The analysis of deformable 3D shape is often cast in terms of the shape's intrinsic geometry due to its invariance to a wide range of non-rigid deformations. However, object's plasticity in non-rigid transformation often result in transformations that are not completely isometric in the surface's geometry and whose mode of deviation from isometry is an identifiable characteristic of the shape and its deformation modes. In this paper, we propose a novel generative model of the variations of the intrinsic metric of de formable shapes, based on the spectral decomposition of the Laplace-Beltrami operator. To this end, we assume two independent models for the eigenvectors and the eigenvalues of the graph-Laplacian of a 3D mesh which are learned in a supervised way from a set of shapes belonging to the same class. We show how this model can be efficiently learned given a set of 3D meshes, and evaluate the performance of the resulting generative model in shape classification and retrieval tasks. Comparison with state-of-the-art solutions for these problems confirm the validity of the approach.

A Statistical Model of Riemannian Metric Variation for Deformable Shape Analysis

GASPARETTO, ANDREA;TORSELLO, Andrea
2015-01-01

Abstract

The analysis of deformable 3D shape is often cast in terms of the shape's intrinsic geometry due to its invariance to a wide range of non-rigid deformations. However, object's plasticity in non-rigid transformation often result in transformations that are not completely isometric in the surface's geometry and whose mode of deviation from isometry is an identifiable characteristic of the shape and its deformation modes. In this paper, we propose a novel generative model of the variations of the intrinsic metric of de formable shapes, based on the spectral decomposition of the Laplace-Beltrami operator. To this end, we assume two independent models for the eigenvectors and the eigenvalues of the graph-Laplacian of a 3D mesh which are learned in a supervised way from a set of shapes belonging to the same class. We show how this model can be efficiently learned given a set of 3D meshes, and evaluate the performance of the resulting generative model in shape classification and retrieval tasks. Comparison with state-of-the-art solutions for these problems confirm the validity of the approach.
2015
The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
File in questo prodotto:
File Dimensione Formato  
Gasparetto_A_Statistical_Model_2015_CVPR_paper.pdf

accesso aperto

Tipologia: Documento in Post-print
Licenza: Accesso gratuito (solo visione)
Dimensione 3.29 MB
Formato Adobe PDF
3.29 MB Adobe PDF Visualizza/Apri
published.pdf

non disponibili

Tipologia: Versione dell'editore
Licenza: Accesso chiuso-personale
Dimensione 1.49 MB
Formato Adobe PDF
1.49 MB Adobe PDF   Visualizza/Apri

I documenti in ARCA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10278/3661439
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 18
  • ???jsp.display-item.citation.isi??? 11
social impact