引导滤波(GuidedFilter)原理及C++实现
写在前面
引导滤波是何恺明读博士的时候提出来的一种去噪保边算法，很有名。作者其主页上给出了该算法的Matlab实现和原文。而且他提出的基于暗通道去雾算法技惊四座，获CVPR2009最佳论文（膜拜），近几年在CV领域的成果也相当丰硕，关于他的研究动态，可以访问http://kaiminghe.com/。
优点：
1、应用面很广、很广；
2、能够克服双边滤波的梯度翻转现象，在滤波后图像的细节上更优；
3、最重要的优点，快，效率高，时间复杂度为O(N)，N是像素个数，也就是说与掩膜窗口尺寸无关了，我们知道传统双边滤波效率是很低的。还有更快的Fast Guide Filter：https://arxiv.org/abs/1505.00996
应用：图像增强、图像融合、图像去雾、图像去噪、羽化、美颜、三维重建等等。
如果你仅仅只是需要运用这个算法，现在opencv 3.0和MATLAB 14都已经添加了guided filter的API，可以直接调用。
opencv中的API如下void cv::ximgproc::guidedFilter()，具体的可以参考opencv的帮助文档关于导向滤波的介绍guidedFilter。
但是需要提醒的是，opencv中guidedFilter()函数包含在ximgproc模块下，但是从官方下载的标准的opencv.exe程序中并不包含该模块，需要分别下载opencv的source文件和contrib模块的source文件，然后自己编译，具体可以参考opencv3.1.0+contrib模块编译总结。
原理
说实话，引导滤波的理论还是蛮深的，不容易讲清楚，我这小菜鸡看了原文，还看了很多博客，也是一知半解。好在作者在原文中给出了伪代码，程序实现起来比较简单，我基于OpenCV写了一个，经过测试，和作者的Matlab实现效果是一样的。
为了不误导读者，还是等我自己完全搞明白了，再详细写原理。这里就推荐几个原理写的好的博客吧：
1、https://www.cnblogs.com/riddick/p/8367591.html
2、白马负金羁-导向滤波(Guided Filter)的解析与实现
3、https://www.cnblogs.com/yzl050819/p/7515250.html
伪代码：
基于OpenCV的C++实现
实现分为两种：灰度图作为引导图、彩色图作为引导图，值得说明的是：两种实现的滤波图像都只能对单通道图像进行处理。若需要处理彩色图像，在main中只需将图像split，然后对各个通道分别滤波，最后merge就可以了。作者还在原文中指出，用彩色图作为引导图能更好地保持边缘细节，我后面的效果也确实印证了这一点。
灰度图作为引导图（main中可以处理彩色图像）
#include
#include
#include
#include //
// GUIDEDFILTER O(1) time implementation of guided filter.
// -guidance image : I(should be a gray - scale / single channel image)
// -filtering input image : p(should be a gray - scale / single channel image)
// -local window radius : r
// -regularization parameter : eps
/
cv::Mat GuidedFilter(cv::Mat& I, cv::Mat& p, int r, double eps){int wsize = 2 * r + 1;//数据类型转换I.convertTo(I, CV_64F, 1.0 / 255.0);p.convertTo(p, CV_64F, 1.0 / 255.0);//meanI=fmean(I)cv::Mat mean_I;cv::boxFilter(I, mean_I, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波//meanP=fmean(P)cv::Mat mean_p;cv::boxFilter(p, mean_p, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波//corrI=fmean(I.*I)cv::Mat mean_II;mean_II = I.mul(I);cv::boxFilter(mean_II, mean_II, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波//corrIp=fmean(I.*p)cv::Mat mean_Ip;mean_Ip = I.mul(p);cv::boxFilter(mean_Ip, mean_Ip, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波//varI=corrI-meanI.*meanIcv::Mat var_I, mean_mul_I;mean_mul_I=mean_I.mul(mean_I);cv::subtract(mean_II, mean_mul_I, var_I);//covIp=corrIp-meanI.*meanpcv::Mat cov_Ip;cv::subtract(mean_Ip, mean_I.mul(mean_p), cov_Ip);//a=conIp./(varI+eps)//b=meanp-a.*meanIcv::Mat a, b;cv::divide(cov_Ip, (var_I+eps),a);cv::subtract(mean_p, a.mul(mean_I), b);//meana=fmean(a)//meanb=fmean(b)cv::Mat mean_a, mean_b;cv::boxFilter(a, mean_a, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波cv::boxFilter(b, mean_b, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波//q=meana.