Relative pose transformation between poses of 2 frames

Question

I want to calculate the relative pose transformation between poses of 2 frames/images that are taken from the camera. I have the ground truth poses of those frames in 3x4 matrix [R t] form. What is the formula for calculating the relative pose of those 2 images? Also, does finding the relative poses between 1.frame to 2.frame and 2.frame to 1.frame make difference in terms of result?

I am not so sure of the mathematical formula that is needed for relative pose.

Answer 1

"Between" is a directionless notion.

Transformations have direction.

You need to know which way your transformations go, and you need to keep track of that.

Assuming you have object poses relative to the camera frame, those matrices should be called

Now, if you want the pose of the second object in the first object's frame, this is:

You should, for ease of calculation (inversion), work with 4x4 matrices.