title: Point-based manifold harmonics.
abstract: 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.
authors.affiliation: Department of Computer Science, University of Texas at Dallas, Dallas, TX 75252, USA. yxl072100@utdallas.edu
authors.forename: Yang
authors.initials: Y
authors.lastname: Liu
authors.forename: Balakrishnan
authors.initials: B
authors.lastname: Prabhakaran
authors.forename: Xiaohu
authors.initials: X
authors.lastname: Guo