Intrinsic matrices in stereo camera calibration

Question

Suppose I have two cameras, c1 and c2, observing the same scene. I can now

1. Calibrate each camera independently (e.g., with MATLAB's Camera Calibration App)
2. Calibrate both cameras simultaneously (e.g., with MATLAB's Stereo Camera Calibration App).

Interestingly, the values calculated for the intrinsic parameters of both cameras are different using method 1) and method 2). To me it is not clear why this should be the case. The intrinsic parameters of camera 1 are independent of the ones of camera 2 and vice versa, why should they influence each other? I suppose there is some form of optimization aiming to optimize simultaneously in the stereo case, however I would think that the "stereo optimum" is the same as the combined "single optimum".

Any insight?

Answer 1

You are correct: during stereo calibration the parameters of both cameras are optimized simultaneously, which is why you get the discrepancy.

When you calibrate a single camera, you are minimizing the reprojection errors from projecting the checkerboard points into that one camera. When you calibrate a stereo pair of cameras, you are minimizing the reprojeciton errors from projecting the checkerboard points into both cameras. Since you are minimizing different functions, the results will not be the same. However, the difference should be small.