Ω-arithmetization of ellipses

Authors:
Agathe Chollet;Guy Wallet;Eric Andres;Laurent Fuchs;Gaëlle Largeteau-Skapin;Aurélie Richard
Affiliations:
Laboratoire MIA, Université de La Rochelle, La Rochelle cedex, France;Laboratoire MIA, Université de La Rochelle, La Rochelle cedex, France;Laboratoire XLIM SIC, UMR 6172, Université de Poitiers, France;Laboratoire XLIM SIC, UMR 6172, Université de Poitiers, France;Laboratoire XLIM SIC, UMR 6172, Université de Poitiers, France;Laboratoire XLIM SIC, UMR 6172, Université de Poitiers, France
Venue:
CompIMAGE'10 Proceedings of the Second international conference on Computational Modeling of Objects Represented in Images
Year:
2010

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Abstract

Multi-resolution analysis and numerical precision problems are very important subjects in fields like image analysis or geometrical modeling. In the continuation of our previous works, we propose to apply the method of Ω-arithmetization to ellipses. We obtain a discrete multi-resolution representation of arcs of ellipses. The corresponding algorithms are completely constructive and thus, can be exactly translated into functional computer programs. Moreover, we give a global condition for the connectivity of the discrete curves generated by the method at every scale.