Combinatorial and experimental results for randomized point matching algorithms

Abstract The subject of this paper is the design and analysis of Monte Carlo algorithms for two basic matching techniques used in model-based recognition: alignment, and geometric hashing. We first give analyses of our Monte Carlo algorithms, showing that they are asymptotically faster than their deterministic counterparts while allowing failure probabilities that are provably very small. We then describe experimental results that bear out this speed-up, suggesting that randomization results in significant improvements in running time. Our theoretical analyses are not the best possible; as a step to remedying this we define a combinatorial measure of self-similarity for point sets, and give an example of its power.