用偏微分方程构造过渡面

用偏微分方程的构造曲面是一种新兴的方法，本文借若干算例说明如何用偏微分方程构造两已知曲面之间的过渡面。论文着重讨论用四阶方程构造一阶连续的过渡面。     

加权算术平均与几何平均关系式的新证法

利用函数极小点的性质,得到了若干个正数的加权算术平均与几何平均关系式的新证法     

Isometric Piecewise Polynomial Curves

The main preoccupations of research in computer-aided geometric design have been on shape-specification techniques for polynomial curves and surfaces, and on the continuity between segments or patches. When modelling with such techniques, curves and surfaces can be compressed or expanded arbitrarily. There has been relatively little work on interacting with direct spatial properties of curves and surfaces, such as their arc length or surface area. As a first step, we derive families of parametric piecewise polynomial curves that satisfy various positional and tangential constraints together with arc-length constraints. We call these curves isometric curves. A space curve is defined as a sequence of polynomial curve segments, each of which is defined by the familiar Hermite or Bézier constraints for cubic polynomials; as well, each segment is constrained to have a specified arc length. We demonstrate that this class of curves is attractive and stable. We also describe the numerical techniques used that are sufficient for achieving real time interaction with these curves on low-end workstations.     

基于实时地形校正的InSAR图像匹配算法

针对侧视雷达/可见光图像匹配制导系统中由于雷达图像地形畸变引起的误匹配问题,提出了一种基于干涉合成孔径雷达（InSAR）的实时地形校正图像匹配算法。该算法以侧视雷达成像几何构象为基础,利用InSAR获取的实时地形数据对获取的SAR景象数据进行实时几何校正,生成无畸变的SAR景象数据,然后利用校正后的SAR景象数据与提前安装的可见光基准数据进行基于去均值归一化互相关模板的图像匹配。实验结果表明,通过实时地形校正,该景象匹配算法在复杂地形区域的匹配概率和匹配精度都大大优于传统SAR景象匹配算法,有效地提高了SAR图像匹配制导技术的适用性。     

抗几何失真的视频Hashing算法研究

文中提出了一种基于视频灰度直方图形状的Hashing算法,能有效抵抗各种常见的几何失真和视频处理操作.算法的鲁棒性原理如下:1)由于直方图的形状与像素位置无关,故基于直方图的视频Hashing算法能有效抵抗各种常见的几何攻击;2)由于在计算Hashing前对视频帧进行了平滑预处理,故算法对加噪攻击、模糊滤波、有损压缩等处理操作有很好的鲁棒性;3)由于计算Hashing前在时间轴上进行了低通滤波预处理,故算法能抵抗帧率变化、帧丢失等时域同步攻击.实验结果表明,所提出的Hashing算法有良好的唯一性和鲁棒性能.     

THz-TDS signal analysis and substance identification via the conformal split

A terahertz time-domain spectroscopy(THz-TDS)imaging system can obtain high-dimensional signals with substance fingerprint information.By introducing geometric algebra,a novel signal analysis approach to THz-TDS signals is developed based on an optical physical mechanism.Using this approach,signals are represented with vectors in the high-dimensional real vector space.Geometric distribution properties and algebraic relationships of THz-TDS signals are deduced.It is proved that every complex refractive index of substances relates to a unique 2-blade,the vectors corresponding to the samples of the same substance are collinear and belong to the intrinsic 2-blade of the substance.When decomposed through the conformal split with respect to a 2-blade,THz-TDS signals of high dimensionality can be related to vectors in a 2-dimensional subspace.Based on the conformal split properties we deduced,two criteria for substance identification on the basis of THz-TDS signals are proposed.Accordingly,a novel substance identification method via the conformal split is presented.In the method,the 2-blade related to each "known" substance is calculated with two vectors corresponding to THz-TDS signals measured from samples of the substance but with dierent thicknesses.Using the conformal split with respect to those 2-blades,an identified vector corresponding to a THz-TDS signal is linearly related to the vector in a 2-dimensional subspace.The substance of a sample can be identified using criteria on the projected vectors in the subspaces.This method can contribute to accurate classification and identification.Finally,two experiments are presented that show the feasibility and accuracy of this method.     

V型立体纸雕的几何理论与算法的研究

立体书是一种独特的纸张艺术形式,有着精细的几何结构.针对一类特殊的V型立体纸雕进行了系统性的研究,给出了V型立体纸雕可实现性的充分条件,使其可以只借助2张支撑面的力量进行打开和关闭,同时在这个过程中所有的面片都保持刚性并且相互不产生自交.基于这些充分条件,文中分别实现了一个计算机辅助交互V型纸雕设计工具,以及一个基于体方法的自动生成算法.     

基于模型修正技术的模拟集成电路几何规划优化方法

为了兼顾模拟集成电路设计优化的求解精度和计算效率,提出一种基于正项式模型修正技术的几何规划优化方法.首先将模拟集成电路的设计目标与约束简化为正项式模型,然后在采用几何规划方法迭代优化的过程中利用晶体管级SPICE仿真不断修正这一正项式模型.实例表明,与传统基于公式的优化方法和基于仿真的优化方法相比,该方法能够在尽量保证计算效率和全局最优解的前提下使优化精度满足晶体管级SPICE仿真的要求.     

多站虚拟量测变换均值无源定位算法

在多站无源均值定位算法中,为了解决部分传感器间夹角过大或过小所导致的定位精度下降问题,提出一种基于虚拟量测变换的多传感器管理无源定位算法.首先在全局坐标系下分析了传感器间夹角对误差几何稀释度(GDOP)的影响,进而得到双站获得较好定位精度的夹角约束关系;其次针对不满足该约束关系的传感器组合提出一种虚拟量测变换定位算法,通过空间管理的方法达到对传感器的优化布站,并结合算法的实施步骤对其原理及特点进行了理论分析,尤其对变换前后的交点精度进行了比较.仿真结果表明虚拟量测算法的定位精度要明显优于均值算法,进而说明该算法的有效性及传感器管理在多站无源定位中的重要作用.     

基于边缘检测的保特征的图像缩放算法

针对Seam Carving算法在实现图像缩放的过程中,对图像边缘几何特征造成破坏的现象,提出一种基于边缘检测的改进Seam Carving算法。首先在Seam Carving算法计算低能量线的同时引入图像边缘检测,其次确定低能量线与边缘的交点,进而提升交点邻域的能量,分散过于集中的低能量线。仿真实验结果表明,该算法能够有效减少Seam Carving算法缩放图像后产生的畸变,很好地保持了图像的重要几何特征。