Matching Surfaces with Characteristic Points

We study approximation algorithms for a matching problem that is motivated by medical applications. Given a small set of points P ⊂ R3 and a surface S, the optimal matching of P with S is represented by a rigid transformation which maps P as ‘close as possible’ to S. Previous solutions either require polynomial runtime of high degree [2] or they make use of heuristic techniques which could be trapped in some local minimum. We propose a modification of the problem setting by introducing subsets of characteristic points Pc ⊆ P and Sc ⊆ S, and assuming that points from Pc must be matched with points from Sc. We will show that especially in the case |Pc | ≥2 this restriction results in new fast and reliable algorithms for the matching problem.