Artículo
Fractal Topological Analysis for 2D Binary Digital Images
Autor/es | Blanco Trejo, Sergio
Alemán Morillo, C. Díaz del Río, Fernando Real Jurado, Pedro |
Departamento | Universidad de Sevilla. Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos Universidad de Sevilla. Departamento de Arquitectura y Tecnología de Computadores Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2019 |
Fecha de depósito | 2021-09-29 |
Publicado en |
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Resumen | Fractal dimension is a powerful tool employed as a measurement of geometric aspects. In this work we
propose a method of topological fractal analysis for 2D binary digital images by using a graph-based topological
model ... Fractal dimension is a powerful tool employed as a measurement of geometric aspects. In this work we propose a method of topological fractal analysis for 2D binary digital images by using a graph-based topological model of them, called Homological Spanning Forest (HSF, for short). Defined at interpixel level, this set of two trees allows to topologically describe the (black and white) connected component distribution within the image with regards to the relationship “to be surrounded by”. This distribution is condensed into a rooted tree, such that its nodes are connected components determined by some special sub-trees of the previous HSF and the levels of the tree specify the degree of nesting of each connected component. We ask for topological auto-similarity by comparing this topological description of the whole image with a regular rooted tree pattern. Such an analysis can be used to directly quantify some characteristics of biomedical images (e.g. cells samples or clinical images) that are not so noticeable when using geometrical approaches. |
Agencias financiadoras | Ministerio de Economía y Competitividad (MINECO). España |
Identificador del proyecto | TEC2016-77785-P
MTM2016-81030-P |
Cita | Blanco Trejo, S., Alemán Morillo, C., Díaz del Río, F. y Real Jurado, P. (2019). Fractal Topological Analysis for 2D Binary Digital Images. Mathematics in Computer Science, 13 (1-2), 11-20. |
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