New Spline Quasi-Interpolant for Fitting 3-D Data on the Sphere: Applications to Medical Imaging

Author

Ameur, El Bachir ; Sbibih, Driss ; Almhdie, Ahmad ; Léger, Christophe

Author_Institution

Univ. Moulay Ismail, Errachidia

Volume

14

Issue

5

fYear

2007

fDate

5/1/2007 12:00:00 AM

Firstpage

333

Lastpage

336

Abstract

In this paper, a new local spline quasi-interpolant is constructed for fitting 3-D data defined on the sphere-like surface S. After mapping the surface S onto a rectangular domain, we use the tensor product of cubic polynomial B-splines and 2pi-periodic uniform algebraic trigonometric B-splines (UAT B-splines) of order four to introduce a new expression of the associated quasi-interpolant Q. The use of UAT B-splines is necessary to enforce some boundary conditions which are useful to ensure the C¹ continuity of the associated surface. The new method is particularly well designed to render 3-D closed surfaces. It has been successfully applied to reconstruct human organs such as the lung and left ventricle of the heart

Keywords

image reconstruction; interpolation; medical image processing; splines (mathematics); UAT; cubic polynomial B-splines; human organs reconstruction; medical imaging; rectangular domain; sphere-like surface; spline quasiinterpolant; uniform algebraic trigonometric B-splines; Biomedical imaging; Boundary conditions; Humans; Image reconstruction; Lungs; Polynomials; Spline; Surface fitting; Surface reconstruction; Tensile stress; B-spline; medical data; quasi-interpolant; sphere- like surface reconstruction; uniform algebraic trigonometric B-splines (UAT B-splines);

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/LSP.2006.888261

Filename

4154717