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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。

If your first shipment is desirable, there will be a big consequent order.

如果贵方第一批运来的货令人满意，随后将有大批续订。

In chapter four, in order to study the micro-process of the compress of the high speed oil-free twin screw compressor, a mathematical model is built based on the conservation of mass and the first principle of thermodynamics.

第四章为了深入研究无油双螺杆压缩机的微观工作过程，以质量守恒定律和热力学第一定律为基础，建立了双螺杆工作过程的数学模型。

As to the remaining parameters, two methods are developed: first, accepting that the projection function complies with a circular function within at least a part of a given field of view, constrained by the obtained object-to-image radial mapping and a constant focal length, the best-fitting point of the optical origin is tested along the optical axis; secondly, referring to the postulation of the exclusively bilateral mapping between an imaged point and its scenic sight ray, a measuring technique is developed to survey the world coordinates which will fabricate a projecting path to the imaged points located on the imageable region of the image plane in order to directly model the projection geometries involved.

而针对其余参数本文提出两种解题方法：其一是根据『在「部分视野角范围」内，鱼眼相机的投射模型符合一典型的「圆形函数」』以标靶实体与其影像尺寸为限制条件，测试光学轴上的最佳视觉参考点、鉴定最适当的投射模型、焦距、及有效的视野角度范围。其二是根据『一视野线排他性地与对应「呈影点」一一映射』参考一呈影点来搜寻空间中对应视野线的绝对座标后，据以演绎相机内部影像形成的模型。

When the contingency table is sparse, we replace it with the first- and second-order marginals and modify the test statistic.

而当列联表有稀少情形发生时，我们将用一阶和二阶边际来取代并且修正检定统计量。

Kawasaki shares and Crystal Run in order to limit price of photovoltaic opened quickly by continuous轰开large single limit, as at the close, the exchange rate of two shares were 62.54 percent and 50.54 percent, meaning that the first Japan funds to buy half of the success of shipments.

川崎股份和水晶运行，以限制价格的迅速开放光伏连续轰开大单一的时限，在接近，两股的汇率是62.54和百分之百分之50.54，这意味着第一个日本资金购买一半成功的出货量。

In order to find the right contractor, you are going to have to ask yourself some questions first.

为了寻找合适的承包商，你是打算要问自己一些问题。

In order to discuss questions conveniently we give some basic knowledge in the first chapter of this article.

本文的第一章给出了将要讨论解法问题所需要的部分预备知识。

The Pade approximation is combined with 3-D frequency-domain finite difference (3D-FDFD) for the first time. The impact of expansion point and the order of rational function on the accuracy and the convergence radius is discussed in this dissertation.

主要包括以下内容：首次将Pade逼近运用到三维频域有限差分法中，详细讨论了Pade逼近中展开点选取、收敛半径与有理阶数的关系问题。

First a corn snake bites the prey in order to obtain a firm grip, then it quickly wraps one or more coils of its body around the victim. The snake squeezes tightly until it suffocates the prey.

首先玉米蛇利用口器牢固地咬住猎物，然后利用自身细长的身体迅速将猎物缠绕几圈，同时身体进行强而有利的收缩，直到猎物窒息而死。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。