Author(s)

Adolfo Horacio Escalona-Buendia¹, Lucila Ivonne Hernández-Martínez², Rarafel Martínez-Vega², Julio Roberto Murillo-Torres², Omar Nieto-Crisóstomo¹

¹Academia de Informática, Universidad Autónoma de la Ciudad de México, Mexico City, Mexico.
²Academia de Matemáticas, Universidad Autónoma de la Ciudad de México, Mexico City, Mexico.

In this work we describe the algorithms to construct the skeletons, simplified 1D representations for a 3D surface depicted by a mesh of points, given the respective eigenfunctions of the Discrete Laplace-Beltrami Operator (LBO). These functions are isometry invariant, so they are independent of the object’s representation including parameterization, spatial position and orientation. Several works have shown that these eigenfunctions provide topological and geometrical information of the surfaces of interest [1] [2]. We propose to make use of that information for the construction of a set of skeletons, associated to each eigenfunction, which can be used as a fingerprint for the surface of interest. The main goal is to develop a classification system based on these skeletons, instead of the surfaces, for the analysis of medical images, for instance.

Skeleton, Centerline, Discrete Laplace-Beltrami Operator Eigenfunctions, Graph Theory

Escalona-Buendia, A. , Hernández-Martínez, L. , Martínez-Vega, R. , Murillo-Torres, J. and Nieto-Crisóstomo, O. (2015) Skeletons of 3D Surfaces Based on the Laplace-Beltrami Operator Eigenfunctions. Applied Mathematics, 6, 414-420. doi: 10.4236/am.2015.62038.