Effective homology of k-D digital objects (partially) calculated in parallel

Abstract

In [18], a membrane parallel theoretical framework for computing (co)homology information of fore- ground or background of binary digital images is developed. Starting from this work, we progress here in two senses: (a) providing advanced topological information, such as (co)homology torsion and effi- ciently answering to any decision or classification problem for sum of k -xels related to be a (co)cycle or a (co)boundary; (b) optimizing the previous framework to be implemented in using GPGPU computing. Discrete Morse theory, Effective Homology Theory and parallel computing techniques are suitably com- bined for obtaining a homological encoding, called algebraic minimal model, of a Region-Of-Interest (seen as cubical complex) of a presegmented k -D digital image.