Geometric Correspondence for Ensembles of Nonregular Shapes

  • Manasi Datar
  • Yaniv Gur
  • Beatriz Paniagua
  • Martin Styner
  • Ross Whitaker
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6892)

Abstract

An ensemble of biological shapes can be represented and analyzed with a dense set of point correspondences. In previous work, optimal point placement was determined by optimizing an information theoretic criterion that depends on relative spatial locations on different shapes combined with pairwise Euclidean distances between nearby points on the same shape. These choices have prevented such methods from effectively characterizing shapes with complex geometry such as thin or highly curved features. This paper extends previous methods for automatic shape correspondence by taking into account the underlying geometry of individual shapes. This is done by replacing the Euclidean distance for intrashape pairwise particle interactions by the geodesic distance. A novel set of numerical techniques for fast distance computations on curved surfaces is used to extract these distances. In addition, we introduce an intershape penalty term that incorporates surface normal information to achieve better particle correspondences near sharp features. Finally, we demonstrate this new method on synthetic and biological datasets.

Keywords

Geodesic Distance Eikonal Equation Implicit Surface Sharp Feature Pairwise Euclidean Distance 
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 2011

Authors and Affiliations

  • Manasi Datar
    • 1
  • Yaniv Gur
    • 1
  • Beatriz Paniagua
    • 2
  • Martin Styner
    • 2
  • Ross Whitaker
    • 1
  1. 1.Scientific Computing and Imaging InstituteUniversity of UtahUSA
  2. 2.University of North CarolinaChapel HillUSA

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