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.
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
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
/home/travis/venv/lib/python3.7/site-packages/scipy/cluster/vq.py:579: UserWarning: One of the clusters is empty. Re-run kmeans with a different initialization. warnings.warn("One of the clusters is empty. "
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 * patch_shape)[::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 * patch_shape)[::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.imshow(astro, cmap=plt.cm.gray) ax.set_title("Image (original)") ax.imshow(fb1_montage, cmap=plt.cm.gray) ax.set_title("K-means filterbank (codebook)\non original image") ax.imshow(astro_dog, cmap=plt.cm.gray) ax.set_title("Image (LGN-like DoG)") ax.imshow(fb2_montage, cmap=plt.cm.gray) ax.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 1.197 seconds)