Some new results on univariate interpolation by weak Cheby-shev spaces, using conditions of Schoenberg-Whitney type and the concept of almost interpolation sets, are given. x1. Introduction Let U denote a nite-dimensional subspace of real-valued functions deened on some set K. We are interested in describing those conngurations T = dimU jT = s: T is called an interpolation set (I-set) w.r.t. U....

The qualitative and quantitative comparison of preand postoperative image data is an important possibility to validate computer assisted surgical procedures. Due to deformations after surgery a non-rigid registration scheme is a prerequisite for a precise comparison. Interactive landmark-based schemes are a suitable approach. Incorporation of a priori knowledge about the anatomical structures t...

The paper develops a rational bi-cubic G2 (curvature continuous) analogue of the non-uniform polynomial C2 cubic B-spline paradigm. These rational splines can exactly reproduce parts of multiple basic shapes, such as cyclides and quadrics, in one by default smoothly-connected structure. The versatility of this new tool for processing exact geometry is illustrated by conceptual design from basic...

In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We obtain the exact uniform approximation error on classes of functions with moduli of continuity bounded above by certain majorants. c ⃝ 2014 Elsevier Inc. All rights reserved. MSC: 41A05; 41A10; 41A28

The integration of shape grammars within a generative system is thought to have good potential to support design applications in the art and cultural domains. Based on a shape decomposing method, two-level generative shape grammars are developed within the application of Zhuang ethnic embroidery design. In our approach, free B-spline curves are used to derive initial design concepts together wi...

This paper first describes an algorithm that finds the approximate finite impulse response (FIR) inverse of an FIR filter by minimizing the inversion (or reconstruction) error constrained to zero-bias. The generalization of the inverse filtering problem in the two channel case is the design of perfect reconstruction filter banks that use critical sampling. These considerations lead to the deriv...

We present a generalization of the commutation formula to irregular subdivision schemes and wavelets. We show how, in the noninterpolating case, the divided differences need to be adapted to the subdivision scheme. As an example we include the construction of an entire family of biorthogonal compactly supported irregular knot B-spline wavelets starting from Lagrangian interpolation.

A new multiresolution decomposition scheme based on constrained B-Spline decimation/interpolation is proposed. The proposed decomposition algorithm is tested on greyscale and color image compression, and the results are compared with DCT based compression. Dithering and postprocessing are applied to the compressed images to deal with artifacts at low bit rate compression.