A new multivariate approximation scheme to scattered data on arbitrary bounded domains in Rd is developed. The approximant is selected from a space spanned (essentially) by corresponding translates of the ‘shifted’ thin-plate spline (‘essentially,’ since the space is augmented by certain functions in order to eliminate boundary effects). This scheme applies to noisy data as well as to noiseless...

Landmark-based thin-plate spline image registration is one of the most commonly used methods for non-rigid medical image registration and anatomical shape analysis. It is well known that this method does not produce a unique correspondence between two images away from the landmark locations because interchanging the role of source and target landmarks does not produce forward and reverse transf...

This thesis investigates the employment of different deformable registration techniques to register pre-operative magnetic resonance and inter-operative ultrasound images during prostate biopsy. Accurate registration ensures appropriate biopsy sampling of malignant prostate tissues and reduces the rate of re-biopsies. Therefore, we provide comparisons and experimental results for some landmarka...

The thin plate spline (TPS) is an e ective tool for modeling coordinate transformations that has been applied successfully in several computer vision applications. Unfortunately the solution requires the inversion of a p p matrix, where p is the number of points in the data set, thus making it impractical for large scale applications. As it turns out, a surprisingly good approximate solution is...

We study a vectorial approximation problem based on thin plate splines with tension involving two positive parameters: one for the control of the oscillations and the other for the control of the divergence and rotational components of the field. The existence and uniqueness of the solution are proved and the solution is explicitly given. As special cases, we study the limit problems as the par...

This work aims to develop a system for predicting age progression in children’s faces from a small exemplar-image set, which is a critical task to assist in the search for missing children. The proposed method consists a facial component extraction module, a facial component distance measurement module, and a face synthesis module. It is developed based on the assumption that two similar facial...