通过分解特征与构建合并树，实现多场数据特征的高效可视化与查询。
Multi-field Visualization: Trait design and trait-induced merge trees
- 将特征分解为笛卡尔组件，简化设计并提升计算效率。
- 引入特质诱导合并树，对张量场等多变量数据进行拓扑分析。
- 支持多种查询方式，适用于科学可视化与跨领域应用。
特征水平集（FLS）通过属性空间中定义的特质来指定域中的特征，在多场数据分析中展现出巨大潜力。本文针对FLS实际应用中的关键挑战——特质设计与特征选择，提出解决方案：首先，通过笛卡尔分解将特质拆分为更简单的成分，使设计更直观、计算更高效；其次，利用字典学习结果自动建议点特质。为增强特征选择能力，提出特质诱导合并树（TIMT），这是对合并树的推广，用于特征水平集的拓扑分析，适用于张量场或一般多变量数据。TIMT的叶节点代表输入数据中距离所定义特质最近的区域，即最符合该特征的区域。该合并树提供了特征的层次结构，支持对最相关且持久特征的查询。方法包含多种树查询技术，可突出不同方面。通过五个来自不同领域的案例研究，展示了该方法的跨应用能力。
原文摘要 · Abstract (English)
Feature level sets (FLS) have shown significant potential in the analysis of multi-field data by using traits defined in attribute space to specify features in the domain. In this work, we address key challenges in the practical use of FLS: trait design and feature selection for rendering. To simplify trait design, we propose a Cartesian decomposition of traits into simpler components, making the process more intuitive and computationally efficient. Additionally, we utilize dictionary learning results to automatically suggest point traits. To enhance feature selection, we introduce trait-induced merge trees (TIMTs), a generalization of merge trees for feature level sets, aimed at topologically analyzing tensor fields or general multi-variate data. The leaves in the TIMT represent areas in the input data that are closest to the defined trait, thereby most closely resembling the defined feature. This merge tree provides a hierarchy of features, enabling the querying of the most relevant and persistent features. Our method includes various query techniques for the tree, allowing the highlighting of different aspects. We demonstrate the cross-application capabilities of this approach through five case studies from different domains.
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