Elastic Shape Analysis of Boundaries of Planar Objects with Multiple Components and Arbitrary Topologies

  • Sebastian Kurtek
  • Hamid LagaEmail author
  • Qian Xie
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9004)


We consider boundaries of planar objects as level set distance functions and present a Riemannian metric for their comparison and analysis. The metric is based on a parameterization-invariant framework for shape analysis of quadrilateral surfaces. Most previous Riemannian formulations of 2D shape analysis are restricted to curves that can be parameterized with a single parameter domain. However, 2D shapes may contain multiple connected components and many internal details that cannot be captured with such parameterizations. In this paper we propose to register planar curves of arbitrary topologies by utilizing the re-parameterization group of quadrilateral surfaces. The criterion used for computing this registration is a proper distance, which can be used to quantify differences between the level set functions and is especially useful in classification. We demonstrate this framework with multiple examples using toy curves, medical imaging data, subsets of the TOSCA data set, 2D hand-drawn sketches, and a 2D version of the SHREC07 data set. We demonstrate that our method outperforms the state-of-the-art in the classification of 2D sketches and performs well compared to other state-of-the-art methods on complex planar shapes.


Binary Image Planar Object Planar Curf Rotational Alignment Deformation Path 
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.



This work is partially funded by the Australian Research Council (ARC) and the South Australian Government, Department of Further Education, Employment, Science and Technology.

Supplementary material

336656_1_En_29_MOESM1_ESM.pdf (2.7 mb)
Supplementary material (pdf 2,774 KB)


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of StatisticsThe Ohio State UniversityColumbusUSA
  2. 2.Phenomics and Bioinformatics Research CentreUniversity of South AustraliaAdelaideAustralia
  3. 3.Australian Centre for Plant Functional Genomics, PtyLtdAdelaideAustralia
  4. 4.Department of StatisticsFlorida State UniversityTallahasseeFlorida

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