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Point-Based
Manifold Harmonics |
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| Project
Members |
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Yang
Liu, Balakrishnan
Prabhakaran, Xiaohu Guo
Department
of Computer Science
University
of Texas at Dallas |
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| Abstract: |
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| 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 symmetric discrete Laplace-Beltrami
Operator (LBO) over the surfaces. Existing converging discrete
LBO proposed by Belkin et al is not guaranteed to be symmetric.
We build a new point-wisely discrete LBO over the point-sampled
surface that is guaranteed to be symmetric, 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 symmetric
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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| Keywords:
point-sampled
surface, Laplace-Beltrami operator, eigen function, manifold harmonics,
spectral analysis |
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