problems in 3D reconstruction by triangulation opencv - opencv

Question

I'm currently working in an stereo vision project, in which I'm supposed to reconstruct 3D points from correspondences found in each camera view, and for that I'm using OpenCV 2.4.7 for C++.
I was able to correctly calibrate both cameras, compute fundamental matrix, compute re-projection matrix and also rectify images.
My problem lies on the final part of the project, which is compute 3D world coordinates from 2D point correspondences. I already tried using cv::triangulatePoints, but the results where points with coordinates (0, 0, 0), no matter what the input points were. I also tried the linear triangulation algorithm by Hartley & Strum, but that didn't give me good results either.
Could somebody give me a hint on what function I should use? Or maybe some tips on how to correctly implement the ones I've talked about. My biggest problem is to find good documentation on the internet, so that's why I decided to ask here.
Thank you!

Answer 1

I tried cv::triangulatePoints also and it calculates garbage. I was forced to implement a linear triangulation method manually, which returns the triangulated 3D point given a stereo pixel correspondence:
Mat triangulate_Linear_LS(Mat mat_P_l, Mat mat_P_r, Mat warped_back_l, Mat warped_back_r)
{
Mat A(4,3,CV_64FC1), b(4,1,CV_64FC1), X(3,1,CV_64FC1), X_homogeneous(4,1,CV_64FC1), W(1,1,CV_64FC1);
W.at<double>(0,0) = 1.0;
A.at<double>(0,0) = (warped_back_l.at<double>(0,0)/warped_back_l.at<double>(2,0))*mat_P_l.at<double>(2,0) - mat_P_l.at<double>(0,0);
A.at<double>(0,1) = (warped_back_l.at<double>(0,0)/warped_back_l.at<double>(2,0))*mat_P_l.at<double>(2,1) - mat_P_l.at<double>(0,1);
A.at<double>(0,2) = (warped_back_l.at<double>(0,0)/warped_back_l.at<double>(2,0))*mat_P_l.at<double>(2,2) - mat_P_l.at<double>(0,2);
A.at<double>(1,0) = (warped_back_l.at<double>(1,0)/warped_back_l.at<double>(2,0))*mat_P_l.at<double>(2,0) - mat_P_l.at<double>(1,0);
A.at<double>(1,1) = (warped_back_l.at<double>(1,0)/warped_back_l.at<double>(2,0))*mat_P_l.at<double>(2,1) - mat_P_l.at<double>(1,1);
A.at<double>(1,2) = (warped_back_l.at<double>(1,0)/warped_back_l.at<double>(2,0))*mat_P_l.at<double>(2,2) - mat_P_l.at<double>(1,2);
A.at<double>(2,0) = (warped_back_r.at<double>(0,0)/warped_back_r.at<double>(2,0))*mat_P_r.at<double>(2,0) - mat_P_r.at<double>(0,0);
A.at<double>(2,1) = (warped_back_r.at<double>(0,0)/warped_back_r.at<double>(2,0))*mat_P_r.at<double>(2,1) - mat_P_r.at<double>(0,1);
A.at<double>(2,2) = (warped_back_r.at<double>(0,0)/warped_back_r.at<double>(2,0))*mat_P_r.at<double>(2,2) - mat_P_r.at<double>(0,2);
A.at<double>(3,0) = (warped_back_r.at<double>(1,0)/warped_back_r.at<double>(2,0))*mat_P_r.at<double>(2,0) - mat_P_r.at<double>(1,0);
A.at<double>(3,1) = (warped_back_r.at<double>(1,0)/warped_back_r.at<double>(2,0))*mat_P_r.at<double>(2,1) - mat_P_r.at<double>(1,1);
A.at<double>(3,2) = (warped_back_r.at<double>(1,0)/warped_back_r.at<double>(2,0))*mat_P_r.at<double>(2,2) - mat_P_r.at<double>(1,2);
b.at<double>(0,0) = -((warped_back_l.at<double>(0,0)/warped_back_l.at<double>(2,0))*mat_P_l.at<double>(2,3) - mat_P_l.at<double>(0,3));
b.at<double>(1,0) = -((warped_back_l.at<double>(1,0)/warped_back_l.at<double>(2,0))*mat_P_l.at<double>(2,3) - mat_P_l.at<double>(1,3));
b.at<double>(2,0) = -((warped_back_r.at<double>(0,0)/warped_back_r.at<double>(2,0))*mat_P_r.at<double>(2,3) - mat_P_r.at<double>(0,3));
b.at<double>(3,0) = -((warped_back_r.at<double>(1,0)/warped_back_r.at<double>(2,0))*mat_P_r.at<double>(2,3) - mat_P_r.at<double>(1,3));
solve(A,b,X,DECOMP_SVD);
vconcat(X,W,X_homogeneous);
return X_homogeneous;
}
the input parameters are two 3x4 camera projection matrices and the left/right corresponding homogeneous pixel coordinates.