Merge pull request #25050 from akretz:fix_issue_24330

Handle degenerate cases in RQDecomp3x3 #25050

The point of the Givens rotations here is to iteratively set the lower left matrix entries to zero. If an element is zero already, we don't need to do anything. This resolves #24330.

### 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.
- [ ] The feature is well documented and sample code can be built with the project CMake

modules/calib3d/src/calibration.cpp

@@ -3188,8 +3188,8 @@ cvRQDecomp3x3( const CvMat *matrixM, CvMat *matrixR, CvMat *matrixQ,
     Qx = ( 0  c  s ), c = m33/sqrt(m32^2 + m33^2), s = m32/sqrt(m32^2 + m33^2)
          ( 0 -s  c )
     */
-    s = matM[2][1];
-    c = matM[2][2];
+    s = std::abs(matM[2][1]) > DBL_EPSILON ? matM[2][1] : 0;
+    c = std::abs(matM[2][1]) > DBL_EPSILON ? matM[2][2] : 1;
     z = 1./std::sqrt(c * c + s * s + DBL_EPSILON);
     c *= z;
     s *= z;
@@ -3207,8 +3207,8 @@ cvRQDecomp3x3( const CvMat *matrixM, CvMat *matrixR, CvMat *matrixQ,
     Qy = ( 0  1  0 ), c = m33/sqrt(m31^2 + m33^2), s = -m31/sqrt(m31^2 + m33^2)
          ( s  0  c )
     */
-    s = -matR[2][0];
-    c = matR[2][2];
+    s = std::abs(matR[2][0]) > DBL_EPSILON ? -matR[2][0] : 0;
+    c = std::abs(matR[2][0]) > DBL_EPSILON ? matR[2][2] : 1;
     z = 1./std::sqrt(c * c + s * s + DBL_EPSILON);
     c *= z;
     s *= z;
@@ -3227,8 +3227,8 @@ cvRQDecomp3x3( const CvMat *matrixM, CvMat *matrixR, CvMat *matrixQ,
          ( 0  0  1 )
     */
 
-    s = matM[1][0];
-    c = matM[1][1];
+    s = std::abs(matM[1][0]) > DBL_EPSILON ? matM[1][0] : 0;
+    c = std::abs(matM[1][0]) > DBL_EPSILON ? matM[1][1] : 1;
     z = 1./std::sqrt(c * c + s * s + DBL_EPSILON);
     c *= z;
     s *= z;

modules/calib3d/test/test_decompose_projection.cpp

@@ -141,4 +141,23 @@ TEST(Calib3d_DecomposeProjectionMatrix, accuracy)
     test.safe_run();
 }
 
+TEST(Calib3d_DecomposeProjectionMatrix, degenerate_cases)
+{
+    for (int i = 0; i < 3; i++)
+    {
+        for (int j = 0; j < 2; j++)
+        {
+            cv::Matx34d P;
+            P(0, i) = 1;
+            P(1, (i + j + 1) % 3) = 1;
+            P(2, (i + 2 * j + 2) % 3) = 1;
+
+            cv::Matx33d K, R;
+            cv::Vec4d t;
+            decomposeProjectionMatrix(P, K, R, t);
+            EXPECT_LT(cv::norm(K * R, P.get_minor<3, 3>(0, 0), cv::NORM_INF), 1e-6);
+        }
+    }
+}
+
 }} // namespace