Approximation Algorithms for a Point-to-Surface Registration Problem in Medical Navigation

  • Darko Dimitrov
  • Christian Knauer
  • Klaus Kriegel
  • Fabian Stehn
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4613)


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 \(\mathcal{S}\), a small point set P ⊂ ℝ3 and an error bound μ we present two algorithms for computing the set \(\mathcal{T}\) of rigid motions, so that the directed Hausdorff distance of P transformed by any of these rigid motions to \(\mathcal{S}\) 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 \(S_c \subset \mathcal{S}\) and P c  ⊂ P which are used to reduce the search space significantly. We restrict our attention to scenarios with |P c | = 2. The algorithms are implemented and compared with respect to their efficiency in different settings.


Characteristic Point Rigid Motion Rigid Transformation Matching Time Segment Tree 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Darko Dimitrov
    • 1
  • Christian Knauer
    • 1
  • Klaus Kriegel
    • 1
  • Fabian Stehn
    • 1
  1. 1.Institut für Informatik, Freie Universität Berlin 

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