*I+meanbcv::Mat q;q = mean_a.mul(I) + mean_b;//数据类型转换I.convertTo(I, CV_8U, 255);p.convertTo(p, CV_8U, 255);q.convertTo(q, CV_8U, 255);return q;}int main(){cv::Mat src = cv::imread("I:\\Learning-and-Practice\\2019Change\\Image process algorithm\\Img\\woman.jpg");if (src.empty()){return -1;}//if (src.channels() > 1) // cv::cvtColor(src, src, CV_RGB2GRAY);//自编GuidedFilter测试double t2 = (double)cv::getTickCount(); //测时间cv::Mat dst1, src_input, I;src.copyTo(src_input);if (src.channels() > 1)cv::cvtColor(src, I, CV_RGB2GRAY); //若引导图为彩色图，则转为灰度图std::vector p,q;if (src.channels() > 1){ //输入为彩色图cv::split(src_input, p);for (int i = 0; i < src.channels(); ++i){dst1 = GuidedFilter(I, p[i], 9, 0.1*0.1);q.push_back(dst1);}cv::merge(q, dst1);}else{ //输入为灰度图src.copyTo(I);dst1 = GuidedFilter(I, src_input, 9, 0.1*0.1);}t2 = (double)cv::getTickCount() - t2;double time2 = (t2 *1000.) / ((double)cv::getTickFrequency());std::cout << "MyGuidedFilter_process=" << time2 << " ms. " << std::endl << std::endl;cv::namedWindow("GuidedImg", CV_WINDOW_NORMAL);cv::imshow("GuidedImg", I);cv::namedWindow("src", CV_WINDOW_NORMAL);cv::imshow("src", src);cv::namedWindow("GuidedFilter_box", CV_WINDOW_NORMAL);cv::imshow("GuidedFilter_box", dst1);cv::waitKey(0);}
效果(核半径=9，eps=0.1*0.1)
引导图 输入图 结果图
引导图 输入图 结果图
彩色图作为引导图（只能处理单通道图像）
#include
#include
#include
#include ///
// GUIDEDFILTER_COLOR O(1) time implementation of guided filter using a color image as the guidance.
//
// -guidance image : I(should be a color(RGB) image)
// -filtering input image : p(should be a gray - scale / single channel image)
// -local window radius : r
// -regularization parameter : eps
///
cv::Mat GuidedFilter_Color(cv::Mat& I, cv::Mat& p, int r, double eps ){int wsize = 2 * r + 1;//数据类型转换I.convertTo(I, CV_64F, 1.0 / 255.0);p.convertTo(p, CV_64F, 1.0 / 255.0);//引导图通道分离if (I.channels() == 1){std::cout<<"I should be a color(RGB) image "< rgb;cv::split(I, rgb);//meanI=fmean(I)cv::Mat mean_I_r, mean_I_g, mean_I_b;cv::boxFilter(rgb[0], mean_I_b, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波cv::boxFilter(rgb[1], mean_I_g, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波cv::boxFilter(rgb[2], mean_I_r, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波//meanP=fmean(P)cv::Mat mean_p;cv::boxFilter(p, mean_p, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波//corrI=fmean(I.*I)cv::Mat mean_II_rr, mean_II_rg, mean_II_rb, mean_II_gb, mean_II_gg, mean_II_bb;cv::boxFilter(rgb[2].mul(rgb[2]), mean_II_rr, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波cv::boxFilter(rgb[2].mul(rgb[1]), mean_II_rg, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波cv::boxFilter(rgb[2].mul(rgb[0]), mean_II_rb, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波cv::boxFilter(rgb[1].mul(rgb[0]), mean_II_gb, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波cv::boxFilter(rgb[1].mul(rgb[1]), mean_II_gg, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波cv::boxFilter(rgb[0].mul(rgb[0]), mean_II_bb, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波//corrIp=fmean(I.*p)cv::Mat mean_Ip_r, mean_Ip_g, mean_Ip_b;mean_Ip_b = rgb[0].mul(p);mean_Ip_g = rgb[1].mul(p);mean_Ip_r = rgb[2].mul(p);cv::boxFilter(mean_Ip_b, mean_Ip_b, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波cv::boxFilter(mean_Ip_g, mean_Ip_g, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波cv::boxFilter(mean_Ip_r, mean_Ip_r, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波//covIp=corrIp-meanI.*meanpcv::Mat cov_Ip_r, cov_Ip_g, cov_Ip_b;cv::subtract(mean_Ip_r, mean_I_r.mul(mean_p), cov_Ip_r);cv::subtract(mean_Ip_g, mean_I_g.mul(mean_p), cov_Ip_g);cv::subtract(mean_Ip_b, mean_I_b.mul(mean_p), cov_Ip_b);//varI=corrI-meanI.