diff --git a/modules/imgproc/include/opencv2/imgproc.hpp b/modules/imgproc/include/opencv2/imgproc.hpp
index 8db6cc5d8d4c5649c18bb2ff0f28f87893711435..c669f2cdef97c400907a07d127b38d98fe88dec0 100644
--- a/modules/imgproc/include/opencv2/imgproc.hpp
+++ b/modules/imgproc/include/opencv2/imgproc.hpp
@@ -2086,12 +2086,12 @@ The function finds lines in a set of points using a modification of the Hough tr
 @param point Input vector of points. Each vector must be encoded as a Point vector \f$(x,y)\f$. Type must be CV_32FC2 or CV_32SC2.
 @param lines Output vector of found lines. Each vector is encoded as a vector<Vec3d> \f$(votes, rho, theta)\f$.
 The larger the value of 'votes', the higher the reliability of the Hough line.
-@param lines_max Max count of hough lines.
+@param lines_max Max count of Hough lines.
 @param threshold Accumulator threshold parameter. Only those lines are returned that get enough
-votes ( \f$>\texttt{threshold}\f$ )
-@param min_rho Minimum Distance value of the accumulator in pixels.
-@param max_rho Maximum Distance value of the accumulator in pixels.
-@param rho_step Distance resolution of the accumulator in pixels.
+votes ( \f$>\texttt{threshold}\f$ ).
+@param min_rho Minimum value for \f$\rho\f$ for the accumulator (Note: \f$\rho\f$ can be negative. The absolute value \f$|\rho|\f$ is the distance of a line to the origin.).
+@param max_rho Maximum value for \f$\rho\f$ for the accumulator.
+@param rho_step Distance resolution of the accumulator.
 @param min_theta Minimum angle value of the accumulator in radians.
 @param max_theta Maximum angle value of the accumulator in radians.
 @param theta_step Angle resolution of the accumulator in radians.
diff --git a/modules/imgproc/src/hough.cpp b/modules/imgproc/src/hough.cpp
index b48b7ea13723e99714bf65fa1422aa966758b66e..9ed6cc5c5710a3250c64c721aa3fd51eb4d36777 100644
--- a/modules/imgproc/src/hough.cpp
+++ b/modules/imgproc/src/hough.cpp
@@ -975,7 +975,9 @@ void HoughLinesPointSet( InputArray _point, OutputArray _lines, int lines_max, i
         for(int n = 0; n < numangle; n++ )
         {
             int r = cvRound( point.at(i).x  * tabCos[n] + point.at(i).y * tabSin[n] - irho_min);
-            accum[(n+1) * (numrho+2) + r+1]++;
+            if ( r >= 0 && r <= numrho) {
+                accum[(n+1) * (numrho+2) + r+1]++;
+            }
         }
 
     // stage 2. find local maximums
diff --git a/modules/imgproc/test/test_houghlines.cpp b/modules/imgproc/test/test_houghlines.cpp
index fca0449b91ad4f508de94819dccf52d6a6187860..e90891274ab58401332ca92dbd26545eb88b7e4d 100644
--- a/modules/imgproc/test/test_houghlines.cpp
+++ b/modules/imgproc/test/test_houghlines.cpp
@@ -299,6 +299,36 @@ TEST_P(HoughLinesPointSetTest, regression)
     run_test();
 }
 
+TEST(HoughLinesPointSet, regression_21029)
+{
+    std::vector<Point2f> points;
+    points.push_back(Point2f(100, 100));
+    points.push_back(Point2f(1000, 1000));
+    points.push_back(Point2f(10000, 10000));
+    points.push_back(Point2f(100000, 100000));
+
+    double rhoMin = 0;
+    double rhoMax = 10;
+    double rhoStep = 0.1;
+
+    double thetaMin = 85 * CV_PI / 180.0;
+    double thetaMax = 95 * CV_PI / 180.0;
+    double thetaStep = 1 * CV_PI / 180.0;
+
+    int lines_max = 5;
+    int threshold = 100;
+
+    Mat lines;
+
+    HoughLinesPointSet(points, lines,
+        lines_max, threshold,
+        rhoMin, rhoMax, rhoStep,
+        thetaMin, thetaMax, thetaStep
+    );
+
+    EXPECT_TRUE(lines.empty());
+}
+
 INSTANTIATE_TEST_CASE_P( ImgProc, StandartHoughLinesTest, testing::Combine(testing::Values( "shared/pic5.png", "../stitching/a1.png" ),
                                                                            testing::Values( 1, 10 ),
                                                                            testing::Values( 0.05, 0.1 ),