代数几何的

An implicit Curve reconstruction method is proposed which represents the curve with all algebraic tensor-product B-spline,and minimizes the tension ofthe B-spline and the approximate geometric distance between the curve and the point set.

提出一种以代数张量积样条曲线作为几何表示形式，基于近似几何误差和薄板能量极小化的隐式重构模型。

Chapter 1 briefs the relation between invariance and computer vision and summarizes the research and application of invariance in computer vision. Chapter 2 first derives the transformations of three camera models, then makes the correpondences between the models and three typical geometrical transformation groups by analysing the transformations respectively. The correspondences supply the theoretical basis for applying geometrical invariants to resolve the problems of computer vision. In Chapter 3, we describe the geometrical invariant theory and prove some geometrical invariants of coplanar points, lines or conics by algebraic method. In order to use the invariants of conic pairs to describe general 2D shapes, we discuss the perspectively invariant representation of planar curves using conies in detail. A system consisted of two TMS320C25 and based on moment invariants is introduced in Chapter 5. The system can recognize more than 30 different shapes of object model or more than 10 plane models with similar shape in real time.

第一章简述了不变性与计算机视觉的关系，以及计算机视觉中的不变性研究和应用概况；第二章推导了计算机视觉中常用三种投影模型的变换关系，通过对这三种变换关系的分析，分别建立了这三种投影模型和几何学中的三种变换群之间的一一对应关系，为几何不变性在计算机视觉中的应用提供了理论基础；在第三章中，我们介绍了几何不变性的理论，并且用代数方法证明了共面点、直线、二次曲线的几何不变量和射影不变量；为了把二次曲线的不变量用于一般二维形状描述，在第四章中我们详细地讨论了用二次曲线实现一般平面曲线的透视不变性表示的方法；第五章介绍了用两片TMS320C25构成的、基于不变矩形特征的运动目标实时识别系统。

This paper mainly study the relations between some algebraic properties of Roe algebras and the coarse geometry of metric spaces, and its applications to the reduced crossed product C-algebras and the coarse Baum-Connes conjecture.

本文主要研究这类C~*-代数的某些性质与底空间几何之间的联系及其在交叉积C~*-代数和粗Baum-Connes猜测中的应用。第一章研究交叉积C~*-代数的Schwartz型谱不变子代数。

A calculating method for finding the induced geodesic torsion was developed by using differential geometry and other mathematics tools.

为了分析线接触共轭齿面的诱导短程挠率，并清楚地诠释有关公式及计算推导的过程，运用微分几何、向量代数、线性代数等数学工具，寻找了一种计算诱导短程挠率的方法。

Conformal Geometric Algebra is a new tool for geometric representation and computation.

共形几何代数是一个新的几何表示和计算工具。

conformal geometric algebra is a kind of new geometric representation and geometric computation tool, and it has properties of geometric intuitiveness, compactness, high efficiency, unification and elegance.

摘 要：共形几何代数是一种新的几何表示和几何计算工具，它具有直观、简洁、高效、统一、雅致等特性。

After introducing the basic knowledge of geometric algebra such as outer product,inner product and geometric product,this paper focused on the CGA description and computation with graphic reflection,rotation,translation,rigid body motion and screw motion,and gave the experimental demonstrations.

在简单介绍外积、内积和几何积等基本概念之后，重点论述了共形几何代数在图形反射、旋转、平移等变换和刚体运动、螺旋运动等方面的描述和计算方法，并给出了实验示例。

This problem of planar parametric polynomial curve of degree 3 had been discussed perfectly many years ago, making use of invariant of affine transformation.

关于三次代数多项式参数曲线的这一问题早已解决，然而所用的几何不变量方法对于非代数曲线失效。

In the Mathematics Test, three subscores are based on six content areas: pre-algebra, elementary algebra, intermediate algebra, coordinate geometry, plane geometry, and trigonometry.

数学测试部分，共六个方面的内容组成了三个部分的得分：算术、初级代数、中级代数、几何坐标、平面几何、三角形。

In chapter 1, similarity and perturbations of nest subalgebras of factor von Neumann algebras are studied. A similarity theorem is given (see Theorem 1. 2. 3), and it is shown that similar nests in a factor von Neumann algebra are close.

第一章研究因子von Neumann代数中套的相似性和套子代数的摄动，获到一个相似定理（定理1.2.3），其几何意义是：因子von Neumann代数中相似的套聚拢在一起并可向外扩展。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。