Iuricich Federico
IEEE Trans Vis Comput Graph. 2022 Dec;28(12):4966-4979. doi: 10.1109/TVCG.2021.3110663. Epub 2022 Oct 26.
Persistent homology is a fundamental tool in topological data analysis used for the most diverse applications. Information captured by persistent homology is commonly visualized using scatter plots representations. Despite being widely adopted, such a visualization technique limits user understanding and is prone to misinterpretation. This article proposes a new approach for the efficient computation of persistence cycles, a geometric representation of the features captured by persistent homology. We illustrate the importance of rendering persistence cycles when analyzing scalar fields, and we discuss the advantages that our approach provides compared to other techniques in topology-based visualization. We provide an efficient implementation of our approach based on discrete Morse theory, as a new module for the Topology Toolkit. We show that our implementation has comparable performance with respect to state-of-the-art toolboxes while providing a better framework for visually analyzing persistent homology information.
持久同调是拓扑数据分析中的一种基本工具，可用于各种各样的应用。通过持久同调捕获的信息通常使用散点图表示进行可视化。尽管这种可视化技术被广泛采用，但它限制了用户的理解，并且容易产生误解。本文提出了一种用于高效计算持久循环的新方法，持久循环是持久同调捕获的特征的几何表示。我们阐述了在分析标量场时绘制持久循环的重要性，并讨论了我们的方法与其他基于拓扑的可视化技术相比所具有的优势。我们基于离散莫尔斯理论为我们的方法提供了一个高效的实现，作为拓扑工具包的一个新模块。我们表明，我们的实现与最先进的工具箱具有可比的性能，同时为直观地分析持久同调信息提供了一个更好的框架。
