Approximation algorithms for a point-to-surface registration problem in medical navigation

Authors:
Darko Dimitrov;Christian Knauer;Klaus Kriegel;Fabian Stehn
Affiliations:
Institut für Informatik, Freie Universität Berlin;Institut für Informatik, Freie Universität Berlin;Institut für Informatik, Freie Universität Berlin;Institut für Informatik, Freie Universität Berlin
Venue:
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
Year:
2007

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Abstract

We present two absolute error approximation algorithms for a point-to-surface registration problem in 3D with applications in medical navigation systems. For a given triangulated or otherwise dense sampled surface S, a small point set P ⊂ R3 and an error bound µ we present two algorithms for computing the set T of rigid motions, so that the directed Hausdorff distance of P transformed by any of these rigid motions to S is at most the Hausdorff distance of the best semioptimal matching plus the user chosen error bound µ. Both algorithms take advantage of so called characteristic points Sc ⊂ S and Pc ⊂ P which are used to reduce the search space significantly. We restrict our attention to scenarios with |Pc| = 2. The algorithms are implemented and compared with respect to their efficiency in different settings.