Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
A topological approach to digital topology
American Mathematical Monthly
Computer Vision and Image Understanding
On strongly normal tesselations
Pattern Recognition Letters
Thinning algorithms on rectangular, hexagonal, and triangular arrays
Communications of the ACM
Local and global topology preservation in locally finite sets of tiles
Information Sciences: an International Journal
Algorithms and Data Structures for Computer Topology
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Cell complexes and digital convexity
Digital and image geometry
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Journal of Mathematical Imaging and Vision
Strongly normal sets of contractible tiles in N dimensions
Pattern Recognition
Thinning on quadratic, triangular, and hexagonal cell complexes
IWCIA'08 Proceedings of the 12th 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
Binary images, M-vectors, and ambiguity
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
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This paper provides a theoretical foundation of a thinning method due to Kovalevsky for 2D digital binary images modelled by cell complexes or, equivalently, by Alexandroff T"0 topological spaces, whenever these are constructed from polygonal tilings. We analyze the relation between local and global simplicity of cells, and prove their equivalence under certain conditions. For the proof we apply a digital Jordan theorem due to Neumann-Lara/Wilson which is valid in any connected planar locally Hamiltonian graph. Therefore we first prove that the incidence graph of the cell complex constructed from any polygonal tiling has these properties, showing that it is a triangulation of the plane. Moreover, we prove that the parallel performance of Kovalevsky's thinning method preserves topology in the sense that the numbers of connected components, for both the object and of the background, remain the same.