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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。

By introducing two pairs of conjugate exponent parameters and, and using the improved Euler-Maclaurin＇s summation formula for estimating the weight coefficient, a reverse Hilbert-type inequality with a best constant factor is proved.

本文通过引入两对共轭指数参量与及应用改进的Euler-Maclaurin求和公式以估算权系数，证明了一个具有最佳常数因子的逆向Hilbert型不等式；作为应用，还给出了相应的等价式及一些特殊结果。

For a connected graph G we denote by d the number of pairs of vertices at distance k.

设G是一个连通图，我们用记号d来表示图G中所有距离为k的顶点对的个数。

The short tandem repeats is a kind of DNA sequence formed repeatedly and connectively subjected to a core unit of several base pairs.The non-interfered multi-PCR was applied with 3 loci in the same reaction system.By using the technique of denaturing polyacrylamide gel electrophoresis and silver stain,the allele frequencies distributions of 3loci:F13A01,FESFPS and vWA in 10 minority populations only resided in Yunnan Province:Bai,Dai,Achang,Jingpo,Deang,Lahu,Bulang,Hani,Pumi and Jino.A satisfactory result was obtained and some significant genetic differences were noticed in different populations.

短串联重复序列是由几个碱基对作为核心单位串联重复形成的-类DNA序列，应用3个位点在同一反应体系中进行互不干扰的多重PCR，采用高分辨力的聚丙烯酰胺凝胶电泳分离、银染法显影技术，对云南省特有的白族、傣族、阿昌族、景颇族、德昂族、拉族、布朗族、哈尼族、普米族和基诺族等10个少数民族的F13AO1、FESFPS和vWA3个位点等位基因的基因频率分布进行了调查，获得了满意的结果，在不同群体中发现一些有意义的遗传差异。

Contract bridge is a four-person card game played between two pairs of partners.

桥牌是一个4人纸牌游戏的合作伙伴对两起。

Sort-and-Incremental Algorithm Step 4: Intersections of adjacent h-plane pairs in stack form half a convex polygon.

相邻半平面的交点组成相邻半平面的交点组成半个凸多边形。半个凸多边形。

The state of freedom which is one of the most famous monuments in the world is presented by france to american.the monumentist basol designed and spent 10years on it.it made of coper,and supported by a special steel framework.before it was transported to american,it must be took a place and a basement.the place is on a island of the entrance of the Newyork harbour.when 1884,a monument at a 151 feet heigh was stand up in pairs.at the second year,i was taken to pieses and transported to american.until at the end of novemeber in 1886,the state is made up and was officely presented to american.from that moment,the great monument is a sysmbol of freedom to the people which passed through newyork habour and made his homes in american.

世界上最著名的纪念碑之一的自由女神雕像是在19世纪时由法国人民赠送给美国的。这座由雕像家奥古斯特。巴索尔地设计的巨大雕像是用10年时间雕像刻成的。这座雕像的主体是用铜制成的，由艾菲尔特制的金属框架支撑着。在雕像被运往美国之前，必须为它选好一块场地，同时必须建造一个基座。场地选在了纽约港入口处的一个鸟上。到1884年，一座高度达151英尺的雕像在巴黎竖立起来了。第二年，它被拆成若干小块，运到美国。到1886年10月底，这座雕像被重新组装起来，由巴索尔地正式赠送给美国人民。从那时起，这座伟大的纪念碑对通过纽约港进入美国定居的千百万人来说就一直是自由的象征。

Pairs will often breed soon after this temperature drop. Copulation occurs over a period of several weeks.

在这个温度下，不久后它们就会经常交配，交配将会在好几个星期里均有发生。

Sepals 3(or 5); lateral sepals free or connate, margins entire or serrate; lower sepal large, petaloid, usually navicular, funnelform, saccate, or cornute, tapering or abruptly constricted into a nectariferous spur broadly or narrowly filiform, straight, curved, incurved, or ± coiled, swollen at tip, or pointed, rarely 2-lobed, rarely without spur. Petals 5, free, upper petal flat or cucullate, small or large, often crested abaxially, lateral petals free or united in pairs. Stamens 5, alternating with petals, connate or nearly so into a ring surrounding ovary and stigma, falling off in one piece before stigma ripens; filaments short, flat with a scalelike appendage inside; anthers 2-celled, connivent, opening by a slit or pore.

萼片3(或5)；侧萼片离生或者合生，边缘全缘或者有锯齿；更低的萼片大，瓣状，通常舟形，漏斗状，囊状，或具角状突起，渐减突然或缢缩进一分泌蜜汁具距或宽狭丝状，花瓣5，离生，上面的花瓣平坦的或者兜状，雄蕊5，与花瓣互生，合生或者近合生成环而围绕子房和柱头，在柱头成熟之前完整地从上面落下；花丝短，扁平，在里面的有一鳞片状附属物；花药2室，靠合，通过一条裂缝或者孔开裂。

The prolactin gene was studied as a candidate gene for the prolificacy of Small Tail Han sheep. Single nucleotide polymorphisms of exon 1 to exon 5 of PRL gene were detected in high fecundity breeds and low fecundity breeds (Dorset, Texel and Corriedale sheep) with five pairs of primers by PCR-SSCP.

设计5对引物，采用PCR-SSCP技术检测催乳素（prolactin，PRL）基因外显子1至外显子5在高繁殖力绵羊品种和低繁殖力绵羊品种（多赛特、特克塞尔和考力代）中的单核苷酸多态性，同时研究该基因对小尾寒羊高繁殖力的影响。

The production moved off-Broadway to New York City, where she won the Joseph E. Calloway award for her performance, and was profiled in American Theater Magazine as one of ten young theater artists to watch.

生产提出过百老汇的新的纽约市，在那里她赢得了约瑟夫calloway奖，她的表现，并于异型在美国的战区杂志之一， 10战区的青年艺术家观赏。

It's a risk tradeoff, and I believe that adding test support code usually wins.

这是一个风险的权衡，我相信添加测试代码通常会占上风。