diff --git a/modules/imgproc/src/imgwarp.cpp b/modules/imgproc/src/imgwarp.cpp
index 5822726eee..a7f8eee449 100644
--- a/modules/imgproc/src/imgwarp.cpp
+++ b/modules/imgproc/src/imgwarp.cpp
@@ -50,6 +50,8 @@
 #include "precomp.hpp"
 #include "opencl_kernels_imgproc.hpp"
 
+using namespace cv;
+
 namespace cv
 {
 #if IPP_VERSION_X100 >= 710
@@ -6475,11 +6477,13 @@ CV_IMPL void
 cvLogPolar( const CvArr* srcarr, CvArr* dstarr,
             CvPoint2D32f center, double M, int flags )
 {
+    Mat src_with_border; // don't scope this variable (it holds image data)
+
     cv::Ptr<CvMat> mapx, mapy;
 
     CvMat srcstub, *src = cvGetMat(srcarr, &srcstub);
     CvMat dststub, *dst = cvGetMat(dstarr, &dststub);
-    CvSize ssize, dsize;
+    CvSize dsize;
 
     if( !CV_ARE_TYPES_EQ( src, dst ))
         CV_Error( CV_StsUnmatchedFormats, "" );
@@ -6487,7 +6491,6 @@ cvLogPolar( const CvArr* srcarr, CvArr* dstarr,
     if( M <= 0 )
         CV_Error( CV_StsOutOfRange, "M should be >0" );
 
-    ssize = cvGetMatSize(src);
     dsize = cvGetMatSize(dst);
 
     mapx.reset(cvCreateMat( dsize.height, dsize.width, CV_32F ));
@@ -6500,7 +6503,7 @@ cvLogPolar( const CvArr* srcarr, CvArr* dstarr,
         double* exp_tab = _exp_tab;
 
         for( rho = 0; rho < dst->width; rho++ )
-            exp_tab[rho] = std::exp(rho/M);
+            exp_tab[rho] = std::exp(rho/M) - 1.0;
 
         for( phi = 0; phi < dsize.height; phi++ )
         {
@@ -6522,6 +6525,13 @@ cvLogPolar( const CvArr* srcarr, CvArr* dstarr,
     }
     else
     {
+        const int ANGLE_BORDER = 1;
+        Mat src_ = cv::cvarrToMat(src);
+        cv::copyMakeBorder(src_, src_with_border, ANGLE_BORDER, ANGLE_BORDER, 0, 0, BORDER_WRAP);
+        srcstub = src_with_border; src = &srcstub;
+        CvSize ssize = cvGetMatSize(src);
+        ssize.height -= 2*ANGLE_BORDER;
+
         int x, y;
         CvMat bufx, bufy, bufp, bufa;
         double ascale = ssize.height/(2*CV_PI);
@@ -6558,7 +6568,7 @@ cvLogPolar( const CvArr* srcarr, CvArr* dstarr,
                 double phi = bufa.data.fl[x]*ascale;
 
                 mx[x] = (float)rho;
-                my[x] = (float)phi;
+                my[x] = (float)phi + ANGLE_BORDER;
             }
 #else
             for( x = 0; x < dsize.width; x++ )
@@ -6599,11 +6609,13 @@ CV_IMPL
 void cvLinearPolar( const CvArr* srcarr, CvArr* dstarr,
             CvPoint2D32f center, double maxRadius, int flags )
 {
+    Mat src_with_border; // don't scope this variable (it holds image data)
+
     cv::Ptr<CvMat> mapx, mapy;
 
     CvMat srcstub, *src = (CvMat*)srcarr;
     CvMat dststub, *dst = (CvMat*)dstarr;
-    CvSize ssize, dsize;
+    CvSize dsize;
 
     src = cvGetMat( srcarr, &srcstub,0,0 );
     dst = cvGetMat( dstarr, &dststub,0,0 );
@@ -6611,10 +6623,7 @@ void cvLinearPolar( const CvArr* srcarr, CvArr* dstarr,
     if( !CV_ARE_TYPES_EQ( src, dst ))
         CV_Error( CV_StsUnmatchedFormats, "" );
 
-    ssize.width = src->cols;
-    ssize.height = src->rows;
-    dsize.width = dst->cols;
-    dsize.height = dst->rows;
+    dsize = cvGetMatSize(dst);
 
     mapx.reset(cvCreateMat( dsize.height, dsize.width, CV_32F ));
     mapy.reset(cvCreateMat( dsize.height, dsize.width, CV_32F ));
@@ -6632,7 +6641,7 @@ void cvLinearPolar( const CvArr* srcarr, CvArr* dstarr,
 
             for( rho = 0; rho < dsize.width; rho++ )
             {
-                double r = maxRadius*(rho+1)/dsize.width;
+                double r = maxRadius*rho/dsize.width;
                 double x = r*cp + center.x;
                 double y = r*sp + center.y;
 
