A topological characterization of thinning
Theoretical Computer Science
Discrete Applied Mathematics
Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
3D medial surfaces and 3D skeletons
IAPR Proceedings of the international workshop on Visual form: analysis and recognition
Topological segmentation of discrete surfaces
International Journal of Computer Vision
A new characterization of three-dimensional simple points
Pattern Recognition Letters
On topology preservation in 3D thinning
CVGIP: Image Understanding
Detection of 3-D Simple Points for Topology Preserving Transformations with Application to Thinning
IEEE Transactions on Pattern Analysis and Machine Intelligence
Simple points, topological numbers and geodesic neighborhoods in cubic grids
Pattern Recognition Letters
A 3D fully parallel thinning algorithm for generating medial faces
Pattern Recognition Letters
A fully parallel 3D thinning algorithm and its applications
Computer Vision and Image Understanding
A 3D 6-subiteration thinning algorithm for extracting medial lines
Pattern Recognition Letters
A parallel 3D 12-subiteration thinning algorithm
Graphical Models and Image Processing
Some Topological Properties of Surfaces in Z3
Journal of Mathematical Imaging and Vision
A medial-surface oriented 3-d two-subfield thinning algorithm
Pattern Recognition Letters
Three-Dimensional Topology Preserving Reduction on the 4-Subfields
IEEE Transactions on Pattern Analysis and Machine Intelligence
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 New 3D 6-Subiteration Thinning Algorithm Based on P-Simple Points
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Strong thinning and polyhedric approximation of the surface of a voxel object
Discrete Applied Mathematics
A 3D 12-subiteration thinning algorithm based on P-simple points
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
A 3D 6-subiteration curve thinning algorithm based on P-simple points
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Computers in Biology and Medicine
Computers in Biology and Medicine
Pattern Recognition Letters
A 3D fully parallel surface-thinning algorithm
Theoretical Computer Science
An Automatic Correction of Ma's Thinning Algorithm Based on P-simple Points
Journal of Mathematical Imaging and Vision
Computer Vision and Image Understanding
Powerful Parallel and Symmetric 3D Thinning Schemes Based on Critical Kernels
Journal of Mathematical Imaging and Vision
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In this paper, we propose two 3D symmetrical thinning algorithms based on the parallel deletion of P-simple points. The first one permits surface skeletons to be obtained. The second one permits curve skeletons to be extracted, and as far as we know, this is the only symmetrical curve thinning algorithm which preserves topology. These algorithms have been conceived in order to obtain precise results on simple specific objects (parallelepipeds). Consequently, we can predict the number of deletion iterations, the number of deleted points, and the skeleton of these objects obtained by the two algorithms, which is hardly ever possible to assess with other algorithms even on these simple objects.