From deaf632881ea697e5feaeea245816db053c58b37 Mon Sep 17 00:00:00 2001
From: Rostislav Vasilikhin <savuor@gmail.com>
Date: Sat, 28 Jan 2023 10:56:13 +0100
Subject: [PATCH] Merge pull request #23179 from
 savuor:port34_stddev_calib_fisheye

Backport to 3.4 of the fisheye calibration uncertainty fix

* uncertainties fix

* trailing whitespace

* comment added
---
 modules/calib3d/src/fisheye.cpp       | 7 ++++++-
 modules/calib3d/test/test_fisheye.cpp | 6 +++---
 2 files changed, 9 insertions(+), 4 deletions(-)

diff --git a/modules/calib3d/src/fisheye.cpp b/modules/calib3d/src/fisheye.cpp
index a562bd2bb2..0e9034ca19 100644
--- a/modules/calib3d/src/fisheye.cpp
+++ b/modules/calib3d/src/fisheye.cpp
@@ -1527,13 +1527,18 @@ 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());
 }
diff --git a/modules/calib3d/test/test_fisheye.cpp b/modules/calib3d/test/test_fisheye.cpp
index 2e12cd8985..789e4db4af 100644
--- a/modules/calib3d/test/test_fisheye.cpp
+++ b/modules/calib3d/test/test_fisheye.cpp
@@ -398,9 +398,9 @@ TEST_F(fisheyeTest, EstimateUncertainties)
     cv::internal::EstimateUncertainties(objectPoints, imagePoints, param,  rvec, tvec,
                                         errors, err_std, thresh_cond, check_cond, rms);
 
-    EXPECT_MAT_NEAR(errors.f, cv::Vec2d(1.29837104202046,  1.31565641071524), 1e-10);
-    EXPECT_MAT_NEAR(errors.c, cv::Vec2d(0.890439368129246, 0.816096854937896), 1e-10);
-    EXPECT_MAT_NEAR(errors.k, cv::Vec4d(0.00516248605191506, 0.0168181467500934, 0.0213118690274604, 0.00916010877545648), 1e-10);
+    EXPECT_MAT_NEAR(errors.f, cv::Vec2d(1.34250246865020720, 1.36037536429654530), 1e-10);
+    EXPECT_MAT_NEAR(errors.c, cv::Vec2d(0.92070526160049848, 0.84383585812851514), 1e-10);
+    EXPECT_MAT_NEAR(errors.k, cv::Vec4d(0.0053379581373996041, 0.017389792901700545, 0.022036256089491224, 0.0094714594258908952), 1e-10);
     EXPECT_MAT_NEAR(err_std, cv::Vec2d(0.187475975266883, 0.185678953263995), 1e-10);
     CV_Assert(fabs(rms - 0.263782587133546) < 1e-10);
     CV_Assert(errors.alpha == 0);
-- 
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