3 research outputs found
Fractal Topological Analysis for 2D Binary Digital Images
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.Ministerio de Economía y Competitividad TEC2016-77785-PMinisterio de Economía y Competitividad MTM2016-81030-
Searching combinatorial optimality using graph-based homology information
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