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Elastic Shape Matching of Parameterized Surfaces Using Square Root Normal Fields

  • Ian H. Jermyn
  • Sebastian Kurtek
  • Eric Klassen
  • Anuj Srivastava
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7576)

Abstract

In this paper we define a new methodology for shape analysis of parameterized surfaces, where the main issues are: (1) choice of metric for shape comparisons and (2) invariance to reparameterization. We begin by defining a general elastic metric on the space of parameterized surfaces. The main advantages of this metric are twofold. First, it provides a natural interpretation of elastic shape deformations that are being quantified. Second, this metric is invariant under the action of the reparameterization group. We also introduce a novel representation of surfaces termed square root normal fields or SRNFs. This representation is convenient for shape analysis because, under this representation, a reduced version of the general elastic metric becomes the simple \(\ensuremath{\mathbb{L}^2}\) metric. Thus, this transformation greatly simplifies the implementation of our framework. We validate our approach using multiple shape analysis examples for quadrilateral and spherical surfaces. We also compare the current results with those of Kurtek et al. [1]. We show that the proposed method results in more natural shape matchings, and furthermore, has some theoretical advantages over previous methods.

Keywords

Linear Interpolation Spherical Surface Shape Analysis Surface Graph Riemannian Metrics 
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 2012

Authors and Affiliations

  • Ian H. Jermyn
    • 1
  • Sebastian Kurtek
    • 2
  • Eric Klassen
    • 3
  • Anuj Srivastava
    • 4
  1. 1.Department of Mathematical SciencesDurham UniversityDurhamEngland
  2. 2.Department of StatisticsThe Ohio State UniversityColumbusUSA
  3. 3.Department of MathematicsFlorida State UniversityTallahasseeUSA
  4. 4.Department of StatisticsFlorida State UniversityTallahasseeUSA

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