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 introduces decorated merge trees (DMTs) as a novel invariant for persistent
spaces. DMTs combine both π 0 and H n information into a single data structure that …

Comparative visualization of scalar fields is often facilitated using similarity measures such
as edit distances. In this paper, we describe a novel approach for similarity analysis of scalar …

This thesis presents a uniform treatment of different distances used in the applied topology
literature. We introduce the notion of a locally persistent category, which is a category with a …

Merge trees, a type of topological descriptors, serve to identify and summarize the
topological characteristics associated with scalar fields. They have great potential for …

The Gromov-Hausdorff distance ($ d_\mathrm {GH} $) provides a natural way of quantifying
the dissimilarity between two given metric spaces. It is known that computing $ d_\mathrm …

In this paper we introduce some new algebraic and geometric perspectives on networked
space communications. Our main contribution is a novel definition of a time-varying graph …

Merge trees are a type of topological descriptors that record the connectivity among the
sublevel sets of scalar fields. They are among the most widely used topological tools in …