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2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops
Anisotropic Laplace-Beltrami eigenmaps: Bridging Reeb graphs and skeletons
Anchorage, AK, USA
June 23-June 28
ISBN: 978-1-4244-2339-2
Yonggang Shi, Lab of Neuro Imaging, UCLA School of Medicine, USA
Rongjie Lai, Department of Mathematics, UCLA, USA
Sheila Krishna, Department of Neurology, UCLA School of Medicine, USA
Nancy Sicotte, Department of Neurology, UCLA School of Medicine, USA
Ivo Dinov, Lab of Neuro Imaging, UCLA School of Medicine, USA
Arthur W. Toga, Lab of Neuro Imaging, UCLA School of Medicine, USA
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.
Citation:
Yonggang Shi, Rongjie Lai, Sheila Krishna, Nancy Sicotte, Ivo Dinov, Arthur W. Toga, "Anisotropic Laplace-Beltrami eigenmaps: Bridging Reeb graphs and skeletons," cvprw, pp.1-7, 2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, 2008
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