Sheaves for Visual Encodings and Visual Fusion
Dhruv Meduri (University of Utah), Youjia Zhou (University of Utah), Bei Wang (University of Utah)
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Presentation
- Session
- From design spaces to visual design
- Time
- Thursday, Nov 12, 14:00 – 14:12 (US/Eastern) · session 13:00 – 14:30
- Room
- Hall Essex north
- Presenting from
- Boston
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Abstract
In visualization, visual encodings map data attributes to perceptual channels such as position, color, and size, while visual fusion integrates multiple channels into a coherent representation within a shared frame of reference. In mathematics, sheaf theory provides a formal framework for relating local structure to global structure. In this paper, we introduce a sheaf-theoretic framework for analyzing visual encodings and visual fusion, and argue that this perspective advances the theoretical foundations of visualization. Through four case studies---including composite scientific visualizations, glyph-based scatter plots, and edge blending for graphs and hypergraphs---we demonstrate that sheaves provide a rigorous and unifying formulation of these processes. Motivated by sheaf-theoretic approaches to data fusion and grounded in these case studies, we propose a set of axioms that formalize the requirements for a sheaf-based theory of visual fusion. Together, our results establish a principled mathematical foundation for understanding and designing visual encodings and fusion as coherent local-to-global constructions.
For Practitioners
Data scientists may find this work valuable because it provides a mathematically rigorous, sheaf-theoretic framework for designing visual fusion algorithms. Its generality enables practitioners to develop novel fusion methods across a broad range of data types and application domains.