`Continuous' functions on digital pictures
Pattern Recognition Letters
A Jordan surface theorem for three-dimensional digital spaces
Discrete & Computational Geometry
Digitally continuous functions
Pattern Recognition Letters
Simple points, topological numbers and geodesic neighborhoods in cubic grids
Pattern Recognition Letters
A Classical Construction for the Digital Fundamental Group
Journal of Mathematical Imaging and Vision
A new local property of strong n-surfaces
Pattern Recognition Letters
The equivalence between two definitions of digital surfaces
Information Sciences—Informatics and Computer Science: An International Journal
Some Topological Properties of Surfaces in Z3
Journal of Mathematical Imaging and Vision
Topological Algorithms for Digital Image Processing
Topological Algorithms for Digital Image Processing
Polyhedra generation from lattice points
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
A concise characterization of 3D simple points
Discrete Applied Mathematics
Non-product property of the digital fundamental group
Information Sciences—Informatics and Computer Science: An International Journal
Graphs and Hypergraphs
Digital fundamental group and Euler characteristic of a connected sum of digital closed surfaces
Information Sciences: an International Journal
The k-fundamental group of a closed k-surface
Information Sciences: an International Journal
Equivalent (k0,k1)-covering and generalized digital lifting
Information Sciences: an International Journal
Minimal simple closed 18-surfaces and a topological preservation of 3D surfaces
Information Sciences: an International Journal
Information Sciences: an International Journal
Connected sum of digital closed surfaces
Information Sciences: an International Journal
Discrete homotopy of a closed k-surface
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Ultra regular covering space and its automorphism group
International Journal of Applied Mathematics and Computer Science
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In order to discuss digital topological properties of a digital image (X,k), many recent papers have used the digital fundamental group and several digital topological invariants such as the k-linking number, the k-topological number, and so forth. Owing to some difficulties of an establishment of the multiplicative property of the digital fundamental group, a k-homotopic thinning method can be essentially used in calculating the digital fundamental group of a digital product with k-adjacency. More precisely, let $\mathit{SC}_{k_{i}}^{n_{i},l_{i}}$ be a simple closed k i -curve with l i elements in $\mathbf{Z}^{n_{i}},i\in\{1,2\}$ . For some k-adjacency of the digital product $\mathit{SC}_{k_{1}}^{n_{1},l_{1}}\times\mathit{SC}_{k_{2}}^{n_{2},l_{2}}\subset\mathbf{Z}^{n_{1}+n_{2}}$ which is a torus-like set, proceeding with the k-homotopic thinning of $\mathit{SC}_{k_{1}}^{n_{1},l_{1}}\times\mathit{SC}_{k_{2}}^{n_{2},l_{2}}$ , we obtain its k-homotopic thinning set denoted by DT k . Writing an algorithm for calculating the digital fundamental group of $\mathit{SC}_{k_{1}}^{n_{1},l_{1}}\times\mathit {SC}_{k_{2}}^{n_{2},l_{2}}$ , we investigate the k-fundamental group of $(\mathit{SC}_{k_{1}}^{n_{1},l_{1}}\times\mathit{SC}_{k_{2}}^{n_{2},l_{2}},k)$ by the use of various properties of a digital covering (Z脳Z,p 1脳p 2,DT k ), a strong k-deformation retract, and algebraic topological tools. Finally, we find the pseudo-multiplicative property (contrary to the multiplicative property) of the digital fundamental group. This property can be used in classifying digital images from the view points of both digital k-homotopy theory and mathematical morphology.