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
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
On the language of standard discrete planes and surfaces
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
Enumeration formula for (2,n)-cubes in discrete planes
Discrete Applied Mathematics
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The aim of this article is to provide some arithmetical tools in order to study the local properties of digital hyperplanes. With the help of the new general notion of configuration, we investigate the arrangement of the different combinatorial structures contained in a digital hyperplane. The regularity of this deployment is controlled by two arithmetical functions that we call code(I) and boundary(I). By using these two simple tools, we prove that the local configurations in a functional digital hyperplane only depends on its normal vector and that their number is less than the size of the chosen neighborhood.