@@ -6643,6 +6652,13 @@ void cvLinearPolar( const CvArr* srcarr, CvArr* dstarr,
     }
     else
     {
+        const int ANGLE_BORDER = 1;
+        Mat src_ = cv::cvarrToMat(src);
+        cv::copyMakeBorder(src_, src_with_border, ANGLE_BORDER, ANGLE_BORDER, 0, 0, BORDER_WRAP);
+        srcstub = src_with_border; src = &srcstub;
+        CvSize ssize = cvGetMatSize(src);
+        ssize.height -= 2*ANGLE_BORDER;
+
         int x, y;
         CvMat bufx, bufy, bufp, bufa;
         const double ascale = ssize.height/(2*CV_PI);
@@ -6669,15 +6685,12 @@ void cvLinearPolar( const CvArr* srcarr, CvArr* dstarr,
 
             cvCartToPolar( &bufx, &bufy, &bufp, &bufa, 0 );
 
-            for( x = 0; x < dsize.width; x++ )
-                bufp.data.fl[x] += 1.f;
-
             for( x = 0; x < dsize.width; x++ )
             {
                 double rho = bufp.data.fl[x]*pscale;
                 double phi = bufa.data.fl[x]*ascale;
                 mx[x] = (float)rho;
-                my[x] = (float)phi;
+                my[x] = (float)phi + ANGLE_BORDER;
             }
         }
     }
diff --git a/modules/imgproc/test/test_imgwarp.cpp b/modules/imgproc/test/test_imgwarp.cpp
index 0568cbce0a..8246754387 100644
--- a/modules/imgproc/test/test_imgwarp.cpp
+++ b/modules/imgproc/test/test_imgwarp.cpp
@@ -1744,4 +1744,86 @@ TEST(Imgproc_Remap, DISABLED_memleak)
     }
 }
 
+
+TEST(Imgproc_linearPolar, identity)
+{
+    const int N = 33;
+    Mat in(N, N, CV_8UC3, Scalar(255, 0, 0));
+    in(cv::Rect(N/3, N/3, N/3, N/3)).setTo(Scalar::all(255));
+    cv::blur(in, in, Size(5, 5));
+    cv::blur(in, in, Size(5, 5));
+
+    Mat src = in.clone();
+    Mat dst;
+
+    Rect roi = Rect(0, 0, in.cols - ((N+19)/20), in.rows);
+
+    for (int i = 1; i <= 5; i++)
+    {
+        linearPolar(src, dst,
+            Point2f((N-1) * 0.5f, (N-1) * 0.5f), N * 0.5f,
+            CV_WARP_FILL_OUTLIERS | CV_INTER_LINEAR | CV_WARP_INVERSE_MAP);
+
+        linearPolar(dst, src,
+            Point2f((N-1) * 0.5f, (N-1) * 0.5f), N * 0.5f,
+            CV_WARP_FILL_OUTLIERS | CV_INTER_LINEAR);
+
+        double psnr = cvtest::PSNR(in(roi), src(roi));
+        EXPECT_LE(25, psnr) << "iteration=" << i;
+    }
+
+#if 0
+    Mat all(N*2+2,N*2+2, src.type(), Scalar(0,0,255));
+    in.copyTo(all(Rect(0,0,N,N)));
+    src.copyTo(all(Rect(0,N+1,N,N)));
+    src.copyTo(all(Rect(N+1,0,N,N)));
+    dst.copyTo(all(Rect(N+1,N+1,N,N)));
+    imwrite("linearPolar.png", all);
+    imshow("input", in); imshow("result", dst); imshow("restore", src); imshow("all", all);
+    cv::waitKey();
+#endif
+}
+
+
+TEST(Imgproc_logPolar, identity)
+{
+    const int N = 33;
+    Mat in(N, N, CV_8UC3, Scalar(255, 0, 0));
+    in(cv::Rect(N/3, N/3, N/3, N/3)).setTo(Scalar::all(255));
+    cv::blur(in, in, Size(5, 5));
+    cv::blur(in, in, Size(5, 5));
+
+    Mat src = in.clone();
+    Mat dst;
+
+    Rect roi = Rect(0, 0, in.cols - ((N+19)/20), in.rows);
+
+    double M = N/log(N * 0.5f);
+    for (int i = 1; i <= 5; i++)
+    {
+        logPolar(src, dst,
+            Point2f((N-1) * 0.5f, (N-1) * 0.5f), M,
+            CV_WARP_FILL_OUTLIERS | CV_INTER_LINEAR | CV_WARP_INVERSE_MAP);
+
+        logPolar(dst, src,
+            Point2f((N-1) * 0.5f, (N-1) * 0.5f), M,
+            CV_WARP_FILL_OUTLIERS | CV_INTER_LINEAR);
+
+        double psnr = cvtest::PSNR(in(roi), src(roi));
+        EXPECT_LE(25, psnr) << "iteration=" << i;
+    }
+
+#if 0
+    Mat all(N*2+2,N*2+2, src.type(), Scalar(0,0,255));
+    in.copyTo(all(Rect(0,0,N,N)));
+    src.copyTo(all(Rect(0,N+1,N,N)));
+    src.copyTo(all(Rect(N+1,0,N,N)));
+    dst.copyTo(all(Rect(N+1,N+1,N,N)));
+    imwrite("logPolar.png", all);
+    imshow("input", in); imshow("result", dst); imshow("restore", src); imshow("all", all);
+    cv::waitKey();
+#endif
+}
+
+
 /* End of file. */