2015-12-232015-12-232012Molina Abril, H. y Real Jurado, P. (2012). Homological spanning forest framework for 2D image analysis. Annals of Mathematics and Artificial Intelligence, 64, 385-409.http://hdl.handle.net/11441/32176A 2D topology-based digital image processing framework is presented here. This framework consists of the computation of a flexible geometric graph-based structure, starting from a raster representation of a digital image I. This structure is called Homological Spanning Forest (HSF for short), and it is built on a cell complex associated to I. The HSF framework allows an efficient and accurate topological analysis of regions of interest (ROIs) by using a four-level architecture. By topological analysis, we mean not only the computation of Euler characteristic, genus or Betti numbers, but also advanced computational algebraic topological information derived from homological classification of cycles. An initial HSF representation can be modified to obtain a different one, in which ROIs are almost isolated and ready to be topologically analyzed. The HSF framework is susceptible of being parallelized and generalized to higher dimensions.application/pdfengAtribución-NoComercial-CompartirIgual 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-sa/4.0/Computational algebraic topologyImage processingObject recognitionHomology with coefficients in a fieldChain homotopy operatorChain homotopy equivalenceDiscrete Morse Theoryinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1007/s10472-012-9297-7