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Hierarchical Organization of Shapes for Efficient Retrieval

  • Shantanu Joshi
  • Anuj Srivastava
  • Washington Mio
  • Xiuwen Liu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3023)

Abstract

This paper presents a geometric approach to perform: (i) hierarchical clustering of imaged objects according to the shapes of their boundaries, and (ii) testing of observed shapes for classification. An intrinsic metric on nonlinear, infinite-dimensional shape space, obtained using geodesic lengths, is used for clustering. This analysis is landmark free, does not require embedding shapes in ℝ2, and uses ordinary differential equations for flows (as opposed to partial differential equations). Intrinsic analysis also leads to well defined shape statistics such as means and covariances, and is computationally efficient. Clustering is performed in a hierarchical fashion. At any level of hierarchy clusters are generated using a minimum dispersion criterion and an MCMC-type search algorithm. Cluster means become elements to be clustered at the next level. Gaussian models on tangent spaces are used to pose binary or multiple hypothesis tests for classifying observed shapes. Hierarchical clustering and shape testing combine to form an efficient tool for shape retrieval from a large database of shapes. For databases with n shapes, the searches are performed using log(n) tests on average. Examples are presented for demonstrating these tools using shapes from Kimia shape database and the Surrey fish database.

Keywords

Simulated Annealing Hierarchical Organization Shape Space Multiple Hypothesis Test Geodesic 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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Shantanu Joshi
    • 1
  • Anuj Srivastava
    • 2
  • Washington Mio
    • 3
  • Xiuwen Liu
    • 4
  1. 1.Department of Electrical Engineering 
  2. 2.Department of Statistics 
  3. 3.Department of Mathematics 
  4. 4.Department of Computer ScienceFlorida State UniversityTallahasseeUSA

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