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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.

MSC:
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
Software:
CHomP; Kenzo; PLEX
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References:
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