Merge pull request #23178 from savuor:stddev_calib_fisheye

Fixes #23057

Parameter uncertainty fixed + ground truth test data fixed

### Pull Request Readiness Checklist

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
- [x] There is a reference to the original bug report and related work
- [x] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
      Patch to opencv_extra has the same branch name.
- [x] The feature is well documented and sample code can be built with the project CMake

modules/calib/src/fisheye.cpp

@@ -1568,13 +1568,18 @@ void cv::internal::EstimateUncertainties(InputArrayOfArrays objectPoints, InputA
 
     Vec<double, 1> sigma_x;
     meanStdDev(ex.reshape(1, 1), noArray(), sigma_x);
-    sigma_x  *= sqrt(2.0 * (double)ex.total()/(2.0 * (double)ex.total() - 1.0));
 
     Mat JJ2, ex3;
     ComputeJacobians(objectPoints, imagePoints, params, omc, Tc, check_cond, thresh_cond, JJ2, ex3);
 
     sqrt(JJ2.inv(), JJ2);
 
+    int nParams = JJ2.rows;
+    // an explanation of that denominator correction can be found here:
+    // R. Hartley, A. Zisserman, Multiple View Geometry in Computer Vision, 2004, section 5.1.3, page 134
+    // see the discussion for more details: https://github.com/opencv/opencv/pull/22992
+    sigma_x  *= sqrt(2.0 * (double)ex.total()/(2.0 * (double)ex.total() - nParams));
+
     errors = 3 * sigma_x(0) * JJ2.diag();
     rms = sqrt(norm(ex, NORM_L2SQR)/ex.total());
 }