Color maps are a commonly used visualization technique in which data are mapped to optical properties, e.g., color or opacity. Color maps, however, do not explicitly convey structures (e.g., positions and scale of features) within data. Topology-based visualizations reveal and explicitly communicate structures underlying data. Although we have a good understanding of what types of features are captured by topological visualizations, our understanding of people's perception of those features is not. This paper evaluates the sensitivity of topology-based isocontour, Reeb graph, and persistence diagram visualizations compared to a reference color map visualization for synthetically generated scalar fields on 2-manifold triangular meshes embedded in 3D. In particular, we built and ran a human-subject study that evaluated the perception of data features characterized by Gaussian signals and measured how effectively each visualization technique portrays variations of data features arising from the position and amplitude variation of a mixture of Gaussians. For positional feature variations, the results showed that only the Reeb graph visualization had high sensitivity. For amplitude feature variations, persistence diagrams and color maps demonstrated the highest sensitivity, whereas isocontours showed only weak sensitivity. These results take an important step toward understanding which topology-based tools are best for various data and task scenarios and their effectiveness in conveying topological variations as compared to conventional color mapping.

翻译：颜色映射是一种常用的可视化技术，它将数据映射到光学属性（如颜色或不透明度）。然而，颜色映射并不能明确传达数据内部的结构（例如特征的位置和尺度）。基于拓扑的可视化能够揭示并明确传达数据背后的结构。尽管我们清楚地了解拓扑可视化能够捕获哪些类型的特征，但人们对这些特征的感知机制尚不明确。本文评估了基于拓扑的等值线、Reeb图和持久性图可视化相对于参考颜色映射可视化，对嵌入三维空间中的二维流形三角网格上合成标量场的敏感性。具体而言，我们设计并开展了一项人类受试者研究，评估由高斯信号表征的数据特征的感知效果，并衡量每种可视化技术如何有效地呈现由高斯混合信号的位置和幅度变化引起的数据特征变化。对于位置特征变化，结果表明仅Reeb图可视化具有高敏感性。对于幅度特征变化，持久性图和颜色映射表现出最高敏感性，而等值线仅显示出弱敏感性。这些结果朝着理解哪种基于拓扑的工具最适合各种数据和任务场景迈出了重要一步，并揭示了它们相对于传统颜色映射在传达拓扑变化方面的有效性。