用于纹理分类的 Gabor 滤波器组

在本例中，我们将了解如何基于 Gabor 滤波器组对纹理进行分类。Gabor 滤波器的频率和方向表示类似于人类视觉系统。

使用各种不同的 Gabor 滤波器核心的实部对图像进行滤波。然后将滤波图像的均值和方差用作分类的特征，为简单起见，分类基于最小二乘误差。

Rotated images matched against references using Gabor filter banks:
original: brick, rotated: 30deg, match result: brick
original: brick, rotated: 70deg, match result: brick
original: grass, rotated: 145deg, match result: brick

import matplotlib.pyplot as plt
import numpy as np
from scipy import ndimage as ndi

from skimage import data
from skimage.util import img_as_float
from skimage.filters import gabor_kernel


def compute_feats(image, kernels):
    feats = np.zeros((len(kernels), 2), dtype=np.double)
    for k, kernel in enumerate(kernels):
        filtered = ndi.convolve(image, kernel, mode='wrap')
        feats[k, 0] = filtered.mean()
        feats[k, 1] = filtered.var()
    return feats


def match(feats, ref_feats):
    min_error = np.inf
    min_i = None
    for i in range(ref_feats.shape[0]):
        error = np.sum((feats - ref_feats[i, :]) ** 2)
        if error < min_error:
            min_error = error
            min_i = i
    return min_i


# prepare filter bank kernels
kernels = []
for theta in range(4):
    theta = theta / 4.0 * np.pi
    for sigma in (1, 3):
        for frequency in (0.05, 0.25):
            kernel = np.real(
                gabor_kernel(frequency, theta=theta, sigma_x=sigma, sigma_y=sigma)
            )
            kernels.append(kernel)


shrink = (slice(0, None, 3), slice(0, None, 3))
brick = img_as_float(data.brick())[shrink]
grass = img_as_float(data.grass())[shrink]
gravel = img_as_float(data.gravel())[shrink]
image_names = ('brick', 'grass', 'gravel')
images = (brick, grass, gravel)

# prepare reference features
ref_feats = np.zeros((3, len(kernels), 2), dtype=np.double)
ref_feats[0, :, :] = compute_feats(brick, kernels)
ref_feats[1, :, :] = compute_feats(grass, kernels)
ref_feats[2, :, :] = compute_feats(gravel, kernels)

print('Rotated images matched against references using Gabor filter banks:')

print('original: brick, rotated: 30deg, match result: ', end='')
feats = compute_feats(ndi.rotate(brick, angle=190, reshape=False), kernels)
print(image_names[match(feats, ref_feats)])

print('original: brick, rotated: 70deg, match result: ', end='')
feats = compute_feats(ndi.rotate(brick, angle=70, reshape=False), kernels)
print(image_names[match(feats, ref_feats)])

print('original: grass, rotated: 145deg, match result: ', end='')
feats = compute_feats(ndi.rotate(grass, angle=145, reshape=False), kernels)
print(image_names[match(feats, ref_feats)])


def power(image, kernel):
    # Normalize images for better comparison.
    image = (image - image.mean()) / image.std()
    return np.sqrt(
        ndi.convolve(image, np.real(kernel), mode='wrap') ** 2
        + ndi.convolve(image, np.imag(kernel), mode='wrap') ** 2
    )


# Plot a selection of the filter bank kernels and their responses.
results = []
kernel_params = []
for theta in (0, 1):
    theta = theta / 4.0 * np.pi
    for frequency in (0.1, 0.4):
        kernel = gabor_kernel(frequency, theta=theta)
        params = f"theta={theta * 180 / np.pi},\nfrequency={frequency:.2f}"
        kernel_params.append(params)
        # Save kernel and the power image for each image
        results.append((kernel, [power(img, kernel) for img in images]))

fig, axes = plt.subplots(nrows=5, ncols=4, figsize=(5, 6))
plt.gray()

fig.suptitle('Image responses for Gabor filter kernels', fontsize=12)

axes[0][0].axis('off')

# Plot original images
for label, img, ax in zip(image_names, images, axes[0][1:]):
    ax.imshow(img)
    ax.set_title(label, fontsize=9)
    ax.axis('off')

for label, (kernel, powers), ax_row in zip(kernel_params, results, axes[1:]):
    # Plot Gabor kernel
    ax = ax_row[0]
    ax.imshow(np.real(kernel))
    ax.set_ylabel(label, fontsize=7)
    ax.set_xticks([])
    ax.set_yticks([])

    # Plot Gabor responses with the contrast normalized for each filter
    vmin = np.min(powers)
    vmax = np.max(powers)
    for patch, ax in zip(powers, ax_row[1:]):
        ax.imshow(patch, vmin=vmin, vmax=vmax)
        ax.axis('off')

plt.show()