Topology-based analysis and visualization of multi-fields data
The use of multifield data (i.e., data characterized by multiple scalar functions) is becoming more and more common in several applications. Multifield data are notoriously difficult to analyze and visualize since their analysis combines the challenges of working with two- or three-dimensional domains with those of dealing with a high-dimensional codomain where color maps are ineffective. Thus, the ability to extract features describing the essential properties of such data becomes crucial. The aim of this project is to develop innovative tools for extracting and visualizing topological features describing a multifield. Many aspects of topology-based analysis of multifield data are still unexplored both from a theoretical and practical standpoint. The first challenge addressed in this project is to develop theoretically grounded tools for the analysis of multifield data, based on topology-based descriptors rooted in multi-persistent homology. The second challenge is to evaluate the significance of such tools in the context of applications. We specifically focus on environmental applications, where we plan to use topological features to segment multifield data for forest monitoring, and to identify regions of non-correlation in time-varying sequences of multifield oceanic data.
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