A SPLINE QUASI-INTERPOLANT FOR FITTING 3D DATA ON THE SPHERE AND APPLICATIONSReport as inadecuate




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1 IRAUS PRISME - Laboratoire Pluridisciplinaire de Recherche en Ingénierie des Systèmes, Mécanique et Energétique 2 MRC-UMIS - Département de Mathématiques et Informatique Université Mohammed 1er

Abstract : In 1, the authors have approached the sphere-like surfaces using the tensor product of an algebraic cubic spline quasiinterpolant with a 2¼-periodic Uniform Algebraic Trigonometric B-splines UAT B-splines of order four. In this paper, we improve the results given in 1, by introducing a new quasi-interpolant based on the tensor product of an algebraic cubic spline quasi-interpolant with a periodic cubic spline quasi-interpolant, obtained by the periodization of an algebraic cubic spline quasi-interpolant. Our approach allows us to obtain an approximating surface which is of class C2 and with an approximation order Oh4. We show that this method is particularly well designed to render 3D closed surfaces, and it has been successfully applied to reconstruct human organs such as the left ventricle of the heart.

keyword : Medical imaging B-spline Quasi-interpolant Sphere-like surface





Author: Christophe Léger - Driss Sbibih - Rachid Harba - Ahmed Boujraf -

Source: https://hal.archives-ouvertes.fr/



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