On the Number of Digital Straight Line Segments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital plane and grid point segments
Computer Vision, Graphics, and Image Processing
On the number of factors of Sturmian words
Theoretical Computer Science
Combinatorics of patterns of a bidimensional Sturmian sequence.
Theoretical Computer Science
Object discretizations in higher dimensions
Pattern Recognition Letters
Digital Planarity of Rectangular Surface Segments
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Discrete Applied Mathematics
On some applications of generalized functionality for arithmetic discrete planes
Image and Vision Computing
On digital plane preimage structure
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Surface area estimation of digitized 3D objects using weighted local configurations
Image and Vision Computing
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In this paper we prove that the function giving the frequency of a class of patterns of digital planes with respect to the slopes of the plane is continuous and piecewise affine, moreover the regions of affinity are precised. It allows to prove some combinatorial properties of a class of patterns called (m, n)-cubes. This study has also some consequences on local estimators of area: we prove that the local estimators restricted to regions of plane never converge to the exact area when the resolution tends to zero for almost all slope of plane. Actually all the results of this paper can be generalized for the regions of hyperplanes for any dimension d ≥ 3. The proofs of some results used in this article are contained in the extended version of this paper [1].