This paper introduces an anisotropic Laplace-Beltrami operator for shape analysis. While keeping useful properties of the standard Laplace-Beltrami operator, it introduces variability in the directions of principal curvature, giving rise to a more intuitive and semantically meaningful diffusion process. Although the benefits of anisotropic diffusion have already been noted in the area of mesh processing (e.g. surface regularization), focusing on the Laplacian itself, rather than on the diffusion process it induces, opens the possibility to effectively replace the omnipresent Laplace-Beltrami operator in many shape analysis methods. After providing a mathematical formulation and analysis of this new operator, we derive a practical implementation on discrete meshes. Further, we demonstrate the effectiveness of our new operator when employed in conjunction with different methods for shape segmentation and matching.

Anisotropic Laplace-Beltrami operators for shape analysis / Andreux, Mathieu; Rodolá, Emanuele; Aubry, Mathieu; Cremers, Daniel. - 8928:(2015), pp. 299-312. (Intervento presentato al convegno 13th European Conference on Computer Vision, ECCV 2014 tenutosi a Zurich; Switzerland) [10.1007/978-3-319-16220-1_21].

Anisotropic Laplace-Beltrami operators for shape analysis

Rodolá, Emanuele;
2015

Abstract

This paper introduces an anisotropic Laplace-Beltrami operator for shape analysis. While keeping useful properties of the standard Laplace-Beltrami operator, it introduces variability in the directions of principal curvature, giving rise to a more intuitive and semantically meaningful diffusion process. Although the benefits of anisotropic diffusion have already been noted in the area of mesh processing (e.g. surface regularization), focusing on the Laplacian itself, rather than on the diffusion process it induces, opens the possibility to effectively replace the omnipresent Laplace-Beltrami operator in many shape analysis methods. After providing a mathematical formulation and analysis of this new operator, we derive a practical implementation on discrete meshes. Further, we demonstrate the effectiveness of our new operator when employed in conjunction with different methods for shape segmentation and matching.
2015
13th European Conference on Computer Vision, ECCV 2014
Anisotropy; Computer vision; Diffusion
04 Pubblicazione in atti di convegno::04b Atto di convegno in volume
Anisotropic Laplace-Beltrami operators for shape analysis / Andreux, Mathieu; Rodolá, Emanuele; Aubry, Mathieu; Cremers, Daniel. - 8928:(2015), pp. 299-312. (Intervento presentato al convegno 13th European Conference on Computer Vision, ECCV 2014 tenutosi a Zurich; Switzerland) [10.1007/978-3-319-16220-1_21].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1228061
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