Scattered data is, by definition, irregularly spaced. Uniform surface schemes are not well adapted to the locally varying nature of such data. Conversely, Triangular B-Spline surfaces2 are more flexible in that they can be built over arbitrary triangulations and thus can be adapted to the scattered data. This paper discusses the use of DMS spline surfaces for approximation of scattered data. A ...

The present work considers the interpolation of the scattered data on the d-sphere by spherical polynomials. We prove bounds on the conditioning of the problem which rely only on the separation distance of the sampling nodes and on the degree of polynomials being used. To this end, we establish a packing argument for well separated sampling nodes and construct strongly localized polynomials on ...

We present a new approach for reconstructing a smooth surface from a set of scattered points in three-dimensional (3D) space. Our algorithm first decomposes a given point set into a quadtree-like data structure known as a strip tree. The strip tree is used to fit a set of least squares quadratic surfaces to the data points. These quadratic surfaces are then degree-elevated to bi-cubic surfaces ...

A new imaging principle for object reconstruction is proposed in Single Photon Emission Computer Tomography (SPECT) which is widely used in nuclear medicine. The quality of SPECT images is largely affected by many adverse factors among which chiefly Compton scattering of gamma rays. Recently we have proposed to exploit Compton scattered radiation to generate new data necessary for object recons...

Healthcare directives in the mid-1990s called for a reduction in cost and an improvement in the quality and efficiency of healthcare. Making these changes critically depended on convenient access to and the integration of detailed administrative, financial, and clinical data. Although sophisticated databases had been developed for each function, the lack of interoperability made it impossible t...

We study Sobolev type estimates for the approximation order resulting from using strictly positive definite kernels to do interpolation on the n-sphere. The interpolation knots are scattered. Our approach partly follows the general theory of Golomb and Weinberger and related estimates. These error estimates are then based on series expansions of smooth functions in terms of spherical harmonics....

Voronoi based interpolation employs the concept of natural neighbors to define an interpolating function over discrete data known at scattered sample points. In this work we review the two main concepts for improving interpolation continuity inside the convex hull of the sample domain and compare four natural neighbor interpolants of C and C continuity. We give a visual presentation of all inte...

Non-uniform rational B-spline (NURBS) surface fitting from data points is wildly used in the fields of computer aided design (CAD), medical imaging, cultural relic representation and object-shape detection. Usually, the measured data acquired from coordinate measuring systems is neither gridded nor completely scattered. The distribution of this kind of data is scattered in physical space, but t...