Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
A topological characterization of thinning
Theoretical Computer Science
Discrete Applied Mathematics
Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
Efficient implementation of a BDD package
DAC '90 Proceedings of the 27th ACM/IEEE Design Automation Conference
A new characterization of three-dimensional simple points
Pattern Recognition Letters
On topology preservation in 3D thinning
CVGIP: Image Understanding
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
Fast binary image processing using binary decision diagrams
Computer Vision and Image Understanding
A parallel 3D 12-subiteration thinning algorithm
Graphical Models and Image Processing
Digital Picture Processing
Skeletonizing Volume Objects Part 2: From Surface to Curve Skeleton
SSPR '98/SPR '98 Proceedings of the Joint IAPR International Workshops on Advances in Pattern Recognition
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)
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
A note on 'A fully parallel 3D thinning algorithm and its applications'
Pattern Recognition Letters
Curve-Skeleton Properties, Applications, and Algorithms
IEEE Transactions on Visualization and Computer Graphics
Pattern Recognition Letters
Two-Dimensional Parallel Thinning Algorithms Based on Critical Kernels
Journal of Mathematical Imaging and Vision
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
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
On the cohomology of 3D digital images
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
An Automatic Correction of Ma's Thinning Algorithm Based on P-simple Points
Journal of Mathematical Imaging and Vision
Automatic Correction of Ma and Sonka's Thinning Algorithm Using P-Simple Points
IEEE Transactions on Pattern Analysis and Machine Intelligence
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In 1996, Ma and Sonka proposed a thinning algorithm which yields curve skeletons for 3D binary images [C. Ma, M. Sonka, A fully parallel 3D thinning algorithm and its applications, Comput. Vis. Image Underst. 64 (3) (1996) 420-433]. This algorithm is one of the most referred thinning algorithms in the context of digital topology: either by its use in medical applications or for comparisons with other thinning algorithms. In 2007, Wang and Basu [T. Wang, A. Basu, A note on 'a fully parallel 3D thinning algorithm and its applications', Pattern Recognit. Lett. 28 (4) (2007) 501-506] wrote a paper in which they claim that Ma and Sonka's 3D thinning algorithm does not preserve topology. As they highlight in their paper, a counter-example was given in 2001, in Lohou's thesis [C. Lohou, Contribution a l'analyse topologique des images: etude d'algorithmes de squelettisation pour images 2D et 3D selon une approche topologie digitale ou topologie discrete. Ph.D. thesis, University of Marne-la-Vallee, France, 2001]. In this paper, it is shown how P-simple points have guided the author towards a proof that Ma and Sonka's algorithm does not always preserve topology. Moreover, the reasoning being very general, it could be reused for such a purpose, i.e., to simplify the proof on the non-topology preservation.