Automated Shape Recognition and Curve Matching using Discrete Invariants

We propose a new type of algorithm for curve matching. Our approach is based on recent theoretical advances regarding integral quantities that are invariant under certain group actions. Concentrating on rigid motions in R2 , we construct discrete integral invariants. As the direct application of numerical quadratures to integral invariants does not result in invariant quantities, we show how to "invariantize" discrete quantities that only depend on samplings of the curves.;The significance of these new discrete invariants is threefold. First, these invariants provide a way to compute invariants for curves given discretely. Second, our approach is not limited to the Special Euclidean group. Third, and most importantly, our discrete invariants are robust with respect to curve samplings.;The performance of the proposed approach is successfully tested on two applications: character recognition and jigsaw puzzle assembly.