On the convex hull of the integer points in a disc
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Digitizations preserving topological and differential geometric properties
Computer Vision and Image Understanding
Sturmian words, Lyndon words and trees
Theoretical Computer Science
Preserving Topology by a Digitization Process
Journal of Mathematical Imaging and Vision
Multigrid Convergence of Calculated Features in Image Analysis
Journal of Mathematical Imaging and Vision
A Comparative Evaluation of Length Estimators of Digital Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
On the min DSS problem of closed discrete curves
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
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
Digitization scheme that assures faithful reconstruction of plane figures
Pattern Recognition
Comparison and improvement of tangent estimators on digital curves
Pattern Recognition
What Does Digital Straightness Tell about Digital Convexity?
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Multi-scale Analysis of Discrete Contours for Unsupervised Noise Detection
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Robust estimation of curvature along digital contours with global optimization
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Experimental comparison of continuous and discrete tangent estimators along digital curves
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Regularization of Discrete Contour by Willmore Energy
Journal of Mathematical Imaging and Vision
Another definition for digital tangents
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Integral based curvature estimators in digital geometry
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
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Discrete geometric estimators approach geometric quantities on digitized shapes without any knowledge of the continuous shape. A classical yet difficult problem is to show that an estimator asymptotically converges toward the true geometric quantity as the resolution increases. For estimators of local geometric quantities based on Digital Straight Segment (DSS) recognition this problem is closely linked to the asymptotic growth of maximal DSS for which we show bounds both about their number and sizes on Convex Digital Polygons. These results not only give better insights about digitized curves but indicate that curvature estimators based on local DSS recognition are not likely to converge. We indeed invalidate a conjecture which was essential in the only known convergence theorem of a discrete curvature estimator. The proof involves results from arithmetic properties of digital lines, digital convexity, combinatorics and continued fractions.