In the early 1990s BCS was involved in some image processing and detection projects arising in both natural resource and defense settings. We were convinced that thin plate spline (TPS) functions could play an important role in developing effective software for image registration and change detection, but initially we encountered some computational challenges when using TPS functions on mid-siz...

This paper is concerned with approximation properties of linear combinations of scattered translates of the thin-plate spline radial basis function | · | log | · | where the translates are taken in the unit disc D in R. We show that the Lp approximation order for this kind of approximation is 2+1/p (for sufficiently smooth functions), which matches Johnson’s upper bound and, thus, gives the sat...

We consider the problem of thin plate spline interpolation to n equally spaced points on a circle, where the number of data points is suuciently large for work of O(n 3) to be unacceptable. We develop an iterative multigrid-type method, each iteration comprising ngrid stages, and n being an integer multiple of 2 ngrid?1. We let the rst grid, V 1 , be the full set of data points, V say, and each...

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This paper presents a survey of past transformation functions for image registration and introduces a new transformation function for registration of images containing rigid as well as nonrigid regions. Included in the survey are similarity transformation, linear transformation, and nonlinear transformation. Nonlinear transformation itself includes thin-plate splines, radial basis functions, ap...

Cranial implants, especially custom made are complex, important and necessary in craniofacial fracture restoration surgery. However, the classical procedure of manual design implant is time consuming complicated. Different computer-based techniques proposed by different researchers, including CAD/CAM, mirroring, reference skull, thin plate spline radial basis functions have been used for crania...

This study presents a general approach for the multi-scale design of variable stiffness composites (VSCs). The first-level problem two-level optimisation strategy (MS2LOS) is solved to determine optimal distribution VSC properties at macroscopic scale satisfying requirements hand. In this phase, laminate modelled as an equivalent homogeneous anisotropic plate whose behaviour described in terms ...

Non-rigid registration requires a smoothness or regularization term for making the warp field regular. Standard models in use here include b-splines and thin plate splines. In this paper, we suggest a regularizer which is based on first principles, is symmetric with respect to source and destination, and fulfills a natural semi-group property for warps. We construct the regularizer from a distr...

Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data and is central to many meshless methods. For a set of N scattered sites, the standard basis for such a space utilizes N globally supported kernels; computing with it is prohibitively expensive for large N . Easil...

MRI is unique in its ability to non-invasively and selectively alter tissue magnetization, and create grid patterns on a soft, deforming body such as the heart muscle. We track motion of myocardial tag lines with energy. minimizing B-spline snakes. Oriented tag templates are first constructed by simulating the MR imaging process. The templates are subsequently correlated with the image data, gi...