Curvature guided level set registration using adaptive finite elements

Authors:
Andreas Dedner;Marcel Lüthi;Thomas Albrecht;Thomas Vetter
Affiliations:
Institut für Angewandte Mathematik, Universität Freiburg, Germany;Department of Computer Science, University of Basel, Switzerland;Department of Computer Science, University of Basel, Switzerland;Department of Computer Science, University of Basel, Switzerland
Venue:
Proceedings of the 29th DAGM conference on Pattern recognition
Year:
2007

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Abstract

We consider the problem of non-rigid, point-to-point registration of two 3D surfaces. To avoid restrictions on the topology, we represent the surfaces as a level-set of their signed distance function. Correspondence is established by finding a displacement field that minimizes the sum of squared difference between the function values as well as their mean curvature.We use a variational formulation of the problem, which leads to a non-linear elliptic partial differential equation for the displacement field. The main contribution of this paper is the application of an adaptive finite element discretization for solving this non-linear PDE. Our code uses the software library DUNE, which in combination with pre- and post-processing through ITK leads to a powerful tool for solving this type of problem. This is confirmed by our experiments on various synthetic and medical examples. We show in this work that our numerical scheme yields accurate results using only a moderate number of elements even for complex problems.