This paper presents a new multiscale curvature-based shape representation technique with application to curve data compression using B-spline wavelets. The evolution of the curve is implemented in the B-spline scale-space, which enjoys a number of advantages over the classical Gaussian scale-space, for instance, the availability of fast algorithms. The B-spline wavelet transforms are used to ef...

This paper presents a new multiscale curvaturebased shape representation technique with application to curve data compression using B-spline wavelets. The evolution of the curve is implemented in the B-spline scale-space, which enjoys a number of advantages over the classical Gaussian scale-space, for instance, the availability of fast algorithms. The B-spline wavelet transforms are used to eff...

This paper is concerned with the description of an algorithm for generating the B-nets of box splines and an algorithm based on subdivision of these B-nets for graphically displaying spline surfaces on a three-or four-directional mesh. The combination of these two algorithms is shown to compare favorably over the other existing algorithms for this purpose. 0 1 x1. Introduction It is well known ...

In this paper we first revisit a classical problem of computing variational splines. We propose to compute local variational splines in the sense that they are interpolatory splines which minimize the energy norm over a subinterval. We shall show that the error between local and global variational spline interpolants decays exponentially over a fixed subinterval as the support of the local vari...

This paper is concerned with the spline interpolation of functions with a boundary layer component. It is shown that polynomial formulas of spline interpolation for such functions lead to significant errors. We proposed nonpolynomial spline interpolation formulas, fitted to a boundary layer component. Nonsmooth and smooth on whole interval interpolants are constructed. The accuracy of construct...

Abstract Given gridded cell-average data of a smooth multivariate function, we present constructive explicit procedure for generating high-order global approximation the function. One contribution is derivation approximations to point-values function directly from data. The second development univariate B-spline-based quasi-interpolation operators using Multivariate spline are obtained by tenso...

Here presented is the interrelationship between Eulerian polynomials, Eulerian fractions and Euler-Frobenius polynomials, Euler-Frobenius fractions, Bsplines, respectively. The properties of Eulerian polynomials and Eulerian fractions and their applications in B-spline interpolation and evaluation of Riemann zeta function values at odd integers are given. The relation between Eulerian numbers a...

Simple geometric proofs are given for the total positivity of the B-spline collocation matrix and the variation diminishing property of the B-spline representation of a spline.

X n Given a sequence of points { i}i=l on a regular quadric S: X T A X = 0 C E d, d >1 3, we study the problem of constructing a G I rational quadratic spline curve lying on 5' that interpolates { X ~ } ~ j . It is shown that a necessary condition for the existence of a nontrivial interpolant is ( X ~ A X 2 ) ( X T i A X i + I ) > 0, i = 1 , 2 , . . . , n 1. Also considered is a Hermite interpo...