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.
This work is funded by the Agence Nationale de la Recherche (ANR-12-JS03-001-01, “Modegy").
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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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Lefèvre, J., Auzias, G. (2015). Spherical Parameterization for Genus Zero Surfaces Using Laplace-Beltrami Eigenfunctions. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_14
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DOI: https://doi.org/10.1007/978-3-319-25040-3_14
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