In this paper, the optimization of quantizer’s segment threshold is done. The quantizer is designed on the basis of approximative spline functions. Coefficients on which we form approximative spline functions are calculated by minimization mean square error (MSE). For coefficients determined in this way, spline functions by which optimal compressor function is approximated are obtained. For the...

A number of criteria exist to select the penalty in penalized spline regression, but the selection of the number of spline basis functions has received much less attention in the literature. We propose to use a maximum likelihood-based criterion to select the number of basis functions in penalized spline regression. The criterion is easy to apply and we describe its theoretical and practical pr...

A 3D T-mesh is basically a partition of a cuboid such that every part is a smaller cuboid. In this paper we define the spline spaces over 3D T-meshes, which would play an important role in adaptive and dynamic implicit surface reconstruction from unorganized point clouds, and present a dimension formula about the spline space over a special kind of T-mesh, i.e., 3D hierarchical T-mesh. The form...

A prescription for constructing dictionaries for cardinal spline spaces on a compact interval is provided. It is proved that such spaces can be spanned by dictionaries which are built by translating a prototype B-spline function of fixed support into the knots of the required cardinal spline space. This implies that cardinal spline spaces on a compact interval can be spanned by dictionaries of ...

Splines and multiresolution are two independent concepts, which – considered together – yield a vast variety of bases for image processing and image analysis. The idea of a multiresolution analysis is to construct a ladder of nested spaces that operate as some sort of mathematical looking glass. It allows to separate coarse parts in a signal or in an image from the details of various sizes. Spl...

Glossary 5 Introduction 6 Definition of the Subject 7 Various Spline Spaces 8 The B-form Representation of Spline Functions 9 Dimension of Multivariate Spline Spaces 10 Approximation Power of Spline Spaces 11 Construction of Finite Elements 12 and Macro-Elements 13 Multivariate Splines for Scattered Data Fitting 14 Multivariate Splines for Numerical Solution 15 of Partial Differential Equations...