Category: Computational topology

Euler calculus
Euler calculus is a methodology from applied algebraic topology and integral geometry that integrates constructible functions and more recently by integrating with respect to the Euler characteristic
SnapPea is free software designed to help mathematicians, in particular low-dimensional topologists, study hyperbolic 3-manifolds. The primary developer is Jeffrey Weeks, who created the first version
Geometric and Topological Inference
Geometric and Topological Inference is a monograph in computational geometry, computational topology, geometry processing, and topological data analysis, on the problem of inferring properties of an u
Persistent homology
Persistent homology is a method for computing topological features of a space at different spatial resolutions. More persistent features are detected over a wide range of spatial scales and are deemed
Simplicial homology
In algebraic topology, simplicial homology is the sequence of homology groups of a simplicial complex. It formalizes the idea of the number of holes of a given dimension in the complex. This generaliz
Topological data analysis
In applied mathematics, topological based data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. Extraction of information from datasets that are high-dimension
Computational topology
Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational complexity theory. A
Digital Morse theory
In mathematics, digital Morse theory is a digital adaptation of continuum Morse theory for scalar volume data. This is not about the Samuel Morse's Morse code of long and short clicks or tones used in
Region connection calculus
The region connection calculus (RCC) is intended to serve for qualitative spatial representation and reasoning. RCC abstractly describes regions (in Euclidean space, or in a topological space) by thei
Computable topology
Computable topology is a discipline in mathematics that studies the topological and algebraic structure of computation. Computable topology is not to be confused with algorithmic or computational topo
Discrete Morse theory
Discrete Morse theory is a combinatorial adaptation of Morse theory developed by . The theory has various practical applications in diverse fields of applied mathematics and computer science, such as
Cubical complex
In mathematics, a cubical complex (also called cubical set and Cartesian complex) is a set composed of points, line segments, squares, cubes, and their n-dimensional counterparts. They are used analog