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Spherical Parameterization for Genus Zero Surfaces Using Laplace-Beltrami Eigenfunctions

  • Julien LefèvreEmail author
  • Guillaume Auzias
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9389)

Abstract

In this work, we propose a fast and simple approach to obtain a spherical parameterization of a certain class of closed surfaces without holes. Our approach relies on empirical findings that can be mathematically investigated, to a certain extent, by using Laplace-Beltrami Operator and associated geometrical tools. The mapping proposed here is defined by considering only the three first non-trivial eigenfunctions of the Laplace-Beltrami Operator. Our approach requires a topological condition on those eigenfunctions, whose nodal domains must be 2. We show the efficiency of the approach through numerical experiments performed on cortical surface meshes.

Keywords

Riemannian manifold Laplace-Beltrami Operator Surface parameterization Nodal domains 

Notes

Aknowledgments

We would like to thank the reviewers for their very constructive comments. In particular a careful observation by one the reviewer is at the origin of the Remark 4 and of important modifications in the structure of the manuscript.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Aix-Marseille Université, LSIS, CNRS UMR 7296MarseilleFrance
  2. 2.Institut de Neurosciences de la Timone UMR 7289Aix Marseille Université CNRSMarseilleFrance

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