Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
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]
Applications of Digital Straight Segments to Economical Image Encoding
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
A Topological Method of Surface Representation
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
Multidimensional cell lists for investigating 3-manifolds
Discrete Applied Mathematics
Journal of Mathematical Imaging and Vision
Polyhedral approximation and practical convex hull algorithm for certain classes of voxel sets
Discrete Applied Mathematics
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
Polyhedral surface approximation of non-convex voxel sets through the modification of convex hulls
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Homological spanning forest framework for 2D image analysis
Annals of Mathematics and Artificial Intelligence
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The paper presents some algorithms in digital geometry based on the topology of cell complexes. The paper contains an axiomatic justification of the necessity of using cell complexes in digital geometry. Algorithms for solving the following problems are presented: tracing of curves and surfaces, recognition of digital straight line segments (DSS), segmentation of digital curves into longest DSS, recognition of digital plane segments, computing the curvature of digital curves, filling of interiors of n-dimensional regions (n=2,3,4), labeling of components (n=2,3), computing of skeletons (n=2, 3).