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
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
Algorithms in digital geometry based on cellular topology
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Thinning on cell complexes from polygonal tilings
Discrete Applied Mathematics
Fast distance transformation on irregular two-dimensional grids
Pattern Recognition
On topology preservation for hexagonal parallel thinning algorithms
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
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This paper deals with a thinning algorithm proposed in 2001 by Kovalevsky, for 2D binary images modelled by cell complexes, or, equivalently, by Alexandroff T0 spaces. We apply the general proposal of Kovalevsky to cell complexes corresponding to the three possible normal tilings of congruent convex polygons in the plane: the quadratic, the triangular, and the hexagonal tilings. For this case, we give a theoretical foundation of Kovalevsky's thinning algorithm: We prove that for any cell, local simplicity is sufficient to satisfy simplicity, and that both are equivalent for certain cells. Moreover, we show that the parallel realization of the algorithm preserves topology, in the sense that the numbers of connected components both of the object and of the background, remain the same. The paper presents examples of skeletons obtained from the implementation of the algorithm for each of the three cell complexes under consideration.