Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
A new characterization of three-dimensional simple points
Pattern Recognition Letters
Simple points, topological numbers and geodesic neighborhoods in cubic grids
Pattern Recognition Letters
The k-Homotopic Thinning and a Torus-Like Digital Image in Zn
Journal of Mathematical Imaging and Vision
Minimal Simple Pairs in the 3-D Cubic Grid
Journal of Mathematical Imaging and Vision
Technical Section: Normals estimation for digital surfaces based on convolutions
Computers and Graphics
Digital Topology on Adaptive Octree Grids
Journal of Mathematical Imaging and Vision
An introduction to simple sets
Pattern Recognition Letters
Minimal simple pairs in the cubic grid
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Determining whether a simplicial 3-complex collapses to a 1-complex is NP-complete
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
3D topological thinning by identifying non-simple voxels
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Simple points and generic axiomatized digital surface-structures
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Digital Imaging: A Unified Topological Framework
Journal of Mathematical Imaging and Vision
Deletion of (26,6)-simple points as multivalued retractions
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
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We recall a possible definition of a simple point which uses the digital fundamental group introduced by Kong (Comput. Graphics 13 (1989) 159). Then, we prove that a more concise but not less restrictive definition can be given. Indeed, we prove that there is no need to consider the fundamental group of the complement of an object in order to characterize its simple points. In order to prove this result, we do not use the fact that "the number of tunnels of X is equal to the number of tunnels in X" but we use the linking number defined in (Proceedings of the Seventh International Workshop on Combinatorial, Image Analysis (IWCIA'00), University of Caen, 2000, p. 59). In so doing, we formalize the proofs of several results stated without proof in the literature (Bertrand, Kong, Morgenthaler).