Learning persistent homology of 3D point clouds

Abstract

In recent years, topological data analysis (TDA) has become a popular tool for studying 3D point clouds. Persistent homology is one of the most important tools of TDA, as it can extract the topological features hidden in a point cloud. However, the time-consuming computation of persistence diagrams severely limits the application of TDA. In this study, we propose an end-to-end TopologyNet that directly fits the output of the topological representations from the input point cloud data. TopologyNet significantly reduces the computation time of producing topological representations compared with the traditional pipeline, while maintaining a small approximating error in practical instances. For point cloud generation, we use TopologyNet as a topological branch to improve the performance of a point cloud autoencoder. Moreover, the additional topological features are used in a latent generative adversarial network to produce new point clouds.