On the convex hull of the integer points in a disc
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Sturmian words, Lyndon words and trees
Theoretical Computer Science
Multigrid Convergence of Calculated Features in Image Analysis
Journal of Mathematical Imaging and Vision
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
A Comparative Evaluation of Length Estimators of Digital Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Analysis and comparative evaluation of discrete tangent estimators
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Journal of Mathematical Imaging and Vision
Fast, accurate and convergent tangent estimation on digital contours
Image and Vision Computing
On the polyhedral complexity of the integer points in a hyperball
Theoretical Computer Science
Some theoretical challenges in digital geometry: A perspective
Discrete Applied Mathematics
Estimation of the derivatives of a digital function with a convergent bounded error
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Convex shapes and convergence speed of discrete tangent estimators
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
Polyhedrization of discrete convex volumes
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part I
Revisiting digital straight segment recognition
DGCI'06 Proceedings of the 13th 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. We study here the convergence of local estimators based on Digital Straight Segment (DSS) recognition. It is closely linked to the asymptotic growth of maximal DSS, for which we show bounds both about their number and sizes. 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 an hypothesis 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, continued fractions and random polytopes.