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Non-rigid Shape Comparison of Implicitly-Defined Curves

  • Sheshadri R. Thiruvenkadam
  • David Groisser
  • Yunmei Chen
Conference paper
  • 987 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3752)

Abstract

We present a novel variational model to find shape-based correspondences between two sets of level curves. While the usual correspondence techniques work with parametrized curves, we use a level-set formulation that enables us to handle curves with arbitrary topology. Given the functions \(\Phi_{1}: (\Omega_{1} \subseteq IR^{2}) \longrightarrow IR\) and \(\Phi_{2}: (\Omega_{2} \subseteq IR^{2}) \longrightarrow IR\) whose 0-level curves we want to match, we search for a diffeomorphism that minimizes the rate of change of the difference in tangential orientation of the zero-level sets. To make the formulation symmetric and to simplify computations, we map the domains of the level-set functions Φ i to a common domain Ω by initial diffeomorphisms that are chosen arbitrarily. We then search for diffeomorphisms from Ω to itself, generating them by flows of certain vector fields on Ω. The resulting correspondences are scale- and rotation-invariant with respect to the curves. We show how this model can be used as a basis to compare curves of different topology. The model was tested on synthetic and MRI cardiac data,with good results.

Keywords

Level Curf Signed Distance Function Correspondence Problem Arbitrary Topology Embed Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Sheshadri R. Thiruvenkadam
    • 1
  • David Groisser
    • 2
  • Yunmei Chen
    • 2
  1. 1.University of CaliforniaLos AngelesUSA
  2. 2.University of FloridaGainesvilleUSA

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