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Camera matrix = [fx 1 cx; 1 fy cy;0 0 1] seems to be wrong it should rather be [fx 0 cx; 1 fy cy;0 0 1] unless you really have a camera with skew = 1.

Besides the procedure yourdescribed looks OK. Only reprojection error = 10 is huge, I'm not sure if this is for purpose but you usually use reprojection error like 1 or 2 pixels.

Camera matrix = [fx 1 cx; 1 1 fy cy;0 0 1] seems to be is wrong it should rather be [fx 0 cx; 1 0 fy cy;0 0 1] unless (or [fx s cx; 0 fy cy;0 0 1] if you really have a camera with non-zero skew = 1.s but this is seldom the case).

Besides the procedure yourdescribed looks OK. Only reprojection error = 10 is huge, I'm not sure if this is for purpose but you usually use reprojection error like 1 or 2 pixels.

Camera matrix = [fx 1 cx; 1 fy cy;0 0 1] is wrong it should be [fx 0 cx; 0 fy cy;0 0 1] (or [fx s cx; 0 fy cy;0 0 1] if you have a camera with non-zero skew s but this is seldom the case).

Besides the procedure yourdescribed you described looks OK. Only reprojection error = 10 is huge, I'm not sure if this is for purpose but you usually should use reprojection error like 1 or 2 pixels.