Massive simulations and arrays of sensing devices, in combination with increasing
computing resources, have generated large, complex, high-dimensional datasets used to …

In topological data analysis and visualization, topological descriptors such as persistence
diagrams, merge trees, contour trees, Reeb graphs, and Morse–Smale complexes play an …

We propose a metric for Reeb graphs, called the functional distortion distance. Under this
distance, the Reeb graph is stable against small changes of input functions. At the same …

Pathology images contain rich information of cell appearance, microenvironment, and
topology features for cancer analysis and diagnosis. Among such features, topology …

This paper presents an efficient algorithm for the progressive approximation of Wasserstein
barycenters of persistence diagrams, with applications to the visual analysis of ensemble …

This paper presents a unified computational framework for the estimation of distances,
geodesics and barycenters of merge trees. We extend recent work on the edit distance 104 …

This article presents a computational framework for the Principal Geodesic Analysis of
merge trees (MT-PGA), a novel adaptation of the celebrated Principal Component Analysis …

Physical phenomena in science and engineering are frequently modeled using scalar fields.
In scalar field topology, graph-based topological descriptors such as merge trees, contour …

This paper presents a robust and efficient method for tracking topological features in time-
varying scalar data. Structures are tracked based on the optimal matching between …

This paper presents a new approach for the visualization and analysis of the spatial
variability of features of interest represented by critical points in ensemble data. Our …