A Comparative Study of the Perceptual Sensitivity of Topological Visualizations to Feature Variations

TL;DR

This study compares the perceptual sensitivity of topology-based visualizations to feature variations in data, revealing their strengths and limitations in conveying data structures compared to traditional color maps.

Contribution

It provides the first human-subject evaluation of how different topology-based visualizations perceive feature variations in data.

Findings

Reeb graph visualization is highly sensitive to positional feature variations.

Persistence diagrams and color maps effectively detect amplitude variations.

Isocontours show weak sensitivity to feature variations.

Abstract

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.