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

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...

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Bibliographic Details
Published in:IEEE signal processing letters 2007-05, Vol.14 (5), p.333-336
Main Authors: Ameur, E.B., Sbibih, D., Almhdie, A., Leger, C.
Format: Article
Language:English
Subjects:
Algebra
B-spline
Biomedical imaging
Boundary conditions
Continuity
Fittings
Human
Humans
Image reconstruction
Lungs
Mathematical analysis
medical data
Organs
Polynomials
quasi-interpolant
sphere- like surface reconstruction
Spline
Splines
Surface fitting
Surface reconstruction
Tensile stress
Tensors
uniform algebraic trigonometric B-splines (UAT B-splines)
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Summary: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 C 1 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
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2006.888261