Threshold-Based Graph Reconstruction Using Discrete Morse Theory

TL;DR

This paper introduces a novel noise model for density functions to improve the topological and geometric reconstruction of connected graphs using discrete Morse theory.

Contribution

It presents a new noise model that enhances graph reconstruction accuracy through discrete Morse theory, addressing previous limitations.

Findings

Effective reconstruction of connected graphs demonstrated

Improved topological accuracy over existing methods

Enhanced geometric fidelity in reconstructed graphs

Abstract

Discrete Morse theory has recently been applied in metric graph reconstruction from a given density function concentrated around an (unknown) underlying embedded graph. We propose a new noise model for the density function to reconstruct a connected graph both topologically and geometrically.