Mesh Learning Using Persistent Homology on the Laplacian Eigenfunctions

2019/04/21 by Yunhao Zhang, Haowen Liu, Zhang, Yunhao +5 · 1 citation
Computer Science · Medicine · #Advanced Neuroimaging Techniques and Applications #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1904.09639

openalex publication_date 2019/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use persistent homology along with the eigenfunctions of the Laplacian to study similarity amongst triangulated 2-manifolds. Our method relies on studying the lower-star filtration induced by the eigenfunctions of the Laplacian. This gives us a shape descriptor that inherits the rich information encoded in the eigenfunctions of the Laplacian. Moreover, the similarity between these descriptors can be easily computed using tools that are readily available in Topological Data Analysis. We provide experiments to illustrate the effectiveness of the proposed method.

Citations

• The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
• Laplace–Beltrami spectra as ‘Shape-DNA’ of surfaces and solids

Cited by

• Simplicial Complex Representation Learning

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