We present a novel 2D/3D deformable registration method, called Registration Efficiency and Accuracy through Learning Metric on Shape (REALMS), that can support real-time Image-Guided Radiation Therapy (IGRT ). The method consists of two stages: planning-time learning and registration. In the planning-time learning, it firstly models the patient’s 3D deformation space from the patient’s time-va...

During the registration procedure, redundant data are usually generated. We present two different approaches for data reduction. The first method is based on recursive volumetric division for determining locally saturated regions. The second method uses an interpolating surface obtained through Radial Basis Functions. Some numerical tests regarding data reduction and quality preservation are de...

An effective technique for identifying nonlinear discrete-time systems using raisedcosine radial basis function (RBF) networks is presented. Raised-cosine RBF networks are bounded-input bounded-output stable systems, and the network output is a continuously differentiable function of the past input and the past output. The evaluation speed of an n-dimensional raised-cosine RBF network is high b...

We prove that the well known Lp-error estimates for radial basis function interpolation are optimal provided that the underlying function space is the native Hilbert space of the basis function. Furthermore we give upper bounds for the approximation orders in case of best L1-approximation using radial basis functions.

We discuss the problem of constrained approximation and interpolation of scattered data by using compactly supported radial basis functions, subjected to the constraint of preserving positivity. The approaches are presented to compute positive approximation and interpolation by solving the two corresponding optimization problems. Numerical experiments are provided to illustrate that the propose...

This paper presents a new approach for Radial Basis Function (RBF) interpolation on a sphere. Standard approaches use the Euclidian metrics for the distance calculation of two points. However, for interpolation on a sphere, more naturally is computation of the distance as the shortest distance over the surface on a sphere, i.e. spherical distance of two points is more natural for interpolation ...

The accuracy of interpolation by a radial basis function φ is usually very satisfactory provided that the approximant f is reasonably smooth. However, for functions which have smoothness below a certain order associated with the basis function φ, no approximation power has yet been established. Hence, the purpose of this study is to discuss the Lp-approximation order (1 ≤ p ≤ ∞) of interpolatio...

Error estimates for radial basis function interpolation are usually based on the concept of native Hilbert spaces. We investigate how good the well known L p-error estimates are by giving lower bounds. Furthermore we study the process of best L 1-approximation and provide upper bounds for the approximation orders in this case.