Noisy colored point set matching

In this paper we tackle the problem of matching two colored point sets in R3 under the bottleneck distance. First we present an exact matching algorithm that requires the computation of intersections of complex algebraic surfaces. To avoid this, we also present an approximate algorithm that is implementable and has improved asymptotic cost at the price of having the risk of ”missing” some solutions. For the case of sets with very different cardinality, we speed up calculations by using a Lossless Filtering preprocess that discards the zones of the bigger set where matches cannot occur. We provide formal and experimental discussion on the running time and accuracy of the approximate algorithm (with and without Lossless Filtering preprocess).

• Type: Journal
• Year: 2011
• Where: DAM
• Authors: Yago Diez, Joan Antoni Sellarès
• Keywords: Approximate Algorithm, DAM 2011, Exact Matching Algorithm, Lossless Filtering Preprocess, Theoretical Computer Science