Conceptualization of Object Compositions Using Persistent Homology

TL;DR

This paper introduces a topological shape analysis method using persistent homology to learn and represent shape concepts from object point cloud data, capturing meaningful shape commonalities and demonstrating good generalization.

Contribution

It presents a novel hierarchical topological analysis framework that uncovers hidden shape concepts from object segments using persistent homology.

Findings

Persistent groups of shape commonalities are semantically meaningful.

The approach generalizes well across different datasets.

Shape concepts can be effectively represented through topological analysis.

Abstract

A topological shape analysis is proposed and utilized to learn concepts that reflect shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects. Therein constellations are decomposed and described in an hierarchical manner - from single segments to segment groups until a single group reflects an entire object. ii) a topology analysis of the description space in which segment decompositions are exposed in. Inspired by Persistent Homology, hidden groups of shape commonalities are revealed from object segment decompositions. Experiments show that extracted persistent groups of commonalities can represent semantically meaningful shape concepts. We also show the generalization capability of the proposed approach considering samples of external datasets.