Why is the pointsToWorld back-projection inverted?

Hi I have a question regarding the use of estimateWorldCameraPose and pointsToWorld of the Computer Vision Toolbox.

When I estimate the orientation and the location of the camera relative to the planar scene of points using estimateWorldCameraPose,

and then, using the camera orientation and postion thus obtained, I back-project the points to world coordinates (sans depth) using pointsToWorld,

why are the back-projected points inverted relative to the original world points?

The below code illustrates the question:

% Create a matrix of planar world points
[wx,wy]=meshgrid(0:20:100,0:40:200);
worldPoints=[wx(:) wy(:) zeros(size(wy(:)))];

% Remove one (so we can recognize the orientation later)
worldPoints(2,:)=[];

% Create a set of image points. For this example they are the same as the world
% points (but 2D)
imagePoints=worldPoints(:,[1 2]);


% Create arbitraty camera intrinsics
focalLength    = [800, 800];
principalPoint = [320, 240];
imageSize      = [480, 640];
intrinsics = cameraIntrinsics(focalLength,principalPoint,imageSize);

% Estimate the orientation and the location of the camera relative to the planar
% scene of points
[worldOri,worldLoc] = estimateWorldCameraPose(worldPoints(:,[1 2]),worldPoints,intrinsics);

% Using the estimates, back project the points to world coordinates (sans depth)
backProjectPoints = pointsToWorld(intrinsics,worldOri,worldLoc,imagePoints);

% Plot the worldPoints and the back projection
figure
scatter(worldPoints(:,1),worldPoints(:,2))
hold on
scatter(backProjectPoints(:,1),backProjectPoints(:,2))
title('Why inverted?');

Answer 1

[Qu Cao]

You may need to convert the camera world pose to extrinsics using cameraPoseToExtrinsics:

[worldOri,worldLoc] = estimateWorldCameraPose(worldPoints(:,[1 2]),worldPoints,intrinsics);

[rotationMatrix,translationVector] = cameraPoseToExtrinsics(worldOri,worldLoc);

backProjectPoints = pointsToWorld(intrinsics,rotationMatrix,translationVector,imagePoints);

[Duijnhouwer]

That works :) Thanks Qu!