diff --git a/modules/imgproc/src/shapedescr.cpp b/modules/imgproc/src/shapedescr.cpp
index 007bf9ac62..ccb006b90c 100644
--- a/modules/imgproc/src/shapedescr.cpp
+++ b/modules/imgproc/src/shapedescr.cpp
@@ -340,9 +340,10 @@ double cv::contourArea( InputArray _contour, bool oriented )
 namespace cv
 {
 
-static inline Point2f getOfs(int i, float eps)
+static inline Point2f getOfs(float eps)
 {
-    return Point2f(((i & 1)*2 - 1)*eps, ((i & 2) - 1)*eps);
+    RNG& rng = theRNG();
+    return Point2f(rng.uniform(-eps, eps), rng.uniform(-eps, eps));
 }
 
 static RotatedRect fitEllipseNoDirect( InputArray _points )
@@ -419,7 +420,7 @@ static RotatedRect fitEllipseNoDirect( InputArray _points )
         float eps = (float)(s/(n*2)*1e-3);
         for( i = 0; i < n; i++ )
         {
-            Point2f p = ptsf_copy[i] + getOfs(i, eps);
+            const Point2f p = ptsf_copy[i] + getOfs(eps);
             ptsf_copy[i] = p;
         }
 
@@ -744,7 +745,7 @@ cv::RotatedRect cv::fitEllipseDirect( InputArray _points )
         for( i = 0; i < n; i++ )
         {
             Point2f p = is_float ? ptsf[i] : Point2f((float)ptsi[i].x, (float)ptsi[i].y);
-            Point2f delta = getOfs(i, eps);
+            const Point2f delta = getOfs(eps);
             double px = (p.x + delta.x - c.x)*scale, py = (p.y + delta.y - c.y)*scale;
 
             A.at<double>(i,0) = px*px;
diff --git a/modules/imgproc/test/test_fitellipse.cpp b/modules/imgproc/test/test_fitellipse.cpp
index 3e6d0478ca..169751acab 100644
--- a/modules/imgproc/test/test_fitellipse.cpp
+++ b/modules/imgproc/test/test_fitellipse.cpp
@@ -102,4 +102,15 @@ TEST(Imgproc_FitEllipse_JavaCase, accuracy) {
     EXPECT_NEAR(e.size.height, sqrt(2.)*2, 0.4);
 }
 
+TEST(Imgproc_FitEllipse_HorizontalLine, accuracy) {
+    vector<Point2f> pts({{-300, 100}, {-200, 100}, {-100, 100}, {0, 100}, {100, 100}, {200, 100}, {300, 100}});
+    const RotatedRect el = fitEllipse(pts);
+
+    EXPECT_NEAR(el.center.x, -100, 100);
+    EXPECT_NEAR(el.center.y, 100, 1);
+    EXPECT_NEAR(el.size.width, 1, 1);
+    EXPECT_GE(el.size.height, 150);
+    EXPECT_NEAR(el.angle, 90, 0.1);
+}
+
 }} // namespace
diff --git a/modules/imgproc/test/test_fitellipse_ams.cpp b/modules/imgproc/test/test_fitellipse_ams.cpp
index 92e7f2e7a2..5c672bec89 100644
--- a/modules/imgproc/test/test_fitellipse_ams.cpp
+++ b/modules/imgproc/test/test_fitellipse_ams.cpp
@@ -337,4 +337,15 @@ TEST(Imgproc_FitEllipseAMS_Issue_7, accuracy) {
     EXPECT_TRUE(checkEllipse(ellipseAMSTest, ellipseAMSTrue, tol));
 }
 
+TEST(Imgproc_FitEllipseAMS_HorizontalLine, accuracy) {
+    vector<Point2f> pts({{-300, 100}, {-200, 100}, {-100, 100}, {0, 100}, {100, 100}, {200, 100}, {300, 100}});
+    const RotatedRect el = fitEllipseAMS(pts);
+
+    EXPECT_NEAR(el.center.x, -100, 100);
+    EXPECT_NEAR(el.center.y, 100, 1);
+    EXPECT_NEAR(el.size.width, 1, 1);
+    EXPECT_GE(el.size.height, 150);
+    EXPECT_NEAR(el.angle, 90, 0.1);
+}
+
 }} // namespace
diff --git a/modules/imgproc/test/test_fitellipse_direct.cpp b/modules/imgproc/test/test_fitellipse_direct.cpp
index 4ae8c4dc76..e41c52764d 100644
--- a/modules/imgproc/test/test_fitellipse_direct.cpp
+++ b/modules/imgproc/test/test_fitellipse_direct.cpp
@@ -337,4 +337,15 @@ TEST(Imgproc_FitEllipseDirect_Issue_7, accuracy) {
     EXPECT_TRUE(checkEllipse(ellipseDirectTest, ellipseDirectTrue, tol));
 }
 
+TEST(Imgproc_FitEllipseDirect_HorizontalLine, accuracy) {
+    vector<Point2f> pts({{-300, 100}, {-200, 100}, {-100, 100}, {0, 100}, {100, 100}, {200, 100}, {300, 100}});
+    const RotatedRect el = fitEllipseDirect(pts);
+
+    EXPECT_NEAR(el.center.x, 0, 100);
+    EXPECT_NEAR(el.center.y, 100, 1);
+    EXPECT_NEAR(el.size.width, 2, 2);
+    EXPECT_NEAR(el.size.height, 600, 100);
+    EXPECT_NEAR(el.angle, 90, 0.1);
+}
+
 }} // namespace