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

This handbook provides an up-to-date compendium of fundamental computer science
topics, techniques, and applications. Along with updating and revising many of the existing …

We present an algorithm for determining the Morse complex of a two or three-dimensional
grayscale digital image. Each cell in the Morse complex corresponds to a topological …

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 …

The Morse-Smale (MS) complex has proven to be a useful tool in extracting and visualizing
features from scalar-valued data. However, efficient computation of the MS complex for large …

Large-scale simulations are increasingly being used to study complex scientific and
engineering phenomena. As a result, advanced visualization and data analysis are also …

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 …

In this paper we present an efficient framework for computation of persistent homology of
cubical data in arbitrary dimensions. An existing algorithm using simplicial complexes is …

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 …

An important goal of scientific data analysis is to understand the behavior of a system or
process based on a sample of the system. In many instances it is possible to observe both …