Laplace-Beltrami nodal counts: a new signature for 3D shape analysis

Authors:
Rongjie Lai;Yonggang Shi;Ivo Dinov;Tony F. Chan;Arthur W. Toga
Affiliations:
Department of Mathematics, University of California, Los Angeles, CA;Laboratory of Neuro Imaging, Dept. of Neurology, UCLA School of Medicine, Los Angeles, CA;Laboratory of Neuro Imaging, Dept. of Neurology, UCLA School of Medicine, Los Angeles, CA;Department of Mathematics, University of California, Los Angeles, CA;Laboratory of Neuro Imaging, Dept. of Neurology, UCLA School of Medicine, Los Angeles, CA
Venue:
ISBI'09 Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to Macro
Year:
2009

Citing 2
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Abstract

In this paper we develop a new approach of analyzing 3D shapes based on the eigen-system of the Laplace-Beltrami operator. While the eigenvalues of the Laplace-Beltrami operator have been used previously in shape analysis, they are unable to differentiate isospectral shapes. To overcome this limitation, we propose here a new signature based on nodal counts of the eigenfunctions. This signature provides a compact representation of the geometric information that is missing in the eigenvalues. In our experiments, we demonstrate that the proposed signature can successfully classify anatomical shapes with similar eigenvalues.