Differential topology, and specifically Morse theory, provide a suitable setting for formalizing
and solving several problems related to shape analysis. The fundamental idea behind …

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

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 …

Algorithms and Theory of Computation Handbook, Second Edition: Special Topics and
Techniques provides an up-to-date compendium of fundamental computer science topics …

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 …

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

The ever-growing amount of data stored in digital databases raises the question of how to
organize and extract useful knowledge. This paper outlines some current developments in …

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 …

We combine topological and geometric methods to construct a multiresolution
representation for a function over a two-dimensional domain. In a preprocessing stage, we …