Sturmian words, Lyndon words and trees
Theoretical Computer Science
Optimal Time Computation of the Tangent of a Discrete Curve: Application to the Curvature
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital straightness: a review
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
Discrete Representation of Straight Lines
IEEE Transactions on Pattern Analysis and Machine Intelligence
Maximal digital straight segments and convergence of discrete geometric estimators
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Analysis and comparative evaluation of discrete tangent estimators
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Supercover model and digital straight line recognition on irregular isothetic grids
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Continued fractions and digital lines with irrational slopes
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Computing the characteristics of a subsegment of a digital straight line in logarithmic time
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Discrete Applied Mathematics
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This paper presents new results about digital straight segments, their recognition and related properties They come from the study of the arithmetically based recognition algorithm proposed by I Debled-Rennesson and J.-P Reveillès in 1995 [1] We indeed exhibit the relations describing the possible changes in the parameters of the digital straight segment under investigation This description is achieved by considering new parameters on digital segments: instead of their arithmetic description, we examine the parameters related to their combinatoric description As a result we have a better understanding of their evolution during recognition and analytical formulas to compute them We also show how this evolution can be projected onto the Stern-Brocot tree These new relations have interesting consequences on the geometry of digital curves We show how they can for instance be used to bound the slope difference between consecutive maximal segments.