曲面平滑的自适应几何扩散

1.引 言 本文的目的是用求解偏微分方程（PDE）的方法来消除离散三角形曲面的噪声,所使用的方程是热传导方程到曲面的推广.热传导方程应用于图像处理已有二十余年的历史,有关参考文献相当丰富（见[1,11,12,19]）.众所周知,对于给定的初始图像ρ0,热传导方程　　在τ时刻的解与用Gauss滤波器Gσ（x）=　（当标准差σ=2τ,时）和ρ0作卷积的结果相同.容易看出Gρ和ρ0的卷积运算相当于对ρ0做加权平均,当标准离差σ变大时,该加权平均在一个较大的范围实现,这解释了热传导方程的滤波作用.近来热传导方程已推广到空间曲面[4,5]以及高维空间中的二维流形（见[3]）,对     

A Generalization of the Mean Size Formula of Wavelet Packets in Lp

The purpose of this paper is to investigate the mean size formula of wavelet packets in Lp for 0 〈 p ≤ ∞. We generalize a mean size formula of wavelet packets given in terms of the p-norm joint spectral radius and we also give some asymptotic formulas for the Lp-norm or quasi-norm on the subdivision trees. All results will be given in the general setting,     

Polynomial Reproduction in Subdivision

We study conditions on the matrix mask of a vector subdivision scheme ensuring that certain polynomial input vectors yield polynomial output again. The conditions are in terms of a recurrence formula for the vectors which determine the structure of polynomial input with this property. From this recurrence, we obtain an algorithm to determine polynomial input of maximal degree. The algorithm can be used in the design of masks to achieve a high order of polynomial reproduction.     

Regularity of multiwavelets

The motivation for this paper is an interesting observation made by Plonka concerning the factorization of the matrix symbol associated with the refinement equation for B-splines with equally spaced multiple knots at integers and subsequent developments which relate this factorization to regularity of refinable vector fields over the real line. Our intention is to contribute to this train of ideas which is partially driven by the importance of refinable vector fields in the construction of multiwavelets. The use of subdivision methods will allow us to consider the problem almost entirely in the spatial domain and leads to exact characterizations of differentiability and Hölder regularity in arbitrary L _p spaces. We first study the close relationship between vector subdivision schemes and a generalized notion of scalar subdivision schemes based on bi-infinite matrices with certain periodicity properties. For the latter type of subdivision scheme we will derive criteria for convergence and Hölder regularity of the limit function, which mainly depend on the spectral radius of a bi-infinite matrix induced by the subdivision operator, and we will show that differentiability of the limit functions can be characterized by factorization properties of the subdivision operator. By switching back to vector subdivision we will transfer these results to refinable vectors fields and obtain characterizations of regularity by factorization and spectral radius properties of the symbol associated to the refinable vector field. Finally, we point out how multiwavelets can be generated from orthonormal refinable bi-infinite vector fields.     

On polynomial symbols for subdivision schemes

Given a dilation matrix A :ℤ^d→ℤ^d, and G a complete set of coset representatives of 2π(A ^−Tℤ^d/ℤ^d), we consider polynomial solutions M to the equation ∑ _g∈G M(ξ+g)=1 with the constraints that M≥0 and M(0)=1. We prove that the full class of such functions can be generated using polynomial convolution kernels. Trigonometric polynomials of this type play an important role as symbols for interpolatory subdivision schemes. For isotropic dilation matrices, we use the method introduced to construct symbols for interpolatory subdivision schemes satisfying Strang–Fix conditions of arbitrary order. Research partially supported by the Danish Technical Science Foundation, Grant No. 9701481, and by the Danish SNF-PDE network.     

Effect of the subdivision strategy on convergence and efficiency of some global optimization algorithms

We investigate subdivision strategies that can improve the convergence and efficiency of some branch and bound algorithms of global optimization. In particular, a general class of so called weakly exhaustive simplicial subdivision processes is introduced that subsumes all previously known radial exhaustive processes. This result provides the basis for constructing flexible subdivision strategies that can be adapted to take advantage of various problem conditions.     

编码器动态检测系统高实时性高精度角度基准设计

在编码器动态特性检测中,角度基准的快速反应和精度直接影响着动态特性检测装置的准确性。为实现角度基准的快速响应,提高基准编码器的测角精度,本文设计了高精度快速细分角度基准编码器。首先,通过对目前角度基准不足对编码器动态特性检测影响的分析,得出动态检测精度主要受基准编码器的数据处理延时影响。其次,通过对基准编码器结构、细分电路、处理电路等的设计,完成了23位高实时性角度基准编码器的制作。最后,为提高检测精度,利用RBF神经网络对角度基准进行误差补偿。所设计的角度基准编码器分辨率达到0.15",并且可以在10 r/s速度时,保证逐分辨率输出。经过测量,补偿前基准编码器的精度为1.30",补偿后的基准编码器误差峰峰值不超过2.5",精度优于0.6"。高精度、高实时性角度基准编码器的研制,提高了编码器动态特性检测系统的检测精度,为研究编码器动态特性提供了基础。     

The independence of initial vectors in the subdivision schemes

Starting with an initial vector λ = (λ(κ))κ∈z ∈ ep(Z), the subdivision scheme generates asequence (Snaλ)∞n=1 of vectors by the subdivision operator Saλ(κ) = ∑λ(j)a(k - 2j), k ∈ Z. j∈zSubdivision schemes play an important role in computer graphics and wavelet analysis. It is very interesting tounderstand under what conditions the sequence (Snaλ)∞n=1 converges to an Lp-function in an appropriate sense.This problem has been studied extensively. In this paper we show that the subdivision scheme converges forany initial vector in ep(Z) provided that it does for one nonzero vector in that space. Moreover, if the integertranslates of the refinable function are stable, the smoothness of the limit function corresponding to the vectorλ is also independent of λ.     

Convergence rates of cascade algorithms

We consider solutions of a refinement equation of the form

where is a finitely supported sequence called the refinement mask. Associated with the mask is a linear operator defined on by . This paper is concerned with the convergence of the cascade algorithm associated with , i.e., the convergence of the sequence in the -norm.

Our main result gives estimates for the convergence rate of the cascade algorithm. Let be the normalized solution of the above refinement equation with the dilation matrix being isotropic. Suppose lies in the Lipschitz space , where 0$"> and . Under appropriate conditions on , the following estimate will be established:

where and is a constant. In particular, we confirm a conjecture of A. Ron on convergence of cascade algorithms.

     

Curvature integrability of subdivision surfaces

We examine the smoothness properties of the principal curvatures of subdivision surfaces near irregular points. In particular we give an estimate of their L _p class based on the eigenstructure of the subdivision matrix. As a result we can show that the popular Loop and Catmull–Clark schemes (among many others) have square integrable principal curvatures enabling their use as shape functions in FEM treatments of the thin shell equations.