As I understand, you want to resolve the convention that is used in the output of the PoseCamera2, and you also want an explanation for your observations. The observations can be explained as follows:
Let “E1” and “E2” denote the poses from Camera 1 and Camera 2 .
E1 = [R1, t1; 0, 1]; % E1 matrix
E2 = [R2, t2; 0, 1]; % E2 matrix
In the equations that you have mentioned, the following equality should hold, but based on your figures, you observed that it does not.
E1 = [R, T; 0, 1] * [R2, t2; 0, 1];
E1 = [R * R2, R * t2 + T; 0, 1];
From the observation, the positions of both cameras align when "t2" is shifted by "T". This occurs when "R" and "T" are used to transform the position of camera2 to match the position of camera1, as follows:
% Inverse of the transformation matrix [R, T; 0, 1]
E1 = inv([R, T; 0, 1]) * E2;
E1 = [R', -R' * T; 0, 1] * [R2, t2; 0, 1];
[R1, t1; 0, 1] = [R' * R2, R' * (t2 - T); 0, 1];
As shown in the code snippet above, when comparing “t1” on the LHS with its corresponding value on the RHS, observe that “t1” equals "R' * (t2 - T)". This confirms your observation in Figure1 that "t2" needs to be shifted by "T" for the positions of both cameras to match. The additional rotation aligns the orientations of both cameras. Similarly, the same argument can be made for Figure2.
I hope this helps!
