Topology-faithful nonparametric estimation and tracking of bulk interface networks

TL;DR

This paper introduces a topology-aware nonparametric filtering method for accurately estimating and tracking interface networks in bulk materials, improving upon traditional smoothing techniques by explicitly incorporating topological hierarchy.

Contribution

The paper presents a novel hierarchical filtering approach that explicitly models topological features of interface networks, enhancing microstructural analysis and interface transport quantification.

Findings

Effective estimation of interface geometries in microstructures

Improved accuracy over traditional smoothing methods

A new front-tracking algorithm for interface transport

Abstract

The main focus of this paper is a nonparametric filtering technique for the estimation of interface geometry in bulk materials obtainable from modern imaging measurements. The filtering methodology relies on an assumed hierarchy of topological features present in a typical interface network, such as foam interfaces and grain boundary networks in polycrystalline materials. Each type of topological feature is treated in order of rank in the hierarchy, with the lower-level feature being filtered subject to the positional constraints imposed by the higher-level features. Such a scheme is an alternative to existing surface smoothing/estimation techniques in microstructural materials science, in which the explicit treatment of different elements of the network topology is absent, or at best arbitrarily parameterized. We describe the ramifications of this technique in the usual microstructural applications in which the computation of important physical quantities is predicated on the precise estimation of the interface features. As an additional application, we describe a novel front-tracking algorithm for quantifying the transport of such interfaces.