Point-Based Manifold Harmonics

7 years 8 months ago
Point-Based Manifold Harmonics
—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 [1], 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.
Yang Liu, Balakrishnan Prabhakaran, Xiaohu Guo
Added 28 Sep 2012
Updated 28 Sep 2012
Type Journal
Year 2012
Where TVCG
Authors Yang Liu, Balakrishnan Prabhakaran, Xiaohu Guo
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