Abstract
AbstractWe describe a novel technique for the simultaneous visualization of multiple scalar fields, e.g. representing the members of an ensemble, based on their contour trees. Using tree alignments, a graph‐theoretic concept similar to edit distance mappings, we identify commonalities across multiple contour trees and leverage these to obtain a layout that can represent all trees simultaneously in an easy‐to‐interpret, minimally‐cluttered manner. We describe a heuristic algorithm to compute tree alignments for a given similarity metric, and give an algorithm to compute a joint layout of the resulting aligned contour trees. We apply our approach to the visualization of scalar field ensembles, discuss basic visualization and interaction possibilities, and demonstrate results on several analytic and real‐world examples.
Highlights
Topology-based methods have a long tradition in the visualization of scalar fields
We propose a novel strategy for the joint visualization of many contour trees: the fuzzy contour tree
We describe a layout algorithm that allows an intuitive joint depiction of multiple contour trees in a sensible manner – the fuzzy contour tree
Summary
Topology-based methods have a long tradition in the visualization of scalar fields. Among a variety of methods, the contour tree serves as the well-understood basis for a plethora of techniques, ranging from the straightforward generation of visualization images We consider the example of contour tree visualization of ensemble data sets. Such ensembles result from sampling of parameter spaces and stochastic properties of models, and consist of multiple realizations of a model, called ensemble members. Identification of similarities and differences between members and detection of outliers are among the elementary analysis tasks that should be supported by visualization. The randomized nature of prevalent contour tree layout techniques and their large parameter spaces often result in strongly different representations for very similar scalar fields. In naïve form, these techniques are not suited to the needs of ensemble visualization
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