Transformation from "triangulate" -coordinates to "reconstructScene" -coordinates

We have a calibrated stereo camera system, which we use to both motion estimation and to measure real 3d objects. We solve 3d coordinates by using both

a) disparity map and reconstructScene -function (dense point cloud) and

b) SURF-features and "triangulate" function (sparse point cloud).

The 3d coordinates obtained by these two different methods seem to be in different coordinate system. How can we transform sparse point cloud to the coordinate system of the dense point cloud ie what is the transformation matrix between these two systems? I suppose we should be able to derive the transformation from stereo parameters (and this is also done somewhere in the intrinsic functions of the computer vision toolbox).

Below are rough outlines of both methods:

% Dense point cloud approach
% Rectify images
[J1, J2] = rectifyStereoImages(I1, I2,stereoParameters,'OutputView','full');
% Solve disparities
...
% Backproject
point3D = reconstructScene(disparities, stereoParameters);


% Sparse point cloud approach
% Undistort images
params = stereoParameters.CameraParameters1;
I1 = undistortImage(I1,params);
params = stereoParameters.CameraParameters2;
I2 = undistortImage(I{2},params);
% Detect, extract, and match SURF-features
...
% Backproject   
[XYZ,reprojectionErrors] = triangulate(matchedPoints1,matchedPoints2,stereoParameters);

[Gilad Gottlieb]

Have you managed to solve the problem?

I suspect that it is related to the homography matrix for the rectification.

as indicated in ReconstructScene, the dense point cloud suppose to be represented in camera 1 coordinate system, however when i darw sparse points in the same figure they seems to be translated apart.

Answer 1

[Leo Leo]

i have the same question

Answer 2

[Holger Mettelsiefen]

I think this question is similar, and the accepted answer works out:

https://www.mathworks.com/matlabcentral/answers/1780505-match-the-coordinate-systems-of-triangulate-and-reconstructscene-with-disparitysgm