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Extraction of Dominant Extremal Structures in Volumetric Data Using Separatrix Persistence
Author(s) -
Günther D.,
Seidel H.P.,
Weinkauf T.
Publication year - 2012
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2012.03222.x
Subject(s) - scalar field , computation , scalar (mathematics) , topological data analysis , discrete morse theory , computer science , morse theory , noise (video) , algorithm , measure (data warehouse) , mathematics , topology (electrical circuits) , geometry , artificial intelligence , mathematical analysis , combinatorics , data mining , image (mathematics) , mathematical physics
Extremal lines and surfaces are features of a 3D scalar field where the scalar function becomes minimal or maximal with respect to a local neighborhood. These features are important in many applications, e.g. computer tomography, fluid dynamics, cell biology. We present a novel topological method to extract these features using discrete Morse theory. In particular, we extend the notion of ‘separatrix persistence’ from 2D to 3D, which gives us a robust estimation of the feature strength for extremal lines and surfaces. Not only does it allow us to determine the most important (parts of) extremal lines and surfaces, it also serves as a robust filtering measure of noise‐induced structures. Our purely combinatorial method does not require derivatives or any other numerical computations.