A new characterization of three-dimensional simple points
Pattern Recognition Letters
Detection of 3-D Simple Points for Topology Preserving Transformations with Application to Thinning
IEEE Transactions on Pattern Analysis and Machine Intelligence
Contractible transformations do not change the homology groups of graphs
Discrete Mathematics
Some properties of contractible transformations on graphs
Discrete Mathematics
Simple points, topological numbers and geodesic neighborhoods in cubic grids
Pattern Recognition Letters
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Journal of Mathematical Imaging and Vision - Special issue on topology and geometry in computer vision
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Journal of the ACM (JACM)
Topology-Preserving Deletion of 1's from 2-, 3- and 4-Dimensional Binary Images
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
A concise characterization of 3D simple points
Discrete Applied Mathematics
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Pattern Recognition
Minimal Simple Pairs in the 3-D Cubic Grid
Journal of Mathematical Imaging and Vision
New Characterizations of Simple Points in 2D, 3D, and 4D Discrete Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Topology on Adaptive Octree Grids
Journal of Mathematical Imaging and Vision
Computer Vision and Image Understanding
Active contours under topology control genus preserving level sets
CVBIA'05 Proceedings of the First international conference on Computer Vision for Biomedical Image Applications
A topology preserving level set method for geometric deformable models
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the detection of simple points in higher dimensions using cubical homology
IEEE Transactions on Image Processing
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The notion of a simple point plays an important role in topology-preserving thinning, skeletonization and simplification of digital images. This paper presents new dimension-independent characterizations of simple points, simple edges and simple cliques based on the notion of a digital contractible space and contractible transformations of digital spaces. We show that a given digital space can be transformed to a normal digital space by the removal of simple points, edges and cliques while preserving topology. We describe a topology-preserving thinning algorithm, which transforms a given digital image to a normal one.