Anisotropic Laplace-Beltrami eigenmaps: Bridging Reeb graphs and skeletons

• Published in: 2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops 2008-07, Vol.2008, p.1-7
• Main Authors: Yonggang Shi, Rongjie Lai, Krishna, S., Sicotte, N., Dinov, I., Toga, A.W.
• Format: Article
• Language: English
• Subjects: Anisotropic magnetoresistance; Biomedical computing; Biomedical imaging; Eigenvalues and eigenfunctions; Geometry; Neuroimaging; Robustness; Shape; Skeleton; Topology
• ISSN: 2160-7508; 1063-6919; 2160-7516; 1063-6919
• DOI: 10.1109/CVPRW.2008.4563018

In this paper we propose a novel approach of computing skeletons of robust topology for simply connected surfaces with boundary by constructing Reeb graphs from the eigen-functions of an anisotropic Laplace-Beltrami operator. Our work brings together the idea of Reeb graphs and skeletons by incorporating a flux-based weight function into the Laplace-Beltrami operator. Based on the intrinsic geometry of the surface, the resulting Reeb graph is pose independent and captures the global profile of surface geometry. Our algorithm is very efficient and it only takes several seconds to compute on neuroanatomical structures such as the cingulate gyrus and corpus callosum. In our experiments, we show that the Reeb graphs serve well as an approximate skeleton with consistent topology while following the main body of conventional skeletons quite accurately.