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Searching high order invariants in computer imagery. (English) Zbl 1247.68305
Summary: We present a direct computational application of homological perturbation theory (HPT, for short) to computer imagery. More precisely, the formulas of the \(A _{\infty }\)-coalgebra maps \(\varDelta _{2}\) and \(\varDelta _{3}\) using the notion of an AT-model of a digital image and the HPT technique are implemented. The method has been tested on some specific examples, showing the usefulness of this computational tool for distinguishing 3D digital images.

68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
55P43 Spectra with additional structure (\(E_\infty\), \(A_\infty\), ring spectra, etc.)
55P10 Homotopy equivalences in algebraic topology
68W30 Symbolic computation and algebraic computation
68U10 Computing methodologies for image processing
68-04 Software, source code, etc. for problems pertaining to computer science
55-04 Software, source code, etc. for problems pertaining to algebraic topology
CHomP; Kenzo; PLEX
Full Text: DOI
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