Radial Basis Functions (RBFs) are widely used in science, engineering and finance for constructing nonlinear models of observed data. Most applications employ activation functions from a relatively small list, including Gaussians, multi-quadrics and thin plate splines. We introduce several new candidate compactly supported RBFs for approximating functions in L (R) via overdetermined least squar...

Thin plate splines are highly useful for the approximation of functions of two variables, partly because they provide the interpolant to scattered function values that minimizes a 2-norm of second derivatives. On the other hand, they have the severe disadvantage that the explicit calculation of a thin plate spline approximation requires a log function to be evaluated m times, where m is the num...

This thesis will focus on applying smoothing splines to magnetic resonance image (MRI) analysis. Some additional work on support vector machine with a hybrid loss function will be discussed. We apply smoothing splines to both the structural MRI and functional MRI. For the structural MRI, we fit thin plate splines to overlapping blocks of the image with different configurations of knots. The opt...

A comparison of several statistical techniques common in species distribution modeling was developed during this study to evaluate and obtain the statistical model most accurate to predict the distribution of different forest tree species (in our case presence/absence data) according environmental variables. During the process we have developed maximum entropy (MaxEnt), classification and regre...

The meshless local Petrov–Galerkin (MLPG) method with radial basis functions (RBFs), and the higher order shear and normal deformable plate theory (HOSNDPT) are used to analyze static infinitesimal deformations of thick laminated composite elastic plates under different boundary conditions. Two types of RBFs, namely, multiquadrics (MQ) and thin plate splines (TPS), are employed for constructing...

We present in this paper an algorithm for surface reconstruction using thin plate splines on scattered patches or points on smooth surfaces. The algorithm is an improved version of Szeliski’s Variational Spline Fitting algorithm (SVSF). In particular, we introduce a different derivation of the discrete equations for the energy corresponding to the thin plat model. The results obtained on simula...

This study utilizes two-dimensional geometric morphometric techniques to address molar shape variation in extinct and extant prosimians using the relative orientation of selected homologous molar landmarks (paraconid, protoconid, metaconid, entoconid, hypoconid, hypoconulid, metaconulid, and the intersection of the cristid obliqua with the protolophid). Molar shape was studied using Thin-Plate ...

This study utilizes two-dimensional geometric morphometric techniques to address molar shape variation in extinct and extant prosimians using the relative orientation of selected homologous molar landmarks (paraconid, protoconid, metaconid, entoconid, hypoconid, hypoconulid, metaconulid, and the intersection of the cristid obliqua with the protolophid). Molar shape was studied using Thin-Plate ...

The advent of dynamic radiotherapy modeling and treatment techniques requires an infrastructure to weigh the merits of various interventions (breath holding, gating, tracking). The creation of treatment planning models that account for motion and deformation can allow the relative worth of such techniques to be evaluated. In order to develop a treatment planning model of a moving and deforming ...