ExTreeM: Scalable Augmented Merge Tree Computation via Extremum Graphs

Over the last decade merge trees have been proven to support a plethora of visualization and analysis tasks since they effectively abstract complex datasets. This paper describes the ExTreeM-Algorithm: A scalable algorithm for the computation of merge trees via extremum graphs. The core idea of ExTreeM is to first derive the extremum graph \mathcal{G} of an input scalar field f defined on a cell complex \mathcal{K} , and subsequently compute the unaugmented merge tree of f on \mathcal{G} instead of \mathcal{K} ; which are equivalent. Any merge tree algorithm can be carried out significantly faster on \mathcal{G} , since \mathcal{K} in general contains substantially more cells than \mathcal{G} . To further speed up computation, ExTreeM includes a tailored procedure to derive merge trees of extremum graphs. The computation of the fully augmented merge tree, i.e., a merge tree domain segmentation of \mathcal{K} , can then be performed in an optional post-processing step. All steps of ExTreeM consist of procedures with hig