Camera calibration - estimating the skew encreases the mean reprojection error ?

Hello,

I work on a system based on a calibrated camera (pin-hole model). Some specificities of the system make me believe that the skew parameter from the intrinsic parameters of the camera may not be equal to 0. The reasons why are not in the scope of my question.

To do the calibration, I use the function estimateCameraParameters from the computer vision toolbox. On my calibration data, a standard calibration gives me a mean reprojection error up to 0.03 pixels. But when I calibrate with the option ‘EstimateSkew’ at true, the mean reprojection reaches 0.36 pixels, an order of magnitude higher than before.

Given that the constraint skew = 0 is released, the calibration process has one degree of freedom more than when fixing skew to 0. I was so expecting to see the minimized criterion (the mean reprojection error) decrease. It is clearly not the case.

Am I wrong on my reasoning? Can somebody explain why allowing skew to be different from 0 downgrades the results?

You can find in attachment a MATLAB script where both calibration modes are used, a .mat file with the coordinates of the detected points for the calibration (input of the MATLAB script).