We provide an overview of spline and wavelet techniques with an emphasis on applications in pattern recognition. The presentation is divided in three parts. In the first one, we argue that the spline representation is ideally suited for all processing tasks that require a continuous model of the underlying signals or images. We show that most forms of spline fitting (interpolation, least-square...

Bivariate splines with various degrees are considered in this paper. A matrix form of the extended smoothness conditions for these splines is presented. Upon this form, the multivariate spline method for numerical solution of partial differential equations (PDEs) proposed by Awanou, Lai, and Wenston in [The multivariate spline method for scattered data fitting and numerical solutions of partial...

We propose a construction of a Hermite cubic spline-wavelet basis on the interval and hypercube. The basis is adapted to homogeneous Dirichlet boundary conditions. The wavelets are orthogonal to piecewise polynomials of degree at most seven on a uniform grid. Therefore, the wavelets have eight vanishing moments, and the matrices arising from discretization of differential equations with coeffic...

An effective texture feature is very important for accurate image retrieval with less computational complexity. The spline wavelets based texture features, mean and standard deviation of the magnitudes of the subband coefficients in the wavelet frame decomposition, are proposed for image retrieval. The experiments are performed on a database of 1792 texture images to check the retrieval perform...

There are many applications where the shape of objects needs to be encoded, such as CAD, 3D modelling, signature encoding [9], as well as region oriented video coding techniques [1], where the shape information is described by a binary mask having the same values for all the pixels inside the shape. The binary mask indicates the region(s) in which the texture of the object needs to be coded [7]...

This paper presents an algorithm based on the wavelet decomposition, for feature extraction from the ECG signal and recognition of four types of Ventricular Arrhythmias. A set of Discrete Wavelet Transform (DWT) coefficients, which contain the maximum information about the arrhythmia, was selected from the wavelet decomposition. The algorithm is applied on the ECG registrations from the MIT-BIH...

In this article, we utilize spline wavelets to establish an adaptive multilevel numerical scheme for timedependent convection-dominated diffusion problems within the frameworks of Galerkin formulation and Eulerian-Lagrangian localized adjoint methods (ELLAM). In particular, we shall use linear Chui-Quak semiorthogonal wavelets, which have explicit expressions and compact supports. Therefore, bo...

While it is well known that the mth order 5-spline Nm(x) with integer knots generates a multiresolution analysis, • • • C V_x c V0 C • ■ • , with the with order of approximation, we prove that i//(x) := Ú1mJ¡{2x 1), where L2m(x) denotes the (2m)th order fundamental cardinal interpolatory spline, generates the orthogonal complementary wavelet spaces Wk . Note that for m = 1 , when the ß-spline N...

This article is a survey of some recent developments which concern two multilevel approximation schemes: (a) Nonlinear n-term approximation from piecewise polynomials generated by anisotropic dyadic partitions in R, and (b) Nonlinear n-term approximation from sequences of hierarchical spline bases generated by multilevel triangulations in R. A construction is given of sequences of bases consist...