Implementing Persistence-Based Clustering of Point Clouds in the Topology ToolKit

Ryan Cotsakis , Jim Shaw , Julien Tierny (1) , Joshua A Levine

1 APR - Algorithmes, Programmes et Résolution

We show how the scalar field topology features of the Topology ToolKit (TTK) can be leveraged in a pipeline for persistence-based clustering of point clouds. While TTK provides numerous features for computing topological structures of scalar fields on unstructured meshes, prior to this work, it allowed for only basic point cloud input. In this work, we implemented two new modules in TTK: one for sampling scalar fields based on either distance or density of the point cloud and a second for computing persistence-based clusters. Both modules provide heuristics for automatically specifying key thresholds so as to simplify user interaction. This document outlines the implementation details of the two modules and provides experimental results that demonstrate their modularity and utility.

Domaines: Traitement des images [eess.IV]; Mathématique discrète [cs.DM]; Logiciel mathématique [cs.MS]; Géométrie algorithmique [cs.CG]; Vision par ordinateur et reconnaissance de formes [cs.CV]; Synthèse d'image et réalité virtuelle [cs.GR]

Ryan Cotsakis, Jim Shaw, Julien Tierny, Joshua A Levine. Implementing Persistence-Based Clustering of Point Clouds in the Topology ToolKit. Topological Methods in Data Analysis and Visualization VI, Springer, pp.343-357, 2021, Mathematics and Visualization, ⟨10.1007/978-3-030-83500-2_17⟩. ⟨hal-02950542⟩