Patterns in discretized parabolas and length estimation

Authors:
Alain Daurat;Mohamed Tajine;Mahdi Zouaoui
Affiliations:
LSIIT, CNRS, UMR, Université de Strasbourg, Illkirch-Graffenstaden, France;LSIIT, CNRS, UMR, Université de Strasbourg, Illkirch-Graffenstaden, France;LSIIT, CNRS, UMR, Université de Strasbourg, Illkirch-Graffenstaden, France
Venue:
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Year:
2009

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Abstract

We estimate the frequency of the patterns in the discretization of parabolas, when the resolution tends to zero. We deduce that local estimators of length almost never converge to the length for the parabolas.