patch_shape[0] * patch_shape[1])[::8]
fb2, _ = kmeans2(patches2, n_filters, minit='points')
fb2 = fb2.reshape((-1,) + patch_shape)
fb2_montage = montage(fb2, rescale_intensity=True)

# -- plotting
fig, axes = plt.subplots(2, 2, figsize=(7, 6))
ax = axes.ravel()

ax[0].imshow(astro, cmap=plt.cm.gray)
ax[0].set_title("Image (original)")

ax[1].imshow(fb1_montage, cmap=plt.cm.gray, interpolation='nearest')
ax[1].set_title("K-means filterbank (codebook)\non original image")

ax[2].imshow(astro_dog, cmap=plt.cm.gray)
ax[2].set_title("Image (LGN-like DoG)")

ax[3].imshow(fb2_montage, cmap=plt.cm.gray, interpolation='nearest')
ax[3].set_title("K-means filterbank (codebook)\non LGN-like DoG image")

for a in ax.ravel():
    a.axis('off')

fig.tight_layout()
plt.show()