并行单型规范分片线性函数极坐标数字预失真器

介绍了一种并行的基于单型规范分片线性（SCPWL）函数的极坐标数字预失真器模型。首先根据分片线性拟合原理引入绝对值型的单型规范分片线性函数,建立模型解析方程并推导出模型参数的最小二乘解,然后根据模型特点设计了数字预失真器的并行实现架构,并对模型架构的工作顺序和参数提取过程进行了介绍。仿真结果表明SCPWL极坐标预失真器远远优于传统的功率回退线性化技术,且与常用的复多项式预失真器相比较,尤其是在过饱和非线性失真情况下,其线性补偿能力要优于后者。     

Sharp error bounds for piecewise linear interpolation of planar curves

Curves are commonly drawn by piecewise linear interpolation, but to worry about the error is rather seldom. In the present paper we give a strong mathematical error analysis for curve segments with bounded curvature and length. Though the result seems very clear, the proof turned out to be unexpectedly hard, comparable to that of the famous four vertex theorem.     

Curvature continuous interpolation of curve meshes

This paper presents a method for local construction of a curvature continuous (GC²) piecewise polynomial surface which interpolates a given rectangular curvature continuous quintic curve mesh. First, we create a C² quintic basic curve mesh, which interpolates the same grid points, preserves the tangent slopes and curvatures but not derivative vectors at the grid points. After estimating twist and higher order mixed partial derivatives for each grid point, we generate locally the so-called C² biquintic basic patches, which serve to compute the first and second order cross-derivative functions of the final interpolation surface. In order to match the tangents and second order derivative vectors of the original boundary curves at the grid points, these basic patches are reparametrized by 5 × 3 and 3 × 5 functions, which lead to vector-valued first and second order cross-derivative functions of degrees 7 and 9 of the final surface patches, and eventually lead to a GC² piecewise polynomial surface of degree 9 × 9, which is then converted to a GC² Bézier composite surface. By arranging the surface patches in a chess-board fashion, the degrees of the final surface patches can be 9 × 5 and 5 × 9. An example for the construction of a GC² ship hull, together with its color-coded curvature maps, is given to illustrate the method. This method is attractive because the final surface has a much lower degree than other similar methods, it allows flexible local modification of the original curve mesh and local editing of the interpolation surface, and it is easily integrated into state-of-the-art geometric modeling systems.     

Surface interpolation of meshes by geometric subdivision

Subdivision surfaces are generated by repeated approximation or interpolation from initial control meshes. In this paper, two new non-linear subdivision schemes, face based subdivision scheme and normal based subdivision scheme, are introduced for surface interpolation of triangular meshes. With a given coarse mesh more and more details will be added to the surface when the triangles have been split and refined. Because every intermediate mesh is a piecewise linear approximation to the final surface, the first type of subdivision scheme computes each new vertex as the solution to a least square fitting problem of selected old vertices and their neighboring triangles. Consequently, sharp features as well as smooth regions are generated automatically. For the second type of subdivision, the displacement for every new vertex is computed as a combination of normals at old vertices. By computing the vertex normals adaptively, the limit surface is G¹ smooth. The fairness of the interpolating surface can be improved further by using the neighboring faces. Because the new vertices by either of these two schemes depend on the local geometry, but not the vertex valences, the interpolating surface inherits the shape of the initial control mesh more fairly and naturally. Several examples are also presented to show the efficiency of the new algorithms.     

Flexible G1 interpolation of quad meshes

Transforming an arbitrary mesh into a smooth G¹ surface has been the subject of intensive research works. To get a visual pleasing shape without any imperfection even in the presence of extraordinary mesh vertices is still a challenging problem in particular when interpolation of the mesh vertices is required. We present a new local method, which produces visually smooth shapes while solving the interpolation problem. It consists of combining low degree biquartic Bézier patches with minimum number of pieces per mesh face, assembled together with G¹-continuity. All surface control points are given explicitly. The construction is local and free of zero-twists. We further show that within this economical class of surfaces it is however possible to derive a sufficient number of meaningful degrees of freedom so that standard optimization techniques result in high quality surfaces.     

