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what is optimal window size for cornerSubPix on chessboard?

In the process of calibrating stereo pairs of cameras, I've recently begun using cornerSubPix, and it generally helps. I am puzzled about the windowSize parameter, though. So far, it seems to do best with a size of (4, 4), judging by the computed reprojection error. I use over 50 image pairs from various angles and distances.

My main question is, why does it need a window size bigger than 1 or 2? Doesn't findChessboard give answers correct to within +/- about 1 pixel?

Also (not really a question) the official calibSample and stereoCalibSample programs use a size of (11, 11) which sometimes yields result worse than the unrefined results. It seems like that should be changed.