Anisotropic Laplace-Beltrami eigenmaps: Bridging Reeb graphs and skeletons

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 incorpor...

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Bibliographic Details
Published in:2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops 2008-07, 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
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Summary: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.
ISSN:2160-7508
2160-7516
DOI:10.1109/CVPRW.2008.4563018