TADD: A computational framework for data analysis using discrete Morse theory. This paper presents a computational framework that allows for a robust extraction of the extremal structure of scalar and vector fields on 2D manifolds embedded in 3D. This structure consists of critical points, separatrices, and periodic orbits. The framework is based on Forman’s discrete Morse theory, which guarantees the topological consistency of the computed extremal structure. Using a graph theoretical formulation of this theory, we present an algorithmic pipeline that computes a hierarchy of extremal structures. This hierarchy is defined by an importance measure and enables the user to select an appropriate level of detail.
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References in zbMATH (referenced in 7 articles , 1 standard article )
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- Wu, Chengyuan; Ren, Shiquan; Wu, Jie; Xia, Kelin: Discrete Morse theory for weighted simplicial complexes (2020)
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- Kotava, Natallia; Knoll, Aaron; Hagen, Hans: Morse-Smale decomposition of multivariate transfer function space for separably-sampled volume rendering (2013)
- Lewiner, Thomas: Critical sets in discrete Morse theories: relating Forman and piecewise-linear approaches (2013)
- Günther, David; Reininghaus, Jan; Prohaska, Steffen; Weinkauf, Tino; Hege, Hans-Christian: Efficient computation of a hierarchy of discrete 3D gradient vector fields (2012)
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- Reininghaus, Jan; Günther, David; Hotz, Ingrid; Prohaska, Steffen; Hege, Hans-Christian: TADD: a computational framework for data analysis using discrete Morse theory (2010)