In this paper, we propose a bio-inspired membrane computational framework for constructing discrete Morse complexes for binary digital images. Our approach is based on the discrete Morse theory and we work with cubical complexes. As example, a parallel algorithm for computing homology groups of binary 3D digital images is designed.
In Reina-Molina et al. (2015), a membrane parallel theoretical framework for computing (co)homology information of foreground 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 efficiently 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 combined 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.
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