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Shape retrieval using hierarchical total Bregman soft clustering.

Meizhu Liu1, Baba C Vemuri, Shun-Ichi Amari

  • 1Department of CISE, University of Florida, E324, CSE Building, PO Box 11612, Gainesville, FL 32611, USA. mliu@cise.ufl.edu

IEEE Transactions on Pattern Analysis and Machine Intelligence
|February 15, 2012
PubMed
Summary
This summary is machine-generated.

This paper introduces total Bregman divergences (tBDs) for shape dissimilarity measurement and proposes a tBD-based center (t-center) for shape representation. A novel soft clustering algorithm based on tBDs is developed and applied to shape retrieval, showing competitive results.

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Area of Science:

  • Computational Geometry
  • Machine Learning
  • Computer Vision

Background:

  • Quantifying shape dissimilarity is crucial for various applications.
  • Existing methods may lack efficiency or robustness in shape comparison.
  • The need for advanced distance measures and representative shape descriptors is evident.

Purpose of the Study:

  • To introduce and analyze total Bregman divergences (tBDs) as a robust measure for shape dissimilarity.
  • To develop a tBD-based shape representative, termed the t-center.
  • To propose a novel clustering algorithm and shape retrieval framework using tBDs.

Main Methods:

  • Utilized total Bregman divergences (tBDs) for shape dissimilarity quantification.
  • Defined and analyzed the t-center as a representative of shape sets.
  • Developed a total Bregman soft clustering algorithm by linking tBD minimization to maximum a posteriori (MAP) estimation in lifted exponential families.
  • Implemented a shape retrieval framework involving boundary point extraction, affine alignment, Gaussian Mixture Model (GMM) representation, and tBD comparison.
  • Applied hierarchical clustering using the proposed algorithm to accelerate retrieval.

Main Results:

  • Established the existence of distributions within the lifted exponential family corresponding to any tBD.
  • Demonstrated the equivalence between MAP estimation and tBD minimization for finding t-centers.
  • Achieved comparable or superior performance against state-of-the-art methods in 2D and 3D shape retrieval tasks.
  • Showcased the efficiency of hierarchical clustering for speeding up the retrieval process.

Conclusions:

  • Total Bregman divergences offer an efficient and robust approach for shape analysis.
  • The t-center provides a reliable representative for sets of shapes.
  • The proposed soft clustering and shape retrieval methods are effective and efficient, outperforming existing techniques.