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
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Thinning on cell complexes from polygonal tilings
Discrete Applied Mathematics
Thinning on quadratic, triangular, and hexagonal cell complexes
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
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Abstract cell complexes (ACC's) were introduced by Ko-valevsky as a means of solving certain connectivity paradoxes in graph-theoretic digital 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 axiomatic combinatorial 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.