Comparative visualization of scalar fields is often facilitated using similarity measures such as edit distances. In this paper, we describe a novel approach for similarity analysis of scalar fields that combines two recently introduced techniques: Wasserstein geodesics/barycenters as well as path mappings, a branch decomposition-independent edit distance. Effectively, we are able to leverage the reduced susceptibility of path mappings to small perturbations in the data when compared with the original Wasserstein distance. Our approach therefore exhibits superior performance and quality in typical tasks such as ensemble summarization, ensemble clustering, and temporal reduction of time series, while retaining practically feasible runtimes. Beyond studying theoretical properties of our approach and discussing implementation aspects, we describe a number of case studies that provide empirical insights into its utility for comparative visualization, and demonstrate the advantages of our method in both synthetic and real-world scenarios. We supply a C++ implementation that can be used to reproduce our results.

翻译：标量场的比较可视化常借助编辑距离等相似性度量。本文提出了一种新颖的标量场相似性分析方法，融合了两种近期引入的技术：Wasserstein测地线/重心以及路径映射——一种独立于分支分解的编辑距离。通过该方法，我们有效利用了路径映射对数据微小扰动敏感性较低的特性，相较于原始Wasserstein距离展现出更优性能。因此，本方法在典型任务（如集合总结、集合聚类及时间序列的时域约简）中表现出卓越的性能与质量，同时保持了实际可行的运行时间。除探讨方法理论性质及实现细节外，我们通过若干案例研究提供了其比较可视化效用的实证分析，并在合成数据与现实场景中验证了方法的优势。我们提供了可复现结果的C++实现代码。