opencv 畫出各種濾波器二維圖像 證明拉普拉斯濾波器是一個高通濾波器

實驗：
將濾波器模板，利用傅里葉變換，轉換到頻域內，將低頻中心由圖像左上角轉換到圖像中心。顯示濾波器模板圖像。
從拉普拉斯濾波器模板圖像中，可以看出，中心部分爲黑色，阻止了低頻信息通過，外圍爲白色，通過了高頻信息。所以拉普拉斯濾波器是一個高通濾波器。

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()