Development of a digital image thinning system on cellular complexes.

The present work focuses on the development and implementation of the algorithm proposed by Kovalesky, to digitally identify an object with its digital skeleton.The proposal will be performed on two cell complexes: quadratic and hexagonal.Once the digital skeleton is generated, it will be compared with the geometric representation defined by Harry Blum in 1967, called Blum's Skeleton.Finally, an analysis of the results obtained is performed to conclude which cellular complex preserves the geometric and topological properties of the initial object, such as bifurcation points, branching and connectivity.It is located in two areas of mathematics, related to Digital Image Processing, in particular, with skeletonization methods: Digital Topology and Digital Geometry.A thinning algorithm proposed in 2001 by Kovalevsky, for binary digital images of dimension two, modeled by cell complexes, is experimented on the hexagonal and quadratic cell complexes.For the hexagonal and quadratic complex, Kovalevsky's algorithm is developed and implemented as a pattern-mapping method within this work.The skeletons obtained in various experiments are analyzed with respect to some topological and geometrical properties, and are compared with Blum's skeleton.