Deformable Shape Retrieval by Learning Diffusion Kernels

  • Yonathan Aflalo
  • Alexander M. Bronstein
  • Michael M. Bronstein
  • Ron Kimmel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6667)


In classical signal processing, it is common to analyze and process signals in the frequency domain, by representing the signal in the Fourier basis, and filtering it by applying a transfer function on the Fourier coefficients. In some applications, it is possible to design an optimal filter. A classical example is the Wiener filter that achieves a minimum mean squared error estimate for signal denoising. Here, we adopt similar concepts to construct optimal diffusion geometric shape descriptors. The analogy of Fourier basis are the eigenfunctions of the Laplace-Beltrami operator, in which many geometric constructions such as diffusion metrics, can be represented. By designing a filter of the Laplace-Beltrami eigenvalues, it is theoretically possible to achieve invariance to different shape transformations, like scaling. Given a set of shape classes with different transformations, we learn the optimal filter by minimizing the ratio between knowingly similar and knowingly dissimilar diffusion distances it induces. The output of the proposed framework is a filter that is optimally tuned to handle transformations that characterize the training set.


Heat Kernel Retrieval Performance Fourier Basis Shape Class Spectral 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 2012

Authors and Affiliations

  • Yonathan Aflalo
    • 1
  • Alexander M. Bronstein
    • 2
  • Michael M. Bronstein
    • 3
  • Ron Kimmel
    • 1
  1. 1.Technion, Israel Institute of TechnologyHaifaIsrael
  2. 2.Dept. of Electrical EngineeringTel Aviv UniversityIsrael
  3. 3.Inst. of Computational Science, Faculty of InformaticsUniversità della Svizzera ItalianaLuganoSwitzerland

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