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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
Full Text:
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