Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Bridging vector and raster representation in GIS
Proceedings of the 6th ACM international symposium on Advances in geographic information systems
On recent trends in discrete geometry in computer science
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Cell complexes, oriented matroids and digital geometry
Theoretical Computer Science - Topology in computer science
Discretization in 2D and 3D Orders
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Homological spanning forest framework for 2D image analysis
Annals of Mathematics and Artificial Intelligence
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Abstract cell complexes (ACC's) were introduced by Kovalevsky as a means of solving certain connectivity paradoxes in graphtheoreticdi gital topology, and to this extent provide an improved theoretical basis for image analysis. We argue that ACC's are a very natural setting for digital convexity, to the extent that their use permits simple, almost trivial formulations of major convexity results such as Caratheodory's, Helly's and Radon's theorems. ACC's also permit the use in digital geometry of axiomaticc ombinatorial geometries such as oriented matroids. We give a brief indication of how standard convexity algorithms from computational geometry applied to the points of an ACC can form a substantial part of digital convexity algorithms.