Anisotropic Laplace-Beltrami Operators for Shape Analysis

  • Mathieu AndreuxEmail author
  • Emanuele Rodolà
  • Mathieu Aubry
  • Daniel Cremers
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8928)


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.


Shape analysis Anisotropic diffusion Curvature Non-rigid matching Segmentation Laplace-Beltrami operator 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Mathieu Andreux
    • 1
    Email author
  • Emanuele Rodolà
    • 2
  • Mathieu Aubry
    • 3
  • Daniel Cremers
    • 2
  1. 1.École polytechniquePalaiseauFrance
  2. 2.Technische Universität MünchenMunichGermany
  3. 3.Université Paris Est LIGM - École des Ponts ParistechChamps-sur-MarneFrance

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