Spherical parameterization for genus zero surfaces using Laplace-Beltrami eigenfunctions

Julien Lefèvre (1) , Guillaume Auzias (1)

1 INT - Institut de Neurosciences de la Timone

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.

Mots clés: Riemannian Manifold; Laplace-Beltrami Operator; Surface Parameterization; Nodal Domains

Domaines: Géométrie différentielle [math.DG]

Julien Lefèvre, Guillaume Auzias. Spherical parameterization for genus zero surfaces using Laplace-Beltrami eigenfunctions. Second International Conference, GSI 2015, Palaiseau, France, October 28-30, 2015, Proceedings, Frank Nielsen Frederic Barbaresco, Oct 2015, Palaiseau, France. ⟨hal-01222933⟩