Non-rigid Shape Comparison of Implicitly-Defined Curves

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


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.


Level Curf Signed Distance Function Correspondence Problem Arbitrary Topology Embed Curve 
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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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