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

El Bachir Ameur, Driss Sbibih, Ahmad Almhdie, Christophe Leger
<span title="">2007</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="" style="color: black;">IEEE Signal Processing Letters</a> </i> &nbsp;
In this paper, a new local spline quasi-interpolant is constructed for fitting 3-D data defined on the sphere-like surface . After mapping the surface onto a rectangular domain, we use the tensor product of cubic polynomial B-splines and 2 -periodic uniform algebraic trigonometric B-splines (UAT B-splines) of order four to introduce a new expression of the associated quasi-interpolant . The use of UAT B-splines is necessary to enforce some boundary conditions which are useful to ensure the 1
more &raquo; ... tinuity 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. Index Terms-B-spline, medical data, quasi-interpolant, sphere-like surface reconstruction, uniform algebraic trigonometric B-splines (UAT B-splines).
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1109/lsp.2006.888261</a> <a target="_blank" rel="external noopener" href="">fatcat:vvk6y76uofar3b6ay43osemtzu</a> </span>
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