Python加权中值滤波器异常：未滤除椒盐噪声反而色彩校正

我尝试在Python中实现加权中值滤波器，发现该滤波器并未滤除我添加到原始图像中的椒盐噪声，反而对整幅图像进行了色彩校正。以下是我的实现代码及运行结果：

import numpy as np
from skimage import io
from matplotlib import pyplot as plt


def add_zg_impuls(img, ratio):
    H, W, ch = img.shape
    length = int(H*W*ch*ratio)
    lin = np.random.randint(0, H, length)
    col = np.random.randint(0, W, length)
    val = np.random.randint(0, 2, length)
    img_impuls = img.copy()
    for i in range(length):
        img_impuls[lin[i], col[i], np.random.randint(0, 3)] = 255 * val[i]
    return img_impuls


def apply_L_filter(img, size, weights):
    h, w,c = img.shape
    cap = size // 2
    new_img = np.zeros_like(img)
   
    for i in range(cap, h - cap):
        for j in range(cap, w - cap):
            for canal in range(c):
                vec = img[i-cap:i+cap+1, j-cap:j+cap+1, canal]
                values = np.reshape(vec, size*size)
                sorted_values = np.sort(values)
                weighted_values = sorted_values * weights.flatten()
                new_img[i, j, canal] = np.sum(weighted_values)
    
    return new_img

image = io.imread("tiffany.bmp")
plt.figure(), plt.imshow(image), plt.title("原始图像"), plt.show()

image_noise= add_zg_impuls(image,0.1)
plt.figure(), plt.imshow(image_noise), plt.title("添加10%椒盐噪声后的图像"), plt.show()

filter_size = 5
filter_weights = np.array([[1, 1, 1, 1, 1], [1, 2, 2, 2, 1], [1, 2, 3, 2, 1], [1, 2, 2, 2, 1], [1, 1, 1, 1, 1]])

filtered_image = apply_L_filter(image_noise, filter_size, filter_weights)
plt.figure(), plt.imshow(filtered_image), plt.title("加权滤波后的图像"), plt.show()

运行结果如图：

问题原因 #

当前的apply_L_filter函数并非加权中值滤波，而是加权求和的线性滤波：你将排序后的像素值与权重相乘后求和，这本质是类似高斯模糊的平滑操作，线性滤波无法有效抑制椒盐噪声——噪声值会被加权平均到周围像素，导致图像模糊而非去除噪声。

正确的加权中值滤波实现 #

加权中值滤波的核心逻辑是：给邻域内每个像素赋予权重，等效于将该像素值重复对应权重次数，然后取这个扩展序列的中值；或者找到排序后累计权重超过总权重一半的那个值。

修正后的代码如下：

import numpy as np
from skimage import io
from matplotlib import pyplot as plt


def add_zg_impuls(img, ratio):
    H, W, ch = img.shape
    length = int(H*W*ch*ratio)
    lin = np.random.randint(0, H, length)
    col = np.random.randint(0, W, length)
    val = np.random.randint(0, 2, length)
    img_impuls = img.copy()
    for i in range(length):
        img_impuls[lin[i], col[i], np.random.randint(0, 3)] = 255 * val[i]
    return img_impuls


def apply_weighted_median_filter(img, size, weights):
    h, w, c = img.shape
    cap = size // 2
    new_img = np.zeros_like(img)
    # 计算总权重
    total_weight = np.sum(weights)
    # 扁平化权重
    flat_weights = weights.flatten()
    
    for i in range(cap, h - cap):
        for j in range(cap, w - cap):
            for canal in range(c):
                # 获取当前邻域的像素值
                vec = img[i-cap:i+cap+1, j-cap:j+cap+1, canal]
                values = vec.flatten()
                # 按权重扩展像素序列后取中值
                expanded = np.repeat(values, flat_weights)
                median_val = np.median(expanded)
                new_img[i, j, canal] = median_val
    
    return new_img

image = io.imread("tiffany.bmp")
plt.figure(), plt.imshow(image), plt.title("原始图像"), plt.show()

image_noise= add_zg_impuls(image,0.1)
plt.figure(), plt.imshow(image_noise), plt.title("添加10%椒盐噪声后的图像"), plt.show()

filter_size = 5
filter_weights = np.array([[1, 1, 1, 1, 1], [1, 2, 2, 2, 1], [1, 2, 3, 2, 1], [1, 2, 2, 2, 1], [1, 1, 1, 1, 1]])

filtered_image = apply_weighted_median_filter(image_noise, filter_size, filter_weights)
plt.figure(), plt.imshow(filtered_image), plt.title("加权中值滤波后的图像"), plt.show()

优化说明 #

若邻域较大，np.repeat生成大数组会影响效率，可改用累计权重的方式直接定位中值位置：

# 替代np.repeat的高效实现
sorted_indices = np.argsort(values)
sorted_values = values[sorted_indices]
sorted_weights = flat_weights[sorted_indices]
cum_weights = np.cumsum(sorted_weights)
median_idx = np.argmax(cum_weights >= total_weight / 2)
median_val = sorted_values[median_idx]

内容的提问来源于stack exchange，提问作者Camelia Birlea