利用高斯差分实现带通滤波

带通滤波器会衰减感兴趣范围(频段)之外的信号频率。在图像分析中，它们可以用来对图像进行去噪，同时减少光照不均匀等低频伪影。带通滤光片可用于查找斑点和边缘等图像特征。

将带通滤波应用于图像的一种方法是从较不模糊的图像中减去用高斯核模糊的图像。这个例子展示了高斯差分方法在带通滤波中的两个应用。

对图像进行去噪并减少阴影

import matplotlib.pyplot as plt
import numpy as np
from skimage.data import gravel
from skimage.filters import difference_of_gaussians, window
from scipy.fftpack import fftn, fftshift

image = gravel()
wimage = image * window('hann', image.shape)  # window image to improve FFT
filtered_image = difference_of_gaussians(image, 1, 12)
filtered_wimage = filtered_image * window('hann', image.shape)
im_f_mag = fftshift(np.abs(fftn(wimage)))
fim_f_mag = fftshift(np.abs(fftn(filtered_wimage)))

fig, ax = plt.subplots(nrows=2, ncols=2, figsize=(8, 8))
ax[0, 0].imshow(image, cmap='gray')
ax[0, 0].set_title('Original Image')
ax[0, 1].imshow(np.log(im_f_mag), cmap='magma')
ax[0, 1].set_title('Original FFT Magnitude (log)')
ax[1, 0].imshow(filtered_image, cmap='gray')
ax[1, 0].set_title('Filtered Image')
ax[1, 1].imshow(np.log(fim_f_mag), cmap='magma')
ax[1, 1].set_title('Filtered FFT Magnitude (log)')
plt.show()

增强图像中的边缘

from skimage.data import camera

image = camera()
wimage = image * window('hann', image.shape)  # window image to improve FFT
filtered_image = difference_of_gaussians(image, 1.5)
filtered_wimage = filtered_image * window('hann', image.shape)
im_f_mag = fftshift(np.abs(fftn(wimage)))
fim_f_mag = fftshift(np.abs(fftn(filtered_wimage)))

fig, ax = plt.subplots(nrows=2, ncols=2, figsize=(8, 8))
ax[0, 0].imshow(image, cmap='gray')
ax[0, 0].set_title('Original Image')
ax[0, 1].imshow(np.log(im_f_mag), cmap='magma')
ax[0, 1].set_title('Original FFT Magnitude (log)')
ax[1, 0].imshow(filtered_image, cmap='gray')
ax[1, 0].set_title('Filtered Image')
ax[1, 1].imshow(np.log(fim_f_mag), cmap='magma')
ax[1, 1].set_title('Filtered FFT Magnitude (log)')
plt.show()