Novel definition and quantitative analysis of branch structure with topological data analysis

While branching network structures abound in nature, their objective analysis is more difficult than expected because existing quantitative methods often rely on the subjective judgment of branch structures. This problem is particularly pronounced when dealing with images comprising discrete particles. Here we propose an objective framework for quantitative analysis of branching networks by introducing the mathematical definitions for internal and external structures based on topological data analysis, specifically, persistent homology. We compare persistence diagrams constructed from images with and without …

analysis cs.cg cs.cv data data analysis definition framework images judgment math.at nature network novel q-bio.qm quantitative quantitative analysis