Pull Request Readiness Checklist

I believe that implementation of fitEllipseDirect function does not correspond to fitzgibbon1999 but to its improvement oy1998NumericallySD

Several arguments in favor of this:

• fitzgibbon1999 suggests to calculate eigenvalues and eigenvectors for 6x6 matrix, but oy1998NumericallySD - for 3x3 matrix M. In implementation we calculate eigenvalues and eigenvectors for 3x3 matrix M
  

  opencv/modules/imgproc/src/shapedescr.cpp

  Lines 782 to 800 in d77dbbe

  	M(0,0) = (DM(2,0) + (DM(2,3)*TM(0,0) + DM(2,4)*TM(1,0) + DM(2,5)*TM(2,0))/Ts)/2.;
  	M(0,1) = (DM(2,1) + (DM(2,3)*TM(0,1) + DM(2,4)*TM(1,1) + DM(2,5)*TM(2,1))/Ts)/2.;
  	M(0,2) = (DM(2,2) + (DM(2,3)*TM(0,2) + DM(2,4)*TM(1,2) + DM(2,5)*TM(2,2))/Ts)/2.;
  	M(1,0) = -DM(1,0) - (DM(1,3)*TM(0,0) + DM(1,4)*TM(1,0) + DM(1,5)*TM(2,0))/Ts;
  	M(1,1) = -DM(1,1) - (DM(1,3)*TM(0,1) + DM(1,4)*TM(1,1) + DM(1,5)*TM(2,1))/Ts;
  	M(1,2) = -DM(1,2) - (DM(1,3)*TM(0,2) + DM(1,4)*TM(1,2) + DM(1,5)*TM(2,2))/Ts;
  	M(2,0) = (DM(0,0) + (DM(0,3)*TM(0,0) + DM(0,4)*TM(1,0) + DM(0,5)*TM(2,0))/Ts)/2.;
  	M(2,1) = (DM(0,1) + (DM(0,3)*TM(0,1) + DM(0,4)*TM(1,1) + DM(0,5)*TM(2,1))/Ts)/2.;
  	M(2,2) = (DM(0,2) + (DM(0,3)*TM(0,2) + DM(0,4)*TM(1,2) + DM(0,5)*TM(2,2))/Ts)/2.;
  	double det = fabs(cv::determinant(M));
  	if (fabs(det) > 1.0e-10)
  	break;
  	eps = (float)(s/(n*2)*1e-2);
  	}
  	if( iter < 2 ) {
  	Mat eVal, eVec;
  	eigenNonSymmetric(M, eVal, eVec);

• fitzgibbon1999 suggests to take eigenvector for positive eigenvalue, but oy1998NumericallySD - for positive cond = 4 * evec(1, :) .* evec(3, :) - evec(2, :) .ˆ 2. In implementation we calculate this cond and take eigenvector accordingly
  

  opencv/modules/imgproc/src/shapedescr.cpp

  Lines 802 to 816 in d77dbbe

  	// Select the eigen vector {a,b,c} which satisfies 4ac-b^2 > 0
  	double cond[3];
  	cond[0]=(4.0 * eVec.at<double>(0,0) * eVec.at<double>(0,2) - eVec.at<double>(0,1) * eVec.at<double>(0,1));
  	cond[1]=(4.0 * eVec.at<double>(1,0) * eVec.at<double>(1,2) - eVec.at<double>(1,1) * eVec.at<double>(1,1));
  	cond[2]=(4.0 * eVec.at<double>(2,0) * eVec.at<double>(2,2) - eVec.at<double>(2,1) * eVec.at<double>(2,1));
  	if (cond[0]<cond[1]) {
  	i = (cond[1]<cond[2]) ? 2 : 1;
  	} else {
  	i = (cond[0]<cond[2]) ? 2 : 0;
  	}
  	double norm = std::sqrt(eVec.at<double>(i,0)*eVec.at<double>(i,0) + eVec.at<double>(i,1)*eVec.at<double>(i,1) + eVec.at<double>(i,2)*eVec.at<double>(i,2));
  	if (((eVec.at<double>(i,0)<0.0 ? -1 : 1) * (eVec.at<double>(i,1)<0.0 ? -1 : 1) * (eVec.at<double>(i,2)<0.0 ? -1 : 1)) <= 0.0) {
  	norm=-1.0*norm;
  	}
  	pVec(0) =eVec.at<double>(i,0)/norm; pVec(1) =eVec.at<double>(i,1)/norm;pVec(2) =eVec.at<double>(i,2)/norm;

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

• I agree to contribute to the project under Apache 2 License.
• 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
• 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