Strange ArUco behavior / OpenCV SolvePnp

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Hi There,

I tested the accuracy of ArUco markers in severeal distances and used for that a board with a not rotated marker, several rotated marker on their z-Axis (known rotation) and several more not rotated marker. All markers are measured in their rotation in relation to the first not rotated marker.

Now I calculate the transformation (with quaternions) from the marker of interest in the reference marker. The output for my accuracy is the angle theta from the axis angles. The strange thing is, that the rotation error of the rotated (5°, 20°, 30°, 45°, 90° 180°) markers is small (max. 1°) and the error of the not roted marker (0°) is large (>2°).

I do the subpixel corner refinement and the detected markers looks fine for me. I can exclude the error of the camera, because changing positions (near to the center of the image or not) does not change the accuracy. As well I switched the IDs.

How can it be, that rotated marker are more accurate then non roated marker. Could it be a singularity on the detection or numeric errors?

Thank you for your help!

Sarah