Planar shape representation and matching under projective transformation

This paper introduces a new representation for planar objects which is invariant to projective transformation. Proposed representation relies on a new shape basis which we refer to as the conic basis. The conic basis takes conic-section coefficients as its dimensions and represents the object as a convex combination of conic-sections. Pairs of conic-sections in this new basis and their projective invariants provides the proposed view invariant representation. We hypothesize that two projectively transformed versions of an object result in the same representation. We show that our hypothesis provides promising recognition performance when we use the nearest neighbor rule to match projectively deformed objects.

► New shape descriptors invariant to projective transformation are introduced. ► A conic basis approximates object shape by piecewise conic sections. ► Distribution of projective invariants computed from conic pairs characterize shapes. ► Promising recognition performance when applied to projectively transformed shapes.