ParkView: Visualizing Monotone Interleavings

Merge trees are a powerful tool from topological data analysis that is frequently used to analyze scalar fields. The similarity between two merge trees can be captured by an interleaving: a pair of maps between the trees that jointly preserve ancestor relations in the trees. Interleavings can have a...

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Vydáno v:IEEE Pacific Visualization Symposium s. 118 - 127
Hlavní autoři: Beurskens, Thijs, Van Den Broek, Steven, Simons, Arjen, Sonke, Willem, Verbeek, Kevin, Ophelders, Tim, Hoffmann, Michael, Speckmann, Bettina
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 22.04.2025
Témata:
Data visualization
Encoding
Hands
Human computer interaction
Human-centered computing-Visualization-Visualization techniques
Image color analysis
Network topology
Networks-Topology analysis and generation
Theory of computation-Design and analysis of algorithms
Time series analysis
Topology
Visual analytics
Visualization
ISSN:2165-8773
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Shrnutí:Merge trees are a powerful tool from topological data analysis that is frequently used to analyze scalar fields. The similarity between two merge trees can be captured by an interleaving: a pair of maps between the trees that jointly preserve ancestor relations in the trees. Interleavings can have a complex structure; visualizing them requires a sense of (drawing) order which is not inherent in this purely topological concept. However, in practice it is often desirable to introduce additional geometric constraints, which leads to variants such as labeled or monotone interleavings. Monotone interleavings respect a given order on the leaves of the merge trees and hence have the potential to be visualized in a clear and comprehensive manner.In this paper, we introduce ParkView: a schematic, scalable encoding for monotone interleavings. ParkView captures both maps of the interleaving using an optimal decomposition of both trees into paths and corresponding branches. We prove several structural properties of monotone interleavings, which support a sparse visual encoding using active paths and hedges that can be linked using a maximum of 6 colors for merge trees of arbitrary size. We show how to compute an optimal path-branch decomposition in linear time and illustrate ParkView on a number of real-world datasets.
ISSN:2165-8773
DOI:10.1109/PacificVis64226.2025.00018