Sridharamurthy Raghavendra, Natarajan Vijay
IEEE Trans Vis Comput Graph. 2023 Feb;29(2):1518-1530. doi: 10.1109/TVCG.2021.3122176. Epub 2022 Dec 29.
Comparative analysis of scalar fields is an important problem with various applications including feature-directed visualization and feature tracking in time-varying data. Comparing topological structures that are abstract and succinct representations of the scalar fields lead to faster and meaningful comparison. While there are many distance or similarity measures to compare topological structures in a global context, there are no known measures for comparing topological structures locally. While the global measures have many applications, they do not directly lend themselves to fine-grained analysis across multiple scales. We define a local variant of the tree edit distance and apply it towards local comparative analysis of merge trees with support for finer analysis. We also present experimental results on time-varying scalar fields, 3D cryo-electron microscopy data, and other synthetic data sets to show the utility of this approach in applications like symmetry detection and feature tracking.
标量场的比较分析是一个重要问题，具有各种应用，包括时变数据中的特征导向可视化和特征跟踪。比较作为标量场抽象简洁表示的拓扑结构能够实现更快且有意义的比较。虽然有许多距离或相似性度量可用于在全局背景下比较拓扑结构，但尚无用于局部比较拓扑结构的已知度量。虽然全局度量有许多应用，但它们并不直接适用于跨多个尺度的细粒度分析。我们定义了树编辑距离的局部变体，并将其应用于合并树的局部比较分析，以支持更精细的分析。我们还展示了时变标量场、3D冷冻电子显微镜数据和其他合成数据集的实验结果，以证明该方法在对称性检测和特征跟踪等应用中的实用性。
