基于暗通道先验的图像去雾算法解析与实现

一、算法背景

何凯明团队于2009年提出的暗通道先验去雾算法《single image haze removal using dark channel prior》，通过统计发现：在无雾图像的局部区域中，至少存在一个颜色通道的像素值趋近于零。这一发现为图像去雾提供了重要的理论依据，其数学模型可表示为：

$$I(x)=J(x)t(x)+A(1-t(x))$$

其中：

• $I(x)$：观测到的有雾图像
• $J(x)$：待恢复的无雾图像
• $t(x)$：透射率
• $A$：全局大气光值
  

二、算法原理

1. 暗通道计算

通过取RGB三通道最小值并进行形态学腐蚀操作：

def dark_channel(img, size=15):
    r, g, b = cv2.split(img)
    min_img = cv2.min(r, cv2.min(g, b))
    kernel = cv2.getStructuringElement(cv2.MORPH_RECT, (size, size))
    return cv2.erode(min_img, kernel)

2. 大气光估计

选取图像中最亮像素的0.1%作为大气光值：

def get_atmo(img, percent=0.001):
    mean_perpix = np.mean(img, axis=2).reshape(-1)
    mean_topper = mean_perpix[:int(img.shape[0] * img.shape[1] * percent)]
    return np.mean(mean_topper)

3. 透射率估计

$$t(x)=1-\omega \cdot dark\_channel\left(\frac{I}{A}\right)$$

def get_trans(img, atom, w=0.95):
    x = img / atom
    return 1 - w * dark_channel(x, 7)

4. 引导滤波优化

使用灰度图作为引导图像进行透射率优化：

# 引导滤波
def guided_filter(p, i, r, e):
    """
    :param p: input image
    :param i: guidance image
    :param r: radius
    :param e: regularization
    :return: filtering output q
    """
    # 1
    mean_I = cv2.boxFilter(i, cv2.CV_64F, (r, r))
    mean_p = cv2.boxFilter(p, cv2.CV_64F, (r, r))
    corr_I = cv2.boxFilter(i * i, cv2.CV_64F, (r, r))
    corr_Ip = cv2.boxFilter(i * p, cv2.CV_64F, (r, r))
    # 2
    var_I = corr_I - mean_I * mean_I
    cov_Ip = corr_Ip - mean_I * mean_p
    # 3
    a = cov_Ip / (var_I + e)
    b = mean_p - a * mean_I
    # 4
    mean_a = cv2.boxFilter(a, cv2.CV_64F, (r, r))
    mean_b = cv2.boxFilter(b, cv2.CV_64F, (r, r))
    # 5
    q = mean_a * i + mean_b
    return q

三、完整实现代码

import cv2
import numpy as np
import os


# 计算雾化图像的暗通道
def dark_channel(img, size=15):
    r, g, b = cv2.split(img)
    min_img = cv2.min(r, cv2.min(g, b))  # 取最暗通道
    kernel = cv2.getStructuringElement(cv2.MORPH_RECT, (size, size))
    dc_img = cv2.erode(min_img, kernel)
    return dc_img


# 估计全局大气光值
def get_atmo(img, percent=0.001):
    mean_perpix = np.mean(img, axis=2).reshape(-1)
    mean_topper = mean_perpix[:int(img.shape[0] * img.shape[1] * percent)]
    return np.mean(mean_topper)


# 估算透射率图
def get_trans(img, atom, w=0.95):
    x = img / atom
    t = 1 - w * dark_channel(x, 15)
    return t


# 引导滤波
def guided_filter(p, i, r, e):
    """
    :param p: input image
    :param i: guidance image
    :param r: radius
    :param e: regularization
    :return: filtering output q
    """
    # 1
    mean_I = cv2.boxFilter(i, cv2.CV_64F, (r, r))
    mean_p = cv2.boxFilter(p, cv2.CV_64F, (r, r))
    corr_I = cv2.boxFilter(i * i, cv2.CV_64F, (r, r))
    corr_Ip = cv2.boxFilter(i * p, cv2.CV_64F, (r, r))
    # 2
    var_I = corr_I - mean_I * mean_I
    cov_Ip = corr_Ip - mean_I * mean_p
    # 3
    a = cov_Ip / (var_I + e)
    b = mean_p - a * mean_I
    # 4
    mean_a = cv2.boxFilter(a, cv2.CV_64F, (r, r))
    mean_b = cv2.boxFilter(b, cv2.CV_64F, (r, r))
    # 5
    q = mean_a * i + mean_b
    return q


def dehaze(im):
    img = im.astype('float64') / 255
    img_gray = cv2.cvtColor(im, cv2.COLOR_BGR2GRAY).astype('float64') / 255
    atom = get_atmo(img)
    trans = get_trans(img, atom)
    trans_guided = guided_filter(trans, img_gray, 20, 0.0001)
    trans_guided = cv2.max(trans_guided, 0.25)
    result = np.empty_like(img)
    for i in range(3):
        result[:, :, i] = (img[:, :, i] - atom) / trans_guided + atom
    return result * 255


if __name__ == '__main__':
    image_path= 'images/img.png'
    im = cv2.imread(image_path)
    img = im.astype('float64') / 255
    img_gray = cv2.cvtColor(im, cv2.COLOR_BGR2GRAY).astype('float64') / 255
    atom = get_atmo(img)
    trans = get_trans(img, atom)
    trans_guided = guided_filter(trans, img_gray, 10, 0.0001)
    trans_guided = cv2.max(trans_guided, 0.25)
    result = np.empty_like(img)
    for i in range(3):
        result[:, :, i] = (img[:, :, i] - atom) / trans_guided + atom
    cv2.imwrite('images/img.png', result * 255)