数字图像处理100问—34 傅立叶变换——高通滤波

提示：内容整理自：https://github.com/gzr2017/ImageProcessing100Wen
CV小白从0开始学数字图像处理

34 傅立叶变换——高通滤波

将imori.jpg灰度化之后进行傅立叶变换并进行高通滤波，之后再用傅立叶逆变换复原！

在这里，我们使用可以去除低频部分，只保留高频部分的高通滤波器。假设从低频的中心到高频的距离为r，我们保留0.2r​的低频分量。

代码如下：

1.引入库

CV2计算机视觉库

import cv2
import numpy as np
import matplotlib.pyplot as plt

2.读入数据

img = cv2.imread("imori.jpg").astype(np.float32)
H, W, C = img.shape

3.灰度化

gray = 0.2126 * img[..., 2] + 0.7152 * img[..., 1] + 0.0722 * img[..., 0]

4.DFT

K = W
L = H
M = W
N = H

G = np.zeros((L, K), dtype=np.complex)

x = np.tile(np.arange(W), (H, 1))
y = np.arange(H).repeat(W).reshape(H, -1)

for l in range(L):
    for k in range(K):
        G[l, k] = np.sum(gray * np.exp(-2j * np.pi * (x * k / M + y * l / N))) / np.sqrt(M * N)

5.高通滤波

_G = np.zeros_like(G)
_G[:H//2, :W//2] = G[H//2:, W//2:]
_G[:H//2, W//2:] = G[H//2:, :W//2]
_G[H//2:, :W//2] = G[:H//2, W//2:]
_G[H//2:, W//2:] = G[:H//2, :W//2]
p = 0.2
_x = x - W // 2
_y = y - H // 2
r = np.sqrt(_x ** 2 + _y ** 2)
mask = np.ones((H, W), dtype=np.float32)
mask[r<(W//2*p)] = 0

_G *= mask

G[:H//2, :W//2] = _G[H//2:, W//2:]
G[:H//2, W//2:] = _G[H//2:, :W//2]
G[H//2:, :W//2] = _G[:H//2, W//2:]
G[H//2:, W//2:] = _G[:H//2, :W//2]

6.IDFT

out = np.zeros((H, W), dtype=np.float32)

for n in range(N):
    for m in range(M):
        out[n,m] = np.abs(np.sum(G * np.exp(2j * np.pi * (x * m / M + y * n / N)))) / np.sqrt(M * N)

out[out>255] = 255
out = out.astype(np.uint8)

7.保存结果

cv2.imshow("result", out)
cv2.waitKey(0)
cv2.imwrite("out.jpg", out)

8.结果