Sobre a teoria das variedades digitais de Evako

Abstract

In the processing of digital images, space and images need to be discreetly representable. In general, such images are manipulated with continuous mathematical technique, via approximations. In the development of our work we have an approach where it is possible to develop a topology and a geometry that can perform discrete representations directly without the necessary approximations. For the construction of this Digital Topology we take as basis the Evako’s Theory of Contractible Graphs and set out for the study of Spaces and Digital Manifold. From this, we will bring concepts and examples of interesting Digital Spaces: Spheres and Digital Manifolds. Finally, we present two special Homotopies between Digital Manifolds: R-Transformations and Compression. Both operations modify the amount of vertices and edges of digital spaces, but preserve their topological aspects. An important fact is that the Euler characteristic of a digital space is a topological invariant preserved by both homotopy.