Development of additive manufacturing in last decade greatly improves tissue engineering. During the manufacturing of porous scaffold, simplified but functionally equivalent models are getting focused for practically reasons. Scaffolds can be classified into regular porous scaffolds and irregular porous scaffolds. Several methodologies are developed to design these scaffolds. A novel method is ...

The problem of interpolation of scattered data on the unit sphere has many applications in geodesy and earth science in which the sphere is taken as a model for the earth. Spherical radial basis functions provide a convenient tool to construct the interpolant. However, the underlying linear systems tend to be ill-conditioned. In this paper, we present an additive Schwarz preconditioner to accel...

A new family of interpolatory stationary subdivision schemes is introduced by using radial basis function interpolation. This work extends earlier studies on interpolatory stationary subdivision schemes in two aspects. First, it provides a wider class of interpolatory schemes; each 2L-point interpolatory scheme has the freedom of choosing a degree (say, m) of polynomial reproducing. Depending o...

We present a method for animating 3D models of animals from existing live video sequences such as wild life documentaries. Videos are first segmented into binary images on which principal component analysis (PCA) is applied. The time-varying coordinates of the images in the PCA space are then used to generate 3D animation. This is done through interpolation with radial basis functions of 3D pos...

Recent technical advances in electromagnetic (EM) tracking have facilitated the use of EM sensors in surgical interventions. Due to the susceptibility to distortions of the EM field when placed in close proximity to metallic objects, they require calibration in situ to maintain an acceptable degree of accuracy. In this paper, a freehand method is presented for calibrating electromagnetic positi...

Until now, only non-oscillatory radial basis functions (RBFs) have been considered in the literature. It has recently been shown that a certain family of oscillatory RBFs based on J Bessel functions give rise to non singular interpolation problems and seem to be the only class of functions not to diverge in the limit of flat basis functions for any node layout. This paper proves another interes...

The method of approximate particular solutions (MAPS) has been recently developed to solve various types of partial differential equations. In the MAPS, radial basis functions play an important role in approximating the forcing term. Coupled with the concept of particular solutions and radial basis functions, a simple and effective numerical method for solving a large class of partial different...

We present a fast direct algorithm for computing symmetric factorizations, i.e. A = WWT , of symmetric positive-definite hierarchical matrices with weak-admissibility conditions. The computational cost for the symmetric factorization scales as O(n log n) for hierarchically off-diagonal low-rank matrices. Once this factorization is obtained, the cost for inversion, application, and determinant c...

A novel concept for estimating smooth functions by selection techniques based on boosting is developed. It is suggested to put radial basis functions with different spreads at each knot and to do selection and estimation simultaneously by a componentwise boosting algorithm. The methodology of various other smoothing and knot selection procedures (e.g. stepwise selection) is summarized. They are...