This system paper presents the Topology ToolKit (TTK), a software platform designed for the
topological analysis of scalar data in scientific visualization. While topological data analysis …

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 …

We present a state‐of‐the‐art report on time‐dependent flow topology. We survey
representative papers in visualization and provide a taxonomy of existing approaches that …

Terrestrial laser scanning (TLS) is a ground-based approach to rapidly acquire 3D point
clouds via Light Detection and Ranging (LiDAR) technologies. Quantifying tree-scale …

We show how discrete Morse theory provides a rigorous and unifying foundation for defining
skeletons and partitions of grayscale digital images. We model a grayscale image as a …

The large-scale structure of the universe is comprised of virialized blob-like clusters, linear
filaments, sheet-like walls and huge near empty three-dimensional voids. Characterizing the …

Morse theory offers a natural and mathematically‐sound tool for shape analysis and
understanding. It allows studying the behavior of a scalar function defined on a manifold …

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 …

This paper introduces an efficient algorithm for persistence diagram computation, given an
input piecewise linear scalar field defined on a-dimensional simplicial complex, with. Our …