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) ov...
| Publié dans: | IEEE transactions on visualization and computer graphics. - 1996. - 18(2012), 10 vom: 08. Okt., Seite 1693-703 |
|---|---|
| Auteur principal: | |
| Autres auteurs: | , |
| Format: | Article en ligne |
| Langue: | English |
| Publié: |
2012
|
| Accès à la collection: | IEEE transactions on visualization and computer graphics |
| Sujets: | Journal Article Research Support, U.S. Gov't, Non-P.H.S. |
| Résumé: | 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 |
|---|---|
| Description: | Date Completed 27.02.2013 Date Revised 10.08.2012 published: Print Citation Status PubMed-not-MEDLINE |
| ISSN: | 1941-0506 |
| DOI: | 10.1109/TVCG.2011.152 |