Projectively invariant decomposition and recognition of planar shapes

An algorithm is presented for computing a decomposition of planar shapes into convex subparts represented by ellipses. The method is invariant to projective transformations of the shape, and thus the ellipses can be used for matching and definition of invariants in the same way as points and lines. The method works for arbitrary planar shapes admitting at least four distinct tangents and is based on finding ellipses with four points of contact to the given shape. The cross ratio computed from the four points on the ellipse can then be used as a projectively invariant index. For a given shape, each pair of ellipses can be used to compute two independent projective invariants. The set of invariants computed for each ellipse pair can be used as indexes to a hash table from which a model hypothesis can be generated