A subdivision collocation method for solving two point boundary value problems of order three

In this paper, we propose a method for the numerical solution of self adjoint singularly perturbed third order boundary value problems in which the highest order derivative is multiplied by a small parameter $\varepsilon$. In this method, first we introduce the derivatives of two scale relations satisfied by the subdivision schemes. After that we use these derivatives to construct the subdivision collocation method for the numerical solution of singularly perturbed boundary value problems. Convergence of the subdivision collocation method is also discussed. Numerical examples are presented to illustrate the proposed method.     

Algebraic Properties of Subdivision Operators with Matrix Mask and Their Applications

Subdivision operators play an important role in wavelet analysis. This paper studies the algebraic properties of subdivision operators with matrix mask, especially their action on polynomial sequences and on some of their invariant subspaces. As an application, we characterize, under a mild condition, the approximation order provided by refinable vectors in terms of the eigenvalues and eigenvectors of polynomial sequences of the associated subdivision operator. Moreover, some necessary conditions, in terms of nondegeneracy and simplicity of eigenvalues of a matrix related to the subdivision operator for the refinable vector to be smooth are given. The main results are new even in the scalar case     

一类与BB型对偶剖分相关的广义差分格式

豆引言考虑二阶椭圆方程的边值问题〔,a.an.a.＆t-。^D一[六（a于）十十…于）」一八x,y）,（x,y）En,（1.1）J“山一而“av”-av”。。、一、。。,\一·。·---,l。。、____（.2）LU一0,（J,y）E厂一go,其中D是多边形区域,厂一JD为0的边界,f（x,y）为o上的已知函数/三L‘（0）,系数a—a（xJ）充分光滑,且存在常数7>O,使得以X,y）>/,对任意（X,y）ED.文[1],[2]已系统地研究了求解口.1）,（l.2）的广义差分法.广义差分法的基本思想是对求解区域0作三角形剖分TA及其对偶剖分T;,然后构造T^上的试探函数空间U。（有限元空间）和耳上的…     

Nanoscale deformation measurement by using the hybrid method of gray-level and holographic interferometry

This study extends the use of holographic interferometry to measure the nanoscale out-of-plane displacement with high surface resolution. It is noted that if the deformation is less than half of the optical wavelength, it is hard to find an obvious fringe pattern. Under such a situation, in general, the phase shift method is used. However, it needs to take more than 3 images for phase shifting and phase reconstruction In this paper, a more simple hybrid method of gray-level and holographic interferometry is used to extract fringe skeletons, in which it just needs to take one or two images for the normal deformation measurement directly, even if there exists no obvious fringe pattern. The displacement field with high surface resolution can also be obtained. The proposed method yielded a theoretical precision of 0.15 nm for out-of-plane displacement with a monochromatic CCD camera of 10-bit gray scale (1024 gray scales) sensitivity and microscale surface resolution for millimeter scale object with 640×480 pixels image resolution by an He–Ne LASER (632.8 nm wavelength) light source. The gray-level method is proposed to calculate the non-obvious interferometry fringe by traditional holographic interferometry hologram, and the result showed that this method works for this purpose.     

利用三次样条插值提高自准直仪的准确度

为了提高自准直仪的准确度,利用三次样条插值法对CCD像元进行细分,并利用直线边缘拟合法检测图像边缘.实验采取独立的测量手段,将自准直仪的实际转角和算法计算得到的角度值进行比较,分析其准确度.实验结果表明,该方法能明显提高自准直仪的准确度,准确度达到0.1角秒.     

消除数字光刻像素栅格衍射影响的研究

提出用优化成像系统设计参量的方法有效消除基于数字微镜阵列的栅格结构及其衍射对微结构成像质量的影响.模拟结果表明,当照明光源的波长为0.365 μm,系统的数值孔径为0.3左右,缩小倍率为10～20×时,栅格像的可见度在0.1以下,DMD的栅格结构对成像质量的影响大幅降低;对微透镜的成像分析发现,合理的成像系统结构参量能有效地减少栅格的影响.如果结合DMD显示图形的可编程特点,优化图形的结构或灰度,则能在像面获得较理想的曝光量分布,达到快速加工二维和三维微结构的目的.实验结果证实了优化系统参量可有效消除DMD栅格的影响.     

基于FPGA的准直测角系统

为了提高线阵CCD准直测角系统的精度、速度、集成度,以及可靠性,提出一种集成于单片FPGA、光积分时间可自适应调节的片上准直测角系统。以FPGA作为系统处理核心,利用高斯滤波算法对CCD输出信号进行数字滤波,利用边缘自动检测算法获得图像的像元级边界,在此基础上应用多项式插值算法对图像边缘位置进行亚像元细分,最终计算出失准角。利用VHDL语言以及MAX+plus II软件完成了系统设计。系统仿真和实验表明,所设计的片上系统具有高精度、高集成度、高可靠性的特点。     

Smoothness of Nonlinear Median-Interpolation Subdivision

We give a refined analysis of the Hölder regularity for the limit functions arising from a nonlinear pyramid algorithm for robust removal of non-Gaussian noise proposed by Donoho and Yu [6,7,17]. The synthesis part of this algorithm can be interpreted as a nonlinear triadic subdivision scheme where new points are inserted based on local quadratic polynomial median interpolation and imputation. We introduce the analogon of the Donoho–Yu scheme for dyadic refinement, and show that its limit functions are in C for >log₄(128/31)=1.0229.... In the triadic case, we improve the lower bound of >log₂(135/121)=0.0997... previously obtained in [6] to >log₃(135/53)=0.8510.... These lower bounds are relatively close to the anticipated upper bounds of log₂(16/7)=1.1982... in the dyadic, respectivly 1 in the triadic cases, and have been obtained by deriving recursive inequalities for the norm of second rather than first order differences of the sequences arising in the subdivision process.     

路图P3(G)的色数

设G是一个图,G的路图P3(G)的顶点集是G中所有三个顶点的路P3, 当G中的两个P3路形成P4路或C3圈时,在P3(G)中它们所代表的两个顶点相邻. 在这篇文章中,我们得到对于一个无三角形的图G, χ(P3(G))≤β(G),其中β(G)表G的点覆盖数. 对于顶点数至少为3的连通图G,χ(P3(G))≤2当且仅当G是二部图, 并且χ(P3(G))=1当且仅当 G是星图. 对于K4的剖分图G,2≤χ(P3(G))≤3. 对于系列平行图和外可平面图G,χ(P3(G))≤3.     

Probability analysis of position errors using uncooled IR stereo camera

This paper analyzes the random phenomenon of 3D positions when tracking moving objects using the infrared (IR) stereo camera, and proposes a probability model of 3D positions. The proposed probability model integrates two random error phenomena. One is the pixel quantization error which is caused by discrete sampling pixels in estimating disparity values of stereo camera. The other is the timing jitter which results from the irregular acquisition-timing in the uncooled IR cameras. This paper derives a probability distribution function by combining jitter model with pixel quantization error. To verify the proposed probability function of 3D positions, the experiments on tracking fast moving objects are performed using IR stereo camera system. The 3D depths of moving object are estimated by stereo matching, and be compared with the ground truth obtained by laser scanner system. According to the experiments, the 3D depths of moving object are estimated within the statistically reliable range which is well derived by the proposed probability distribution. It is expected that the proposed probability model of 3D positions can be applied to various IR stereo camera systems that deal with fast moving objects.