Controllability of piecewise linear systems

The paper deals with a discontinuous control system that consists of two finite-dimensional linear systems; the first describes the motion in a given half-space, the second in the complementary half-space. Necessary and sufficient conditions for local controllability are obtained.     

基于梯度的快速图像插值算法

为解决传统插值算法效果不佳而新发展的边缘方向插值算法计算量大的问题,提出了一种基于梯度检测边缘的快速图像插值算法。该算法通过在原图像每一个3×3邻域内计算二阶梯度,检测边缘是否存在:若存在边缘,则计算一阶梯度判断边缘强弱并自适应得到权值因子,然后进行带权的线性插值;若不存在边缘,则在此邻域内进行双线性插值。实验结果表明,此算法不仅使插值后图像具备整体清晰性和边缘平滑性,有效保持了图像的主观视觉质量,而且相比现有同等效果的插值算法,运算时间至少能降低20%,尤其适用于嵌入式设备图像放大的应用。     

Implementation of piecewise linear fuzzy quantities

Fuzzy information in expert systems and in fuzzy database systems is often represented by means of piecewise linear fuzzy quantities. In this article we describe an implementation of piecewise linear fuzzy quantities and how to perform fuzzy operations on them. This article can be seen as a natural continuation of Baekeland and Kerre [“Operations on piecewise linear fuzzy quantities: A theoretical approach,” Fuzzy Sets Syst., submitted], in which the mathematical properties of piecewise linear fuzzy quantities are investigated. © 1995 John Wiley & Sons, Inc.     

基于LQR和模糊插值的五级倒立摆控制

首先给出五级倒立摆的数学模型并验证了它的可控性;然后在分析与倒立摆系统稳定性有关因素的基础上,结合LQR理论构造出一种非对角型的权重矩阵,并给出了设定该矩阵中各元素的方法;最后设计出一个简单的基于二元分片插值函数的模糊控制器,成功地实现了具有定位功能的五级倒立摆的控制．仿真结果表明该方法是有效的．     

线性拟合联合参数法在图像配准中的应用

提出了一种基于仿透视函数模型和相机响应参数模型共同作用下图像配准算法。首先估算角点匹配以加强匹配精度和速度;由受约束条件控制的分段线性函数近似相机的非线性响应函数,建立起全局参数模型;应用最小二乘法,得到较为精确的参数初始值;最后应用迭代算法降低配准误差。实验结果表明,该算法很好地解决了曝光差异图像配准问题,提高了迭代速度和精确度。     

基于分段插值技术的车削加工有限元精密预测

针对车削加工中存在的复杂曲面粗糙度和数值模拟精度不高的问题,基于慢刀伺服方式对复杂情况下的车削曲面执行粗糙度分析以及数值模拟。首先,利用车削加工的环曲面理论和线性分段插值原理,进行车削加工的有限元二次软件开发,可实现对复杂情况下的车削曲面加工刀具的动态模拟;其次,基于物理分离原则、Coulomb摩擦力模型以及Johnson Cook材料本构模型,构建复杂情况下基于有限元模拟的车削曲面仿真加工模型;最后,基于所提模型对车削曲面的粗糙度进行预测分析。实验结果显示,所提模型的实验测试值与模拟值之间的误差相对率为5.06%,具有很好的预测效果,验证了所提模型预测方法的有效性。     

