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Topology-Based Characterization and Visual Analysis of Feature Evolution in Large-Scale Simulations
(2019)
This manuscript presents a topology-based analysis and visualization framework that enables the effective exploration of feature evolution in large-scale simulations. Such simulations pose additional challenges to the already complex task of feature tracking and visualization, since the vast number of features and the size of the simulation data make it infeasible to naively identify, track, analyze, render, store, and interact with data. The presented methodology addresses these issues via three core contributions. First, the manuscript defines a novel topological abstraction, called the Nested Tracking Graph (NTG), that records the temporal evolution of features that exhibit a nesting hierarchy, such as superlevel set components for multiple levels, or filtered features across multiple thresholds. In contrast to common tracking graphs that are only capable of describing feature evolution at one hierarchy level, NTGs effectively summarize their evolution across all hierarchy levels in one compact visualization. The second core contribution is a view-approximation oriented image database generation approach (VOIDGA) that stores, at simulation runtime, a reduced set of feature images. Instead of storing the features themselves---which is often infeasable due to bandwidth constraints---the images of these databases can be used to approximate the depicted features from any view angle within an acceptable visual error, which requires far less disk space and only introduces a neglectable overhead. The final core contribution combines these approaches into a methodology that stores in situ the least amount of information necessary to support flexible post hoc analysis utilizing NTGs and view approximation techniques.
We 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.