A SPLINE QUASI-INTERPOLANT FOR FITTING 3D DATA ON THE SPHERE AND APPLICATIONS

Christophe Léger (1) , Driss Sbibih (2) , Rachid Harba (1) , Ahmed Boujraf (2)

1 IRAUS - Département Images, Robotique, Automatique et Signal [Orléans]
2 Université Mohammed Premier [Oujda]

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 O(h4). 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.

Mots clés: B-spline; Quasi-interpolant; Sphere-like surface; Medical imaging

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Christophe Léger, Driss Sbibih, Rachid Harba, Ahmed Boujraf. A SPLINE QUASI-INTERPOLANT FOR FITTING 3D DATA ON THE SPHERE AND APPLICATIONS. Eusipco 2012, Aug 2012, Bucarest, Romania. pp.A définir. ⟨hal-00702363⟩