'Fit Quadrilateral (Tetragon) to a blob
After applying different filtering and segmentation techniques, I end up with an image like this:
I have access to some contours detection functions that return a list of points on the edge of that object, or returns a fitted polygon (with many edges though, much more than 4). I want a way to fit a quadrilateral to that shape as I know it is a front face of a shoebox that is supposed to be a quadrilateral. Due to the perspective view, the parallelity is not conserved so I have no constraints for now and just need four line segments encompassing this box.
What I could find until now was only rectangle fitting, which doesn't really returns the result I need as it forces the fitted quadrilateral to be rectangular.
If I had access to the relative angle of the camera to that shoebox and knew the distance of the shoebox from my camera, I could generate a Homography matrix and warp the image such that the shoebox appears rectangular again, but for now I have no access to such information and want to do it based purely vision.
Any known approaches for solving such a problem?
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