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Approximate contour with n-sided polygon

I have segmented a contour which can be approximated by a 5-sided polygon (a square with a corner broken off). Is there a function that makes use of this information? I currently uses approxPolyNP, but that function only uses a maximal distance between the approximation and the contour and not the expected number of corners.

Approximate contour with n-sided polygon

I have segmented a contour which can be approximated by a 5-sided polygon (a square with a corner broken off). Is there a function that makes use of this information? I currently uses approxPolyNP, approxPolyDP, but that function only uses a maximal distance between the approximation and the contour and not the expected number of corners.

Approximate contour with n-sided polygon

I have segmented a contour which can be approximated by a 5-sided polygon (a square with a corner broken off). Is there a function that makes use of this information? I currently uses approxPolyDP, but that function only uses a maximal distance between the approximation and the contour and not the expected number of corners.