Learning spectral descriptors for deformable shape correspondence

R. Litman, A. M. Bronstein

Research output: Contribution to journalArticlepeer-review


Informative and discriminative feature descriptors play a fundamental role in deformable shape analysis. For example, they have been successfully employed in correspondence, registration, and retrieval tasks. In recent years, significant attention has been devoted to descriptors obtained from the spectral decomposition of the Laplace-Beltrami operator associated with the shape. Notable examples in this family are the heat kernel signature (HKS) and the recently introduced wave kernel signature (WKS). The Laplacian-based descriptors achieve state-of-the-art performance in numerous shape analysis tasks; they are computationally efficient, isometry-invariant by construction, and can gracefully cope with a variety of transformations. In this paper, we formulate a generic family of parametric spectral descriptors. We argue that to be optimized for a specific task, the descriptor should take into account the statistics of the corpus of shapes to which it is applied (the 'signal') and those of the class of transformations to which it is made insensitive (the 'noise'). While such statistics are hard to model axiomatically, they can be learned from examples. Following the spirit of the Wiener filter in signal processing, we show a learning scheme for the construction of optimized spectral descriptors and relate it to Mahalanobis metric learning. The superiority of the proposed approach in generating correspondences is demonstrated on synthetic and scanned human figures. We also show that the learned descriptors are robust enough to be learned on synthetic data and transferred successfully to scanned shapes.

Original languageEnglish
Article number6579600
Pages (from-to)171-180
Number of pages10
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number1
StatePublished - Jan 2014
Externally publishedYes


  • Correspondence
  • Deformable shapes
  • Descriptor
  • Diffusion geometry
  • Heat kernel signature (HKS)
  • Laplace-Beltrami operator
  • Mahalanobis distance
  • Metric learning
  • Retrieval
  • Spectral methods
  • Wave kernel signature (WKS)
  • Wiener filter

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics


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