High triangulation error using triangulateMultiview in MATLAB with multi-camera setup

Hello everyone,

I am a Matlab R2021a user. I am encountering issues when triangulating 3D points using the "triangulateMultiview" function. Let me explain: I am using a system of 4 calibrated stereo cameras, and I compute the **intrinsic and extrinsic parameters of my system in a standard way using a checkerboard with the "estimateCameraParameters" function.

The "estimateCameraParameters" function allows calculating extrinsic parameters only between two cameras, so I define a "master" camera relative to which I determine the position and orientation of my other cameras. I have not found any other way to proceed.

I then define my stereo system as follows:

%% CAM 1
Pose_CAM1= rigid3d(eye(3), [0, 0, 0])
Intrin_CAM1=CAM1_INT.Intrinsics
%% CAM 2
Rotation_CAM2=stereoParams12.RotationOfCamera2
Translation_CAM2=stereoParams12.TranslationOfCamera2
[orientation_CAM2, location_CAM2] = extrinsicsToCameraPose(Rotation_CAM2,Translation_CAM2);
Pose_CAM2=rigid3d(orientation_CAM2, location_CAM2)
Intrin_CAM2= CAM2_INT.Intrinsics
%% CAM 3
.
.
. 

%%
ViewID = uint32([1;2;3;4]);
rotations = [{Pose_CAM1.Rotation};{Pose_CAM2.Rotation};{Pose_CAM3.Rotation};{Pose_CAM4.Rotation}];
translations = [{Pose_CAM1.Translation};{Pose_CAM2.Translation};{Pose_CAM3.Translation};{Pose_CAM4.Translation}];

cameraPoses = table(ViewID, rotations, translations);
cameraPoses.Properties.VariableNames = {'ViewId', 'Orientation', 'Location'};
save('cameraPoses.mat','cameraPoses')

%% intrinsics — Camera intrinsics
intrinsics=[Intrin_CAM1,Intrin_CAM2,Intrin_CAM3,Intrin_CAM4];
save('intrinsics.mat','intrinsics')

%%

Then, after loading the trajectory of the points to be triangulated from the different cameras and undistorting the trajectory using the cameras' intrinsic parameters, I triangulate the trajectory point by point:

ViewID=[1;2;3;4];

point=[CAM1(1,1),CAM1(1,2);CAM2(1,1),CAM2(1,2);CAM3(1,1),CAM3(1,2);CAM4(1,1),CAM4(1,2)];
point=pointTrack(ViewID,point);
[Traj(1,:),err(1)]= triangulateMultiview(point,cameraPoses,intrinsics);

for i =  2:length(CAM1(:,2))
    point=[CAM1(i,1),CAM1(i,2);CAM2(i,1),CAM2(i,2);CAM3(i,1),CAM3(i,2);CAM4(i,1),CAM4(i,2)];
    point=pointTrack(ViewID,point);
    [Traj(i,:),err(i)]= triangulateMultiview(point,cameraPoses,intrinsics);
end
%%

However, I noticed that the errors (err) were quite high, around 10 pixels in the image frame. I tried to understand the source of these errors and observed that when using triangulation with two views specifically with the "triangulate" function the error was significantly reduced, to around 2 pixels.

I initially thought this increase in error when switching to multi-view triangulation was due to a calibration issue, but I tested the following:

[worldPoints12,err12] = triangulate(CAM1,CAM2,stereoParams12);

and

ViewID=[1;2];

point=[CAM1(1,1),CAM1(1,2);CAM2(1,1),CAM2(1,2)];
point=pointTrack(ViewID,point);
[Traj(1,:),err(1)]= triangulateMultiview(point,cameraPoses,intrinsics);

for i =  2:length(CAM1(:,2))
    point=[CAM1(i,1),CAM1(i,2);CAM2(i,1),CAM2(i,2)];
    point=pointTrack(ViewID,point);
    [Traj(i,:),err(i)]= triangulateMultiview(point,cameraPoses,intrinsics);
end

The intrinsic and extrinsic parameters come from the same calibration, as shown in the definition of my cameras in the stereo system.

However, the results of the two triangulation methods (Traj from `triangulateMultiview` and worldPoints12 from `triangulate`) are different, and I noticed that mean(err12) is generally four times lower than mean(err).

Do you have an explanation for this?

How can I correctly triangulate my points using all four cameras?

[Qu Cao]

Could you share all of your data (points and intrinsics) so that I can repdocue the issue on my end?

[Giuseppe Cecchelli]

Thank you for your response. I am attaching the data with my answer so that you can reproduce the execution. The files CAMn.txt contain the pixel coordinates of the points to be triangulated in the image frame of camera n (before point undistortion).

I am including the extrinsic parameters (cameraPoses) and intrinsic parameters (intrinsics) that I use for point undistortion and subsequent multi-view triangulation. I am also attaching the stereo parameters between camera 1 and 2 that I use, as in my example.

If I have forgotten something, please do not hesitate to let me know.

Have a great day,

Giuseppe Cecchelli

Answer 1

[mrk]

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