Geometric Modelling of the Thinning by Cell Complexes

Motivation: Thinning is an extremely active area of research because of its primary role in reducing the amount of information that must be processed by algorithms for pattern recognition. Most thinning algorithms are supposed to be topology-preserving, although an accurate statement of what this means is usually left unanswered.Results: The objective of this article is the presentation of a general topology via the concepts of homotopy theory to preserve the thinning. The proposed method can be applied to any decomposition of non-structural cells of the object, given that the cells have a fixed structure.