Multi-field Visualisation via Trait-induced Merge Trees

TL;DR

This paper introduces trait-based merge trees, a novel topological method for analyzing multi-variate data by focusing on feature-level sets, enabling hierarchical querying of relevant features across different applications.

Contribution

It generalizes merge trees to feature level sets using traits, allowing for detailed analysis of tensor and multi-variate data with new query capabilities.

Findings

Effective in analyzing tensor and multi-variate data

Supports hierarchical querying of features

Demonstrated across three diverse case studies

Abstract

In this work, we propose trait-based merge trees a generalization of merge trees to feature level sets, targeting the analysis of tensor field or general multi-variate data. For this, we employ the notion of traits defined in attribute space as introduced in the feature level sets framework. The resulting distance field in attribute space induces a scalar field in the spatial domain that serves as input for topological data analysis. The leaves in the merge tree represent those areas in the input data that are closest to the defined trait and thus most closely resemble the defined feature. Hence, the merge tree yields a hierarchy of features that allows for querying the most relevant and persistent features. The presented method includes different query methods for the tree which enable the highlighting of different aspects. We demonstrate the cross-application capabilities of this approach with three case studies from different domains.