论文标题
使用多分辨率REEB空间之间多场数据之间的拓扑相似性度量
A Topological Similarity Measure between Multi-Field Data using Multi-Resolution Reeb Spaces
论文作者
论文摘要
在数据分析和可视化中，搜索一对形状或数据之间的拓扑相似性是一个重要的问题。已经对使用标量拓扑的计算相似性度量的问题进行了广泛的研究，并证明在形状和数据匹配方面有用。即使基于多场（或多元）基于拓扑的技术揭示了更丰富的拓扑特征，但使用多场拓扑计算相似性测量的研究仍处于起步阶段。在当前的论文中，我们提出了一个基于多分辨率的REEB空间之间的两个分段线性多场之间的新颖相似度度量，这是一种新开发的数据结构，可捕获多场的拓扑结构。总体而言，我们的方法由两个步骤组成：（i）构建与每个多场相对应的多分辨率REEB空间，以及（ii）通过比较多分辨率REEB空间获得的匹配对列表（节点）列表（节点）的相似度度量。我们通过在计算物理学的随时间变化的多场数据中检测核分离点来证明所提出的相似性度量的应用。
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.
