A Topological Similarity Measure between Multi-Field Data using Multi-Resolution Reeb Spaces

TL;DR

This paper introduces a novel topological similarity measure for multi-field data using multi-resolution Reeb spaces, enabling better shape and data comparison by capturing richer topological features.

Contribution

It proposes a new similarity measure based on multi-resolution Reeb spaces for multi-field data, advancing topological data analysis techniques.

Findings

Effective detection of nuclear scission points in physics data

Demonstrated improved shape and data matching capabilities

Introduced a scalable multi-resolution Reeb space construction

Abstract

Searching topological similarity between a pair of shapes or data is an important problem in data analysis and visualization. The problem of computing similarity measures using scalar topology has been studied extensively and proven useful in shape and data matching. Even though multi-field (or multivariate) topology-based techniques reveal richer topological features, research on computing similarity measures using multi-field topology is still in its infancy. In the current paper, we propose a novel similarity measure between two piecewise-linear multi-fields based on their multi-resolution Reeb spaces - a newly developed data-structure that captures the topology of a multi-field. Overall, our method consists of two steps: (i) building a multi-resolution Reeb space corresponding to each of the multi-fields and (ii) proposing a similarity measure for a list of matching pairs (of nodes), obtained by comparing the multi-resolution Reeb spaces. We demonstrate an application of the proposed similarity measure by detecting the nuclear scission point in a time-varying multi-field data from computational physics.