3D Density Histograms for Criteria-driven Edge Bundling

Abstract: This paper presents a graph bundling algorithm that agglomerates edges taking into account both spatial proximity as well as user-defined criteria in order to reveal patterns that were not perceivable with previous bundling techniques. Each edge belongs to a group that may either be an input of the problem or found by clustering one or more edge properties such as origin, destination, orientation, length or domain-specific properties. Bundling is driven by a stack of density maps, with each map capturing both the edge density of a given group as well as interactions with edges from other groups. Density maps are efficiently calculated by smoothing 2D histograms of edge occurrence using repeated averaging filters based on integral images. A CPU implementation of the algorithm is tested on several graphs, and different grouping criteria are used to illustrate how the proposed technique can render different visualizations of the same data. Bundling performance is much higher than on previous approaches, being particularly noticeable on large graphs, with millions of edges being bundled in seconds.