理想滤波器，高斯滤波器，巴特沃斯滤波器的代码

以下是三种常见滤波器的示例代码：

1. 理想滤波器

import numpy as np
import cv2

def ideal_filter(img, d0):
    '''
    理想低通滤波器
    img: 输入图像
    d0: 截止频率
    '''
    # 傅里叶变换
    f = np.fft.fft2(img)
    fshift = np.fft.fftshift(f)
    # 构造理想低通滤波器
    rows, cols = img.shape
    crow, ccol = rows//2, cols//2
    mask = np.zeros((rows, cols), np.uint8)
    for i in range(rows):
        for j in range(cols):
            if np.sqrt((i-crow)**2 + (j-ccol)**2) <= d0:
                mask[i,j] = 1
    # 滤波
    fshift = fshift * mask
    f_ishift = np.fft.ifftshift(fshift)
    img_back = np.fft.ifft2(f_ishift)
    img_back = np.abs(img_back)
    return img_back.astype(np.uint8)

2. 高斯滤波器

import numpy as np
import cv2

def gaussian_filter(img, d0, sigma=1):
    '''
    高斯低通滤波器
    img: 输入图像
    d0: 截止频率
    sigma: 方差，默认为1
    '''
    # 傅里叶变换
    f = np.fft.fft2(img)
    fshift = np.fft.fftshift(f)
    # 构造高斯低通滤波器
    rows, cols = img.shape
    crow, ccol = rows//2, cols//2
    mask = np.zeros((rows, cols), np.float32)
    for i in range(rows):
        for j in range(cols):
            distance = np.sqrt((i-crow)**2 + (j-ccol)**2)
            mask[i,j] = np.exp(-distance**2 / (2*sigma**2))  # 高斯公式
    mask = 1 - mask  # 反转滤波器
    mask = mask.astype(np.float32)
    # 滤波
    fshift = fshift * mask
    f_ishift = np.fft.ifftshift(fshift)
    img_back = np.fft.ifft2(f_ishift)
    img_back = np.abs(img_back)
    return img_back.astype(np.uint8)

3. 巴特沃斯滤波器

import numpy as np
import cv2

def butterworth_filter(img, d0, n=1):
    '''
    巴特沃斯低通滤波器
    img: 输入图像
    d0: 截止频率
    n: 阶数，默认为1
    '''
    # 傅里叶变换
    f = np.fft.fft2(img)
    fshift = np.fft.fftshift(f)
    # 构造巴特沃斯低通滤波器
    rows, cols = img.shape
    crow, ccol = rows//2, cols//2
    mask = np.zeros((rows, cols), np.float32)
    for i in range(rows):
        for j in range(cols):
            distance = np.sqrt((i-crow)**2 + (j-ccol)**2)
            mask[i,j] = 1 / (1 + (distance/d0)**(2*n))  # 巴特沃斯公式
    mask = 1 - mask  # 反转滤波器
    mask = mask.astype(np.float32)
    # 滤波
    fshift = fshift * mask
    f_ishift = np.fft.ifftshift(fshift)
    img_back = np.fft.ifft2(f_ishift)
    img_back = np.abs(img_back)
    return img_back.astype(np.uint8)