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

Abstract

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.

Membrane computing and image processing: a short survey

“…On one hand, Peña-Cantillana et al [41] generate a parallel software using GPUs by CUDA to get the homology groups of 2D shapes based on techniques of spanning trees generated with membrane models where the promoters are compulsory. On the other hand, Reina-Molina et al use PyCUDA (Python plus CUDA) to solve homological problems in a practical way in [138]. But, the complexity to adapt the Morse theory to parallel algorithms is high.…”

RGB image-based data analysis via discrete Morse theory and persistent homology

“…DISCUSSION AND FUTURE DIRECTIONS The goal of this manuscript is to contribute to a path towards predictive topological data analysis based only on RGB images (either publicly or privately available) to improve computational feasibility in an age of an overabundance of visual data. The contribution of this manuscript is the development of methods to bypass computational techniques including parallelized machine learning [29], [30], develop new methods for uncovering statistical properties of image-encoded data [3], and add potential for application-based directions for the theory in algebraic publications such as [31].…”