Towards Multifield Scalar Topology Based on Pareto Optimality

How can the notion of topological structures for single scalar fields be extended to multifields? In this paper we propose a definition for such structures using the concepts of Pareto optimality and Pareto dominance. Given a set of piecewise-linear, scalar functions over a common simplical complex of any dimension, our method finds regions of “consensus” among single fields’ critical points and their connectivity relations. We show that our concepts are useful to data analysis on real-world examples originating from fluid-flow simulations; in two cases where the consensus of multiple scalar vortex predictors is of interest and in another case where one predictor is studied under different simulation parameters. We also compare the properties of our approach with current alternatives.