Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Boolean connection algebras: a new approach to the Region-Connection Calculus
Artificial Intelligence
Topology in Raster and Vector Representation
Geoinformatica
The Mereotopology of Discrete Space
COSIT '99 Proceedings of the International Conference on Spatial Information Theory: Cognitive and Computational Foundations of Geographic Information Science
Topological Relations Between Regions in R² and Z²
SSD '93 Proceedings of the Third International Symposium on Advances in Spatial Databases
Topological Relations between Regions in Raster
SSD '95 Proceedings of the 4th International Symposium on Advances in Spatial Databases
Generalized region connection calculus
Artificial Intelligence
Using Occlusion Calculi to Interpret Digital Images
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Generalized Region Connection Calculus
Artificial Intelligence
Map algebraic characterization of self-adapting neighborhoods
COSIT'09 Proceedings of the 9th international conference on Spatial information theory
Connectivity in the regular polytope representation
Geoinformatica
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Computations in geographic space are necessarily based on discrete versions of space, but much of the existing work on the foundations of GIS assumes a continuous infinitely divisible space. This is true both of quantitative approaches, using Rn, and qualitative approaches using systems such as the Region-Connection Calculus (RCC). This paper shows how the RCC can be modified so as to permit discrete spaces by weakening Stell's formulation of RCC as Boolean connection algebra to what we now call a connection algebra. We show how what was previously considered a problem--with atomic regions being parts of their complements--can be resolved, but there are still obstacles to the interplay between parthood and connection when there are finitely many regions. Connection algebras allow regions that are atomic and also regions that are boundaries of other regions. The modification of the definitions of the RCC5 and RCC8 relations needed in the context of a connection algebra are discussed. Concrete examples of connection algebras are provided by abstract cell complexes. In order to place our work in context we start with a survey of previous approaches to discrete space in GIS and related areas.