实验：
将滤波器模板，利用傅里叶变换，转换到频域内，将低频中心由图像左上角转换到图像中心。显示滤波器模板图像。
从拉普拉斯滤波器模板图像中，可以看出，中心部分为黑色，阻止了低频信息通过，外围为白色，通过了高频信息。所以拉普拉斯滤波器是一个高通滤波器。
import cv2 as cv
import numpy as np
from matplotlib import pyplot as plt
# simple averaging filter without scaling parameter
mean_filter = np.ones((3,3))
# creating a gaussian filter
x = cv.getGaussianKernel(5,10)
gaussian = x*x.T
# different edge detecting filters
# scharr in x-direction
scharr = np.array([[-3, 0, 3],
[-10,0,10],
[-3, 0, 3]])
# sobel in x direction
sobel_x= np.array([[-1, 0, 1],
[-2, 0, 2],
[-1, 0, 1]])
# sobel in y direction
sobel_y= np.array([[-1,-2,-1],
[0, 0, 0],
[1, 2, 1]])
# laplacian
laplacian=np.array([[0, 1, 0],
[1,-4, 1],
[0, 1, 0]])
filters = [mean_filter, gaussian, laplacian, sobel_x, sobel_y, scharr]
filter_name = ['mean_filter', 'gaussian','laplacian', 'sobel_x', \
'sobel_y', 'scharr_x']
fft_filters = [np.fft.fft2(x) for x in filters]
fft_shift = [np.fft.fftshift(y) for y in fft_filters]
mag_spectrum = [np.log(np.abs(z)+1) for z in fft_shift]
for i in range(6):
plt.subplot(2,3,i+1),plt.imshow(mag_spectrum[i],cmap = 'gray')
plt.title(filter_name[i]), plt.xticks([]), plt.yticks([])
plt.show()
各种滤波器模板图像
