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|a 10.1109/TVCG.2011.152
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|a eng
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|a Liu, Yang
|e verfasserin
|4 aut
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|a Point-based manifold harmonics
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|c 2012
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|a Text
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|a ƒaComputermedien
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|a Date Completed 27.02.2013
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|a Date Revised 10.08.2012
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|a published: Print
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|a Citation Status PubMed-not-MEDLINE
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|a This paper proposes an algorithm to build a set of orthogonal Point-Based Manifold Harmonic Bases (PB-MHB) for spectral analysis over point-sampled manifold surfaces. To ensure that PB-MHB are orthogonal to each other, it is necessary to have symmetrizable discrete Laplace-Beltrami Operator (LBO) over the surfaces. Existing converging discrete LBO for point clouds, as proposed by Belkin et al., is not guaranteed to be symmetrizable. We build a new point-wisely discrete LBO over the point-sampled surface that is guaranteed to be symmetrizable, and prove its convergence. By solving the eigen problem related to the new operator, we define a set of orthogonal bases over the point cloud. Experiments show that the new operator is converging better than other symmetrizable discrete Laplacian operators (such as graph Laplacian) defined on point-sampled surfaces, and can provide orthogonal bases for further spectral geometric analysis and processing tasks
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|a Journal Article
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|a Research Support, U.S. Gov't, Non-P.H.S.
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|a Prabhakaran, Balakrishnan
|e verfasserin
|4 aut
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| 700 |
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|a Guo, Xiaohu
|e verfasserin
|4 aut
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|i Enthalten in
|t IEEE transactions on visualization and computer graphics
|d 1996
|g 18(2012), 10 vom: 08. Okt., Seite 1693-703
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