The thin plate spline (TPS) is an effective 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. In practical applications, however, a surprisingly good a...

The aim of this study was to investigate the short- and long-term effects induced by rapid maxillary expansion (RME) on the shape of the maxillary and circummaxillary structures by means of thin-plate spline (TPS) analysis. The sample consisted of 42 patients who were compared with a control sample of 20 subjects. The treated subjects underwent Haas-type RME, followed by fixed appliance therapy...

OBJECTIVE To evaluate the long-term mandibular morphological changes induced by early treatment of class III malocclusion with rapid maxillary expansion (RME) and facial mask (FM). MATERIALS AND METHODS Twenty-five subjects [10 boys, 15 girls; mean age at T1 (start of treatment) 9.3±1.6 years] with class III disharmony were treated with RME and FM therapy followed by fixed appliances. The pat...

OBJECTIVE To investigate the craniofacial morphology in twins with cleft lip and/or palate (OFC) and localize differences, compared with noncleft (NC) twins. DESIGN Retrospective study. SETTING School of Dentistry, University of Michigan. SAMPLE Posteroanterior cephalographs of 32 pairs of dizygotic, concordant, like-sexed twins. The NC group consisted of 20 pairs of noncleft twins. The c...

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...

The use of a 3D model helps to diagnosis and accurately locate a disease where it is neither available, nor can be exactly measured in a 2D image. Therefore, highly accurate software for a 3D model of vessel is required for an accurate diagnosis of patients. We have generated standard vessel because the shape of the arterial is different for each individual vessel, where the standard vessel can...

In this study, we develop a novel nonlinear metric learning method to improve biomarker identification for Alzheimer’s Disease (AD) and Mild Cognitive Impairment (MCI). Formulated under a constrained optimization framework, the proposed method learns a smooth nonlinear feature space transformation that makes the mapped data more linearly separable for SVMs. The thin-plate spline (TPS) is chosen...

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...

Optic flow computation is one of the most fundamental problems in the realm of visual motion. In this contribution, we present a novel optic flow computation method based on a thin-plate spline representation of image brightness data. Using a spline-based description of image brightness data removes the need for presmoothing and provides an algebraic means to compute the optic flow (explicitly)...

This paper presents an algorithm for the rapid evaluation of the vector spline in two dimensions. Our work is an extension of the fast evaluation of thin-plate spline by Beatson and Newsam. The algorithm is based on the fast multipole method and has an asymptotic CPU time estimate of O(N), while the direct calculation requires an amount of work of the order O(N 2), where N is the number of the ...