Shape matching by random sampling

In order to determine the similarity between two planar shapes, which is an important problem in computer vision and pattern recognition, it is necessary to first match the two shapes as well as possible. As sets of allowed transformation to match shapes we consider translations, rigid motions, and similarities. We present a generic probabilistic algorithm based on random sampling for matching shapes which are modelled by sets of curves. The algorithm is applicable to the three considered classes of transformations. We analyze which similarity measure is optimized by the algorithm and give rigorous bounds on the number of samples necessary to get a prespecified approximation to the optimal match within a prespecified probability.