查询词典 invariance theorem

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。

It is shown through performance experiments that this algorithm is of scale invariance and rotation invariance to some extent.

实验结果表明，该算法具有良好的平移、尺度、旋转不变性，证明联系数是一个有效的图像特征。

The further conditions which are given by the space-refletion invariance and the time reversal invariance are also discussed.

讨论了空间反射不变性和时间反演不变性给出的进一步的限制。

There were three major findings.(1) On the basis of the assessment of overall model fit and parameter estimates, the hypothesized second-order confirmatory factor analysis model represented an adequate fit to the sample data.(2) According to the cross-validation analysis, the second-order factorial validity of this scale was very stable.(3) This hypothesized model was invariance across these five important demographical variables, including school, gender, grade, right/left-handedness, and past experience in unintentional injury, via the testing of invariance in the multiple groups.

结果有三项主要的发现：第一、经整体暨个别的残差分析、整体模式之适配与其取代指标，以及估计参数之统计考验等结果，均指出假设此量表为二阶因素分析测量模式是相当恰当的；第二、经交互确认效度分析结果，显示此量表之二阶潜在因素结构是非常稳定；第三、经多组别不变量统计考验结果，指出此量表之二阶潜在因素结构，对於学校别、性别、年级、用手习惯，以及过去伤害经验这些社会人口变项，大致上具有因素个数、因素负荷量、因素变异数，以及测量误差变异数等不变量的特性。

By using methods of passivity and switching control of states of the linear subsystem, both stabilization of the linear subsystem and invariance of the specified region in state space can be guaranteed simultaneously. Hence, a sufficient condition for the robust invariance switching control of this class of systems was derived.

通过基于鲁棒严格无源技术和线性子系统状态反馈的切换控制来镇定线性子系统，同时保证了指定区域的正不变性，从而得到了该类系统鲁棒不变切换控制的充分条件。

The control objective is achieved by firstly using robust passivity to stabilize the linear subsystem, and then with resort to switching control technique to guarantee the invariance of the specified region in state space simultaneously. Hence, a sufficient condition for the robust invariance switching control of this class of systems is derived.

控制思想是首先通过鲁棒无源性技术来镇定线性子系统，再借助切换控制技术得到系统轨迹对于指定区域的正不变性，从而得到了该类系统鲁棒不变切换控制的充分条件。

In spherical polar coordinates, DRSC potential have supersymmetry and shape invariance for θ and r coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schrodinger equation with double ring-shaped Coulomb potential are presented. The normalized angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained.

本文研究了双环形Coulomb势Schrdinger方程的束缚态精确解，所采用的方法是首先对双环形Coulomb势的Schrdinger方程在球坐标系中进行分离变量，得到相应的角向方程和径向方程；证明双环形Coulomb势在角向和径向具有超对称性和形不变性；根据超对称性和形不变性的性质，获得了角动量量子化条件和束缚态的能谱方程，并将归一化角向波函数用Jacobi多项式表示，将归一化径向波函数用Laguerre多项式函数表示。

Secondly, a commentarial review of this field is given to show the last evolution of it. Although many kinds of useful projective invariance have been derived so far, the sorts of 3D object to which they could be used are still very limited. So there are some needs to develop more powerful invariance for the 3D object recognition. Finally, in the last part of this paper, the future researches in this field are proposed.

0引言 众所周知，3D物体识别是计算机视觉研究的一项重要内容，由于其在军事、工业等社会诸多行业中具有潜在的、巨大的应用价值，半个世纪以来受到各国视觉研究者的广泛关注，并提出了众多的理论和方法川，其中基于几何不变性的3D物体识别方法有助于消除由于观察视角、摄像机参数等

By using these convergence theorems,it presents the Silverman-To-eplitz regular theorem and Samaratunga-Sember theorem on the Abelian topologicalgroups,the Vitali-Hahn-Saks theorem on algebras and the weak sequentially completenesstheorem of 〓-dual spaces of sequence spaces,etc.

这是抽象分析中的两个基本定理。作为应用，给出了Abelian拓扑群上的Silverman-Toeplitz正则性定理、Samaratunga-Sember定理、代数上的Vitali-Hahn-Saks定理，以及序列空间的〓对偶空间之弱序列完备性定理等。

Theorem 1 constructs a set of universal measure zero using continuous extension; Theorem 2 verifies absolutely continuous function being of good property under some condition; Theorem 3 reveals some relation between real function and meager.

定理1 主要运用了连续延拓构造了一个泛测度零集；定理2 证明绝对连续函数在一定条件下具有良好的性质；定理3 揭示了实函数与第一纲集的某种关系。

Finally it offers the analysis of the fault-tolerance system as well as its test verification.

这样，运行于空间环境中的系统的设计目标就是在保证系统实时性

However, it is still difficult to find out the real reason of the increase of the keratinized gingiva during the orthodontic extrusion whether it is due to the proliferation of the gingival tissue or to its elastic nature, that is because the proliferation of the fibroblasts as well as the connective tissue changes in volume and the intra-fibers spaces were all immeasurable in most of the studies.

然而，仍然难以找到真正的原因增加的角化牙龈在正畸挤压它是否是由于扩散的牙龈组织或其弹性性质，这是因为增殖的成纤维细胞以及作为结缔组织的变化量和内部纤维空格都是不可估量的，大多数的研究。