This research explores a novel paradigm for preserving topological segmentations in
existing error-bounded lossy compressors. Today's lossy compressors rarely consider …

Persistent homology allows for tracking topological features, like loops, holes and their
higher-dimensional analogues, along a single-parameter family of nested shapes …

The extremum graph is a succinct representation of the Morse decomposition of a scalar
field. It has increasingly become a useful data structure that supports topological feature …

Unstructured data are collections of points with irregular topology, often represented through
simplicial meshes, such as triangle and tetrahedral meshes. Whenever possible such …

We introduce the notion of a Morse sequence, which provides a simple and effective
approach to discrete Morse theory. A Morse sequence is a sequence composed solely of …

In the context of discrete Morse theory, we introduce Morse frames, which are maps that
associate a set of critical simplexes to each simplex of a given complex. The main example …

The Morse-Smale complex is a well studied topological structure that represents the
gradient flow behavior between critical points of a scalar function. It supports multi-scale …

In this paper, we develop the notion of a Morse sequence, which provides an alternative
approach to discrete Morse theory, and which is both simple and effective. A Morse …

Simplicial complexes are widely used to discretize shapes. In low dimensions, a 3D shape is
represented by discretizing its boundary surface, encoded as a triangle mesh, or by …

Tetrahedral meshes are widely used due to their flexibility and adaptability in representing
changes of complex geometries and topology. However, most existing data structures …