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.

翻译：本文提出基于特征诱导的合并树（trait-based merge trees），将合并树推广至特征水平集，旨在分析张量场或一般多变量数据。为此，我们采用特征水平集框架中定义的属性空间特征概念。属性空间中的导出距离场在空间域上生成一个标量场，作为拓扑数据分析的输入。合并树的叶节点表示输入数据中最接近所定义特征的区域，因此最精确地匹配该特征。由此，合并树产生一个特征层次结构，支持查询最相关且最持久的特征。所提方法包含多种树查询方式，可突出不同方面的特征。我们通过三个跨领域案例研究，展示了该方法在跨应用场景中的能力。