Worst-case Analysis of Set Union Algorithms
Journal of the ACM (JACM)
Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
A topological approach to digital topology
American Mathematical Monthly
Digital Picture Processing
A topologically consistent representation for image analysis: the Topological Graph of Frontiers
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Aspects in Topology-Based Geometric Modeling
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
Applications of Digital Straight Segments to Economical Image Encoding
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
Algorithmic and Computer Methods for Three-Manifolds
Algorithmic and Computer Methods for Three-Manifolds
3D image topological structuring with an oriented boundary graph for split and merge segmentation
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Convex hulls in a 3-dimensional space
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Curves, hypersurfaces, and good pairs of adjacency relations
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Algorithms in digital geometry based on cellular topology
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
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The paper presents a new method of investigating topological properties of three-dimensional manifolds by means of computers. Manifolds are represented as block complexes. The paper contains definitions and a theorem necessary to transfer some basic knowledge of the classical topology to finite topological spaces. The method is based on subdividing the given set into blocks of cells in such a way that a k-dimensional block be homeomorphic to a k-dimensional ball. The block structure is described by the data structure known as "cell list" which is generalized here for the multidimensional case. Results of computer experiments are presented.