Primal-dual algorithm

This is an implementation of primal-dual algorithm, based on the C++
source code by Vadim Pisarevsky. It was extended to handle the denoising
based on multiple observations. It also contains documentation and
tests.

modules/optim/test/test_denoise_tvl1.cpp

@@ -0,0 +1,81 @@
+#include "test_precomp.hpp"
+#include "opencv2/highgui.hpp"
+
+void make_noisy(const cv::Mat& img, cv::Mat& noisy, double sigma, double pepper_salt_ratio,cv::RNG& rng){
+    noisy.create(img.size(), img.type());
+    cv::Mat noise(img.size(), img.type()), mask(img.size(), CV_8U);
+    rng.fill(noise,cv::RNG::NORMAL,128.0,sigma);
+    cv::addWeighted(img, 1, noise, 1, -128, noisy);
+    cv::randn(noise, cv::Scalar::all(0), cv::Scalar::all(2));
+    noise *= 255;
+    cv::randu(mask, 0, round(1./pepper_salt_ratio));
+    cv::Mat half = mask.colRange(0, img.cols/2);
+    half = cv::Scalar::all(1);
+    noise.setTo(128, mask);
+    cv::addWeighted(noisy, 1, noise, 1, -128, noisy);
+}
+void make_spotty(cv::Mat& img,cv::RNG& rng, int r=3,int n=1000){
+    for(int i=0;i<n;i++){
+        int x=rng(img.cols-r),y=rng(img.rows-r);
+        if(rng(2)==0){
+            img(cv::Range(y,y+r),cv::Range(x,x+r))=(uchar)0;
+        }else{
+            img(cv::Range(y,y+r),cv::Range(x,x+r))=(uchar)255;
+        }
+    }
+}
+
+bool validate_pixel(const cv::Mat& image,int x,int y,uchar val){
+    printf("test: image(%d,%d)=%d vs %d - %s\n",x,y,(int)image.at<uchar>(x,y),val,(val==image.at<uchar>(x,y))?"true":"false");
+    return (image.at<uchar>(x,y)==val);
+}
+
+TEST(Optim_denoise_tvl1, regression_basic){
+    cv::RNG rng(42);
+    cv::Mat img = cv::imread("lena.jpg", 0), noisy,res;
+    if(img.rows!=512 || img.cols!=512){
+        printf("\tplease, put lena.jpg from samples/c in the current folder\n");
+        printf("\tnow, the test will fail...\n");
+        ASSERT_TRUE(false);
+    }
+
+    const int obs_num=5;
+    std::vector<cv::Mat> images(obs_num,cv::Mat());
+    for(int i=0;i<images.size();i++){
+        make_noisy(img,images[i], 20, 0.02,rng);
+        //make_spotty(images[i],rng);
+    }
+
+    //cv::imshow("test", images[0]);
+    cv::optim::denoise_TVL1(images, res);
+    printf("hello here!\n");
+    //cv::imshow("denoised", res);
+    //cv::waitKey();
+
+#if 0
+    ASSERT_TRUE(validate_pixel(res,248,334,179));
+    ASSERT_TRUE(validate_pixel(res,489,333,172));
+    ASSERT_TRUE(validate_pixel(res,425,507,104));
+    ASSERT_TRUE(validate_pixel(res,489,486,105));
+    ASSERT_TRUE(validate_pixel(res,223,208,64));
+    ASSERT_TRUE(validate_pixel(res,418,3,78));
+    ASSERT_TRUE(validate_pixel(res,63,76,97));
+    ASSERT_TRUE(validate_pixel(res,29,134,126));
+    ASSERT_TRUE(validate_pixel(res,219,291,174));
+    ASSERT_TRUE(validate_pixel(res,384,124,76));
+#endif
+
+#if 1
+    ASSERT_TRUE(validate_pixel(res,248,334,194));
+    ASSERT_TRUE(validate_pixel(res,489,333,171));
+    ASSERT_TRUE(validate_pixel(res,425,507,103));
+    ASSERT_TRUE(validate_pixel(res,489,486,109));
+    ASSERT_TRUE(validate_pixel(res,223,208,72));
+    ASSERT_TRUE(validate_pixel(res,418,3,58));
+    ASSERT_TRUE(validate_pixel(res,63,76,93));
+    ASSERT_TRUE(validate_pixel(res,29,134,127));
+    ASSERT_TRUE(validate_pixel(res,219,291,180));
+    ASSERT_TRUE(validate_pixel(res,384,124,80));
+#endif
+
+}