从图像中提取 Gabor 滤波器 / 初级视觉皮层“简单细胞”

如何构建一个（生物合理的）稀疏字典（或“代码本”或“滤波器组”），例如，用于图像分类，而无需任何花哨的数学，并且仅使用标准的 python 科学库？

请在下面找到一个简短的答案 ;-)

这个简单的例子展示了如何仅使用简单的图像来获得类 Gabor 滤波器 [1]。在我们的示例中，我们使用了宇航员艾琳·柯林斯的照片。 Gabor 滤波器是对哺乳动物初级视觉皮层 (V1) 中发现的“简单细胞” [2]感受野 [3]的良好近似（有关详细信息，请参阅例如 60 年代 Hubel 和 Wiesel 获得诺贝尔奖的工作 [4] [5]）。

这里我们使用 McQueen 的 ‘kmeans’ 算法 [6]，作为一种简单的生物学上合理的赫布式学习规则，我们将其应用于 (a) 原始图像的补丁（视网膜投影），以及 (b) 使用简单的高斯差分 (DoG) 近似的类 LGN [7]图像的补丁。

享受吧 ;-) 请记住，在自然图像补丁上获得 Gabor 滤波器并不是什么高深的科学。

[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

/home/runner/work/scikit-image/scikit-image/doc/examples/features_detection/plot_gabors_from_astronaut.py:57: UserWarning:

One of the clusters is empty. Re-run kmeans with a different initialization.

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, 0.5) - 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()