Note
Go to the end to download the full example code or to run this example in your browser via JupyterLite or Binder
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.
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
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)
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)
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()
Total running time of the script: ( 0 minutes 0.000 seconds)
