Given a finite subset Ξ ⊂ R and data |Ξ , the surface spline interpolant to the data |Ξ is a function s which minimizes a certain seminorm subject to the interpolation conditions |Ξ = |Ξ . It is known that surface spline interpolation is stable on the Sobolev space W in the sense that ‖s‖L∞(Ω) ≤ const ‖f‖Wm , where m is an integer parameter which specifies the surface spline. In this note we sh...

Parametric spline models are used extensively in representing and coding planar curves. For many applications, it is desirable to be able to derive the spline representation from a set of sample points of the planar shape. The problem we address in this paper is to nd a cubic spline model to optimally approximate a given planar shape. We solve this problem by treating the control points which d...

OBJECTIVE Improving and validating sleep scoring algorithms for actigraphs enhances their usefulness in clinical and research applications. The MTI® device (ActiGraph, Pensacola, FL) had not been previously validated for sleep. The aims were to (1) compare the accuracy of sleep metrics obtained via wrist- and hip-mounted MTI® actigraphs with polysomnographic (PSG) recordings in a sample that in...

Battle-Lemari e's wavelet has a nice generalization in the bivariate setting. This generalization is called bivariate box spline wavelets. The magnitude of the lters associated with the bivariate box spline wavelets is shown to converge to an ideal high-pass lter when the degree of the bivariate box spline functions increases to 1. The passing and stopping bands of the ideal lter are dependent ...

The various concepts and ideas that have contributed to univariate spline theory are considered with a view to finding a suitable definition of a multivariate spline. In this way, an overview of the existing more or less complete univariate spline theory is given along with a survey of some of the high points of the current research in multivariate splines. My very first paper dealt with multiv...

Battle-Lemarié’s wavelet has a nice generalization in a bivariate setting. This generalization is called bivariate box spline wavelets. The magnitude of the filters associated with the bivariate box spline wavelets is shown to converge to an ideal high-pass filter when the degree of the bivariate box spline functions increases to `. The passing and stopping bands of the ideal filter are depende...

Splines are part of the standard toolbox for the approximation of functions and curves in Rd . Still, the problem of finding the spline that best approximates an input function or curve is ill-posed, since in general this yields a “spline” with an infinite number of segments. The problem can be regularized by adding a penalty term for the number of spline segments. We show how this idea can be ...

We establish several fundamental properties of analysis-suitable Tsplines which are important for design and analysis. First, we characterize T-spline spaces and prove that the space of smooth bicubic polynomials, defined over the extended T-mesh of an analysis-suitable T-spline, is contained in the corresponding analysis-suitable T-spline space. This is accomplished through the theory of pertu...

In this paper we present a novel approach to construct B-spline wavelets under constraints, taking advantage of the lifting scheme. Constrained B-spline wavelets allow multiresolution analysis of B-splines which fixes positions, tangents and/or high order derivatives at some user specified parameter values, thus extend the ability of B-spline wavelets: smoothing a curve while preserving user sp...

This paper deals with the application of the spline filter as an areal filter for surface metrology. A profile (2D) filter is often applied in orthogonal directions to yield an areal filter for a three-dimensional (3D) measurement. Unlike the Gaussian filter, the spline filter presents an anisotropic characteristic when used as an areal filter. This disadvantage hampers the wide application of ...