discretization

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In the first, preprocessing your image & extract contour then discretize the contour by approxPolyDP() function.

There nothing continuous in image so anything drawn in it is already discrete.

If you need to find polygon for this drawn contour you can use findContours function. Note that last parameter is method that may be used for simplification of extracted contour, so you can control discretization level.

Or if you already has the polygon and only want to simplify it you can use approxPolyDP function.