Tech Report CS-92-31

A Framework for Digital Topology

Eladio Domingues, Angel Frances and Alberto Marquez

June 1992


The main goal of this paper is to show the functional architecture of a framework for digital topology. This architecture has four levels, called the device, logical, conceptual, and continuous levels. In each one of them we can use several models according to a particular problem. The models in the device level represent the physical problem, whereas the models in the continuous level are topological spaces that allow us to use the well-known results of continuous topology (actually, the stronger results of polyhedral topology). The other two levels are used to find a digital solution. The logical level is closer to the device level and is used for processing, for writing algorithms and to show their correctness. The conceptual level is the nearest to the continuous level and it is used to translate results and notions from the continuous level to the logical level.

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