Anisotropic laplace-beltrami operators for shape analysis

Andreux M, Rodola E, Aubry M, Cremers D (2015)

Publication Type: Conference contribution

Publication year: 2015

Journal

Lecture Notes in Computer Science Springer Verlag

Publisher: Springer Verlag

Book Volume: 8928

Pages Range: 299-312

Conference Proceedings Title: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Event location: Zurich, CHE

ISBN: 9783319162195

DOI: 10.1007/978-3-319-16220-1_21

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.

Involved external institutions

École Polytechnique - Université Paris-Saclay FR France (FR) Technische Universität München (TUM) DE Germany (DE) Paris-Est Créteil University / Université Paris-Est Créteil Val-de-Marne (UPEC) / Université Paris XII-Val-de-Marne / University Paris 12 Marne la Vallée FR France (FR)

How to cite

APA:

Andreux, M., Rodola, E., Aubry, M., & Cremers, D. (2015). Anisotropic laplace-beltrami operators for shape analysis. In Lourdes Agapito, Michael M. Bronstein, Carsten Rother (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 299-312). Zurich, CHE: Springer Verlag.

MLA:

Andreux, Mathieu, et al. "Anisotropic laplace-beltrami operators for shape analysis." Proceedings of the 13th European Conference on Computer Vision, ECCV 2014, Zurich, CHE Ed. Lourdes Agapito, Michael M. Bronstein, Carsten Rother, Springer Verlag, 2015. 299-312.

BibTeX: Download