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 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