Topological techniques have proven to be a powerful tool in the analysis and visualization of
large-scale scientific data. In particular, the Morse-Smale complex and its various …

A Laplacian eigenfunction on a manifold or a metric graph imposes a natural partition of the
manifold or the graph. This partition is determined by the gradient vector field of the …

Contour trees are extensively used in scalar field analysis. The contour tree is a data
structure that tracks the evolution of level set topology in a scalar field. Scalar fields are …

In this paper, we present a symbolic computation method for constructing a small
neighborhood U around a known local optimal maximal or minimal point x 0 of a given …

Morse theory provides a powerful framework to study the topology of a manifold from a
function defined on it, but discrete constructions have remained elusive due to the difficulty …

Abstract The Morse-Smale complex is an important tool for global topological analysis in
various problems in computational topology and data analysis. A certified algorithm for …