Discrete analytical hyperplanes
Graphical Models and Image Processing
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
Coexistence of Tricubes in Digital Naive Plane
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
Recognizing arithmetic straight lines and planes
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Euclidean Nets: An Automatic and Reversible Geometric Smoothing of Discrete 3D Object Boundaries
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Recognition of Digital Naive Planes and Polyhedrization
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Defining Discrete Objects for Polygonalization: The Standard Model
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Local Non-planarity of Three Dimensional Surfaces for an Invertible Reconstruction: k-Cuspal Cells
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
Adaptive Pixel Resizing for Multiscale Recognition and Reconstruction
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
About thin arithmetic discrete planes
Theoretical Computer Science
On the language of standard discrete planes and surfaces
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Discrete surfaces segmentation into discrete planes
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Generalized functionality for arithmetic discrete planes
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Generalized perpendicular bisector and circumcenter
CompIMAGE'10 Proceedings of the Second international conference on Computational Modeling of Objects Represented in Images
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A digital naive plane can be represented by repetition of specific elements, called (n,m)-cubes, composed of n × m adjacent voxels. The aim of this paper is to study the class of (n,m)-cubes appearing in a plane in relation with the parametric representation based on the normal vector. Planes are ordered using Farey series coding and we prove the relationship between the segmentation issued from the Farey net and configurations of (n,m)-cubes. This is an original contribution.