We propose a homography estimation method from the contours of planar regions. Standard projective invariants such as cross ratios or canonical frames based on hot points obtained from local differential properties are extremely unstable in real images suffering from pixelization, thresholding artifacts, and other noise sources. We explore alternative constructions based on global convexity properties of the contour such as discrete tangents and concavities. We show that a projective frame can be robustly extracted from arbitrary shapes with at least one appreciable concavity. Algorithmic complexity and stability are theoretically discussed and experimentally evaluated in a number of real applications including projective shape matching, alignment and pose estimation. We conclude that the procedure is computationally efficient and notably robust given the ill-conditioned nature of the problem.
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