梯度优化的有理函数图像插值

目的 对图像纹理区域的细节保持一直以来是图像插值技术的一个难题,为此提出了一种梯度优化的有理函数图像插值算法。方法 首先,构造了一种新的含有可调参数的双变量有理插值函数,随着参数的不同取值,该函数具有不同的表达形式,它是多项式模型和有理模型的有机统一体;其次,根据图像的区域特征,利用等值线方法将图像自适应地划分为纹理区域和平滑区域,纹理区域采用有理模型插值,平滑区域采用多项式模型插值;最后,根据各向同性Sobel算子计算插值单元的图像梯度,确定纹理方向,不同纹理方向的插值单元用相应的权重对中心点进行优化。结果 从客观数据、主观效果、时间复杂度3个方面对重建图像进行评价,客观数据包括峰值信噪比（PSNR）和结构相似性（SSIM）,从实验结果可以看出,本文算法的PSNR平均提高了0.14~1.50 dB,SSIM平均提高了0.005~0.097。从主观效果来看,本文算法的重建图像的纹理细节更加丰富,边缘结构更加清晰,从时间复杂度来看,本文算法的平均运行时间是3.77 s,分别比DFDF（directional filtering and data fusion）、NEDI（new edge-directed interpolation）、RSAI（robust soft-decision adaptive interpolation）、Lee''s、NARM（nonlocal autoregressive model）算法快了3.28倍、5.26倍、53.28倍、43.53倍、418.54倍。特别地,对于Baboon、Barbara、Metal这类纹理细节丰富的图像,本文算法在峰值信噪比和结构相似性上较对比算法有突出优势,主观效果有明显提高。结论 基于构造的双变量有理插值模型,本文提出了一个梯度优化的有理函数图像插值算法,实验结果表明,该算法在图像纹理细节和边缘结构保持方面具有良好的视觉效果,有效提高了插值图像质量,且时间复杂度较低。     

A parametrization of piecewise linear Lyapunov functions via linear programming

In this paper, we present a parametrization of piecewise linear (PWL) Lyapunov functions. To this end, we consider the class of all continuous PWL functions defined over a simplicial partition. We take advantage of a recently developed high level canonical PWL (HL CPWL) representation, which expresses the PWL function in a compact and closed form. Once the parametrization problem is properly stated, we focus on its application to the stabiilty analysis of dynamic systems. We consider uncertain non-linear systems and extend the sector condition obtained by Ohta et al. In addition, we propose a method of selecting an optimal candidate. One of the main advantages of this approach is that the parametrization and choice of the Lyapunov candidate, as well as the stability analysis, result in linear programming problems.     

Stability analysis of piecewise discrete-time linear systems

Presents a stability analysis method for piecewise discrete-time linear systems based on a piecewise smooth Lyapunov function. It is shown that the stability of the system can be established if a piecewise Lyapunov function can be constructed and, moreover, the function can be obtained by solving a set of linear matrix inequalities (LMIs) that is numerically feasible with commercially available software.     

Moment-preserving piecewise linear approximations of signals andimages

Approximation techniques are an important aspect of digital signal and image processing. Many lossy signal compression procedures such as the Fourier transform and discrete cosine transform are based on the idea that a signal can be represented by a small number of transformed coefficients which are an approximation of the original. Existing approximation techniques approach this problem in either a time/spatial domain or transform domain, but not both. This paper briefly reviews various existing approximation techniques. Subsequently, we present a new strategy to obtain an approximation fˆ(x) of f(x) in such a way that it is reasonably close to the original function in the domain of the variable x, and exactly preserves some properties of the transformed domain. In this particular case, the properties of the transformed values that are preserved are geometric moments of the original function. The proposed technique has been applied to single-variable functions, two-dimensional planar curves, and two-dimensional images, and the results obtained are demonstrative     

Some results on linear rational trigonometric interpolation

We present here formulae for calculating the p^th derivative of a linear rational trigonometric interpolant written in barycentric form. We give sets of interpolating points for which the interpolant converges exponentially towards the interpolated function.     

分段线性脉冲神经元模型的簇放电分析

应用一种二维分段线性脉冲神经元模型的简单计算特性,对其簇放电特性进行了详细研究。发现该模型表现出强迫和内禀两类簇放电模式,并分析了内禀簇放电的产生机理及分岔现象。在实验中,应用该模型对一类具有簇放电特性的皮层神经元进行了模拟。