*meanI//variance of I in each local patch : the matrix Sigma in Eqn(14).//Note the variance in each local patch is a 3x3 symmetric matrix :// rr, rg, rb// Sigma = rg, gg, gb// rb, gb, bbcv::Mat var_I_rr, var_I_rg, var_I_rb, var_I_gb, var_I_gg, var_I_bb;cv::subtract(mean_II_rr, mean_I_r.mul(mean_I_r), var_I_rr);cv::subtract(mean_II_rg, mean_I_r.mul(mean_I_g), var_I_rg);cv::subtract(mean_II_rb, mean_I_r.mul(mean_I_b), var_I_rb);cv::subtract(mean_II_gb, mean_I_g.mul(mean_I_b), var_I_gb);cv::subtract(mean_II_gg, mean_I_g.mul(mean_I_g), var_I_gg);cv::subtract(mean_II_bb, mean_I_b.mul(mean_I_b), var_I_bb);//a=conIp./(varI+eps)int cols = p.cols;int rows = p.rows;cv::Mat Mat_a = cv::Mat::zeros(rows, cols,CV_64FC3);std::vector a;cv::split(Mat_a, a);double rr, rg, rb, gg, gb, bb;for (int i = 0; i < rows; ++i){for (int j = 0; j < cols; ++j){rr = var_I_rr.at(i, j); rg = var_I_rg.at(i, j); rb = var_I_rb.at(i, j);gg = var_I_gg.at(i, j); gb = var_I_gb.at(i, j);bb = var_I_bb.at(i, j);cv::Mat sigma = (cv::Mat_(3, 3) << rr, rg, rb,rg, gg, gb,rb, gb, bb);cv::Mat cov_Ip = (cv::Mat_(1, 3) << cov_Ip_r.at(i, j), cov_Ip_g.at(i, j), cov_Ip_b.at(i, j));cv::Mat eye = cv::Mat::eye(3, 3, CV_64FC1);sigma = sigma + eps*eye;cv::Mat sigma_inv = sigma.inv();//求逆矩阵cv::Mat tmp = cov_Ip*sigma_inv;a[2].at(i, j) = tmp.at(0, 0);//ra[1].at(i, j) = tmp.at(0, 1);//ga[0].at(i, j) = tmp.at(0, 2);//b}}//b=meanp-a.*meanIcv::Mat b = mean_p - a[0].mul(mean_I_b) - a[1].mul(mean_I_g) - a[2].mul(mean_I_r);//meana=fmean(a)//meanb=fmean(b)cv::Mat mean_a_r, mean_a_g, mean_a_b, mean_b;cv::boxFilter(a[0], mean_a_b, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波cv::boxFilter(a[1], mean_a_g, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波cv::boxFilter(a[2], mean_a_r, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波cv::boxFilter(b, mean_b, -1, cv::Size(wsize, wsize), cv::Point(-1, -1), true, cv::BORDER_REFLECT);//盒子滤波//q=meana.*I+meanbcv::Mat q = mean_a_r.mul(rgb[2]) + mean_a_g.mul(rgb[1]) + mean_a_b.mul(rgb[0]) + mean_b;//数据类型转换I.convertTo(I, CV_8UC3, 255);p.convertTo(p, CV_8U, 255);q.convertTo(q, CV_8U, 255);return q;
}int main(){cv::Mat I = cv::imread("I:\\Learning-and-Practice\\2019Change\\Image process algorithm\\Img\\woman1.jpeg");cv::Mat P = cv::imread("I:\\Learning-and-Practice\\2019Change\\Image process algorithm\\Img\\woman1.jpeg");if (I.empty() || P.empty()){return -1;}if (P.channels() > 1)cv::cvtColor(P, P, CV_RGB2GRAY);//自编GuidedFilter测试double t2 = (double)cv::getTickCount(); //测时间cv::Mat q;q = GuidedFilter_Color(I, P, 9, 0.2*0.2);t2 = (double)cv::getTickCount() - t2;double time2 = (t2 *1000.) / ((double)cv::getTickFrequency());std::cout << "MyGuidedFilter_process=" << time2 << " ms. " << std::endl << std::endl;cv::namedWindow("GuidedImg");cv::imshow("GuidedImg", I);cv::namedWindow("src");cv::imshow("src", P);cv::namedWindow("GuidedFilter", CV_WINDOW_NORMAL);cv::imshow("GuidedFilter", q);cv::waitKey(0);}
效果(核半径=9，eps=0.1*0.1)
引导图 输入图 结果图
这里的结果图比用灰度图作为引导，边缘保持更好，可以仔细对比观察面部和鼻子。
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