Persistence Atlas for Critical Point Variability in Ensembles
Persistence Atlas for Critical Point Variability in Ensembles
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DOI：
10.1109/tvcg.2018.2864432
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发表时间：
2018-07
影响因子：
5.2
通讯作者：
Guillaume Favelier;Noura Faraj;B. Summa;Julien Tierny
中科院分区：
文献类型：
--
作者：
Guillaume Favelier;Noura Faraj;B. Summa;Julien Tierny
本文提出了一种新的方法来可视化和分析集合数据中以临界点表示的感兴趣特征的空间变异性。我们的框架，称为Persistence Atlas，可以可视化关键点的主要空间模式，以及它们在集合中出现的统计数据。持久性图谱在几何域中以临界点出现的置信度图的形式表示每个主导模式。作为副产品，我们的方法还提供了整个集合的二维布局，突出了全球层面的主要趋势。我们的方法基于持久性地图的新概念，持久性地图是一种测量关键点几何密度的方法，它利用拓扑持久性对噪声的鲁棒性来更好地强调显著特征。我们展示了如何利用谱嵌入将集成成员表示为低维欧几里德空间中的点，其中点之间的距离度量关键点布局之间的不相似性，并且可以轻松执行统计任务，例如聚类。此外，我们还展示了如何利用强制临界点的概念来评估临界点出现的每个集群置信区域。这个框架的大部分步骤都可以简单地并行化，我们将展示如何有效地实现它们。大量的实验证明了我们的方法的相关性。对持久性地图集提供的置信区域的准确性进行定量评估，并使用现成的聚类方法与基线策略进行比较。我们说明了持久性地图集在各种现实生活数据集中的重要性，其中识别和分析了特征布局的明确趋势。我们为我们的方法提供了一个轻量级的基于vtc的c++实现，可用于复制目的。
This paper presents a new approach for the visualization and analysis of the spatial variability of features of interest represented by critical points in ensemble data. Our framework, called Persistence Atlas, enables the visualization of the dominant spatial patterns of critical points, along with statistics regarding their occurrence in the ensemble. The persistence atlas represents in the geometrical domain each dominant pattern in the form of a confidence map for the appearance of critical points. As a by-product, our method also provides 2-dimensional layouts of the entire ensemble, highlighting the main trends at a global level. Our approach is based on the new notion of Persistence Map, a measure of the geometrical density in critical points which leverages the robustness to noise of topological persistence to better emphasize salient features. We show how to leverage spectral embedding to represent the ensemble members as points in a low-dimensional Euclidean space, where distances between points measure the dissimilarities between critical point layouts and where statistical tasks, such as clustering, can be easily carried out. Further, we show how the notion of mandatory critical point can be leveraged to evaluate for each cluster confidence regions for the appearance of critical points. Most of the steps of this framework can be trivially parallelized and we show how to efficiently implement them. Extensive experiments demonstrate the relevance of our approach. The accuracy of the confidence regions provided by the persistence atlas is quantitatively evaluated and compared to a baseline strategy using an off-the-shelf clustering approach. We illustrate the importance of the persistence atlas in a variety of real-life datasets, where clear trends in feature layouts are identified and analyzed. We provide a lightweight VTK-based C++ implementation of our approach that can be used for reproduction purposes.