Merge pull request #27717 from MaximSmolskiy:improve_fitellipsedirect_tests

Improve fitEllipseDirect tests #27717

### Pull Request Readiness Checklist

Previous `fit_and_check_ellipse` implementation was very weak - it only checks that points center lies inside ellipse.
Current implementation `fit_and_check_ellipse` checks that points RMS (Root Mean Square) algebraic distance is quite small. It means that on average points are near boundary of ellipse. Because for points on ellipse algebraic distance is equal to `0` and for points that are close to boundary of ellipse is quite small

See details at https://github.com/opencv/opencv/wiki/How_to_contribute#making-a-good-pull-request

- [x] I agree to contribute to the project under Apache 2 License.
- [x] To the best of my knowledge, the proposed patch is not based on a code under GPL or another license that is incompatible with OpenCV
- [x] The PR is proposed to the proper branch
- [ ] There is a reference to the original bug report and related work
- [ ] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
      Patch to opencv_extra has the same branch name.
- [ ] The feature is well documented and sample code can be built with the project CMake

modules/imgproc/test/test_fitellipse.cpp

@@ -8,31 +8,22 @@
 
 namespace opencv_test { namespace {
 
-// return true if point lies inside ellipse
-static bool check_pt_in_ellipse(const Point2f& pt, const RotatedRect& el) {
-    Point2f to_pt = pt - el.center;
-    double el_angle = el.angle * CV_PI / 180;
+static double algebraic_dist(const Point2f& pt, const RotatedRect& el) {
+    const Point2d to_pt = pt - el.center;
+    const double el_angle = el.angle * CV_PI / 180;
     const Point2d to_pt_el(
         to_pt.x * cos(-el_angle) - to_pt.y * sin(-el_angle),
         to_pt.x * sin(-el_angle) + to_pt.y * cos(-el_angle));
-    const double pt_angle = atan2(to_pt_el.y / el.size.height, to_pt_el.x / el.size.width);
-    const double x_dist = 0.5 * el.size.width * cos(pt_angle);
-    const double y_dist = 0.5 * el.size.height * sin(pt_angle);
-    double el_dist = sqrt(x_dist * x_dist + y_dist * y_dist);
-    return cv::norm(to_pt) < el_dist;
+    return normL2Sqr<double>(Point2d(2 * to_pt_el.x / el.size.width, 2 * to_pt_el.y / el.size.height)) - 1;
 }
 
-// Return true if mass center of fitted points lies inside ellipse
-static bool fit_and_check_ellipse(const vector<Point2f>& pts) {
-    RotatedRect ellipse = fitEllipseDirect(pts); // fitEllipseAMS() also works fine
-
-    Point2f mass_center;
-    for (size_t i = 0; i < pts.size(); i++) {
-        mass_center += pts[i];
+static double rms_algebraic_dist(const vector<Point2f>& pts, const RotatedRect& el) {
+    double sum_algebraic_dists_sqr = 0;
+    for (const auto& pt : pts) {
+        const auto pt_algebraic_dist = algebraic_dist(pt, el);
+        sum_algebraic_dists_sqr += pt_algebraic_dist * pt_algebraic_dist;
     }
-    mass_center /= (float)pts.size();
-
-    return check_pt_in_ellipse(mass_center, ellipse);
+    return sqrt(sum_algebraic_dists_sqr / pts.size());
 }
 
 TEST(Imgproc_FitEllipse_Issue_4515, accuracy) {
@@ -50,7 +41,8 @@ TEST(Imgproc_FitEllipse_Issue_4515, accuracy) {
     pts.push_back(Point2f(333, 319));
     pts.push_back(Point2f(333, 320));
 
-    EXPECT_TRUE(fit_and_check_ellipse(pts));
+    const RotatedRect ellipse = fitEllipseDirect(pts); // fitEllipseAMS() also works fine
+    EXPECT_LT(rms_algebraic_dist(pts, ellipse), 1e-1);
 }
 
 TEST(Imgproc_FitEllipse_Issue_6544, accuracy) {
@@ -66,7 +58,8 @@ TEST(Imgproc_FitEllipse_Issue_6544, accuracy) {
     pts.push_back(Point2f(929.145f, 744.976f));
     pts.push_back(Point2f(917.474f, 791.823f));
 
-    EXPECT_TRUE(fit_and_check_ellipse(pts));
+    const RotatedRect ellipse = fitEllipseDirect(pts); // fitEllipseAMS() also works fine
+    EXPECT_LT(rms_algebraic_dist(pts, ellipse), 5e-2);
 }
 
 TEST(Imgproc_FitEllipse_Issue_10270, accuracy) {