A new scheme of data-driven segmentation is proposed, which is based on detection of object boundary, and volumetric pattern reconstruction as implicit function by using the detected object boundary and the radial basis functions (RBF). By using clinical X-ray CT data, applications in visualization of the pancreatic duct by MINIP of curved thin-slab and in liver segmentation are shown.

In the field of radial basis functions mathematicians have been endeavouring to find infinitely differentiable and compactly supported radial functions. This kind of functions is extremely important. One of the reasons is that its error bound will converge very fast. However there is hitherto no such function which can be expressed in a simple form. This is a famous question. The purpose of thi...

We summarize the combinatorial properties of congruence generation in congruence distributive varieties which are relevant to Baker’s finite basis theorem, explain the extent to which these properties survive in congruence meet-semidistributive varieties, indicate our approach to extending Baker’s theorem to the latter varieties, and pose several problems which our approach does not answer.

Radial basis functions are well-known and successful tools for the interpolation of data in many dimensions. Several radial basis functions of compact support that give rise to nonsingular interpolation problems have been proposed, and in this paper we study a new, larger class of smooth radial functions of compact support which contains other compactly supported ones that were proposed earlier...

We describe a heuristic method for reconstructing a region in the plane from a noisy sample of points. The method uses radial basis functions with Gaussian kernels to compute a fuzzy membership function which provides an implicit approximation for the region.

Existing methods for solving Poisson's equation using basis functions can be made considerably more exible, yet simpler, by using non-orthogonal basis functions. The rst part of this paper describes how such basis sets can be constructed. The second part gives explicit formulas (up to quadratures and matrix inversions) for basis functions being spherical harmonics times radial functions; two ba...

This paper describes an optimized training approach of radial basis function (RBF) classification by reducing a proposed classification-oriented error function. The training approach consists of two distinguished properties. First, radial basis functions, feature weights, and output weights can be updated iteratively; Second, it intrinsically distinguishes different learning contribution from t...