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

This paper presents the state of the art in the area of topology‐based visualization. It
describes the process and results of an extensive annotation for generating a definition and …

Merge trees represent the topology of scalar functions. To assess the topological similarity of
functions, one can compare their merge trees. To do so, one needs a notion of a distance …

Edit distances between merge trees of scalar fields have many applications in scientific
visualization, such as ensemble analysis, feature tracking or symmetry detection. In this …

We present an algorithm for tracking regions in time‐dependent scalar fields that uses
global knowledge from all time steps for determining the tracks. The regions are defined …

Topological structures such as the merge tree provide an abstract and succinct
representation of scalar fields. They facilitate effective visualization and interactive …

Graphs represent general node‐link diagrams and have long been utilized in scientific
visualization for data organization and management. However, using graphs as a visual …

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 …

We present a method to find repeating topological structures in scalar data sets. More
precisely, we compare all subtrees of two merge trees against each other–in an efficient …

We describe a novel technique for the simultaneous visualization of multiple scalar fields, eg
representing the members of an ensemble, based on their contour trees. Using tree …