几何的

Besides, we find a new geometric quantity in adiabatic process, and we made some further researches on it.

我们发现了绝热近似过程新的几何性质，并对此几何性质作进一步讨论。

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。

The models based on geometrical cell and boundary constraints are introduced to describe free-form surfaces.

建立了以几何元胞和边界条件为特征的自由曲线曲面几何形状描述方法。

By comparison between equations of motion of geometrical opticsand that of classical statistical mechanics,we find that there should be an analogy between GO and CSM instead of GO and classical mechanics.

本文将几何光学和经典统计力学的运动方程相比较之后，指出几何光学应与经典统计力学具有相似性，而不是与经典力学具有相似性。

Theory of packing and covering is an important field in combinatorial and discrete geometry.

填充和覆盖理论是组合几何与离散几何中的一个重要分支。

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。

Because projective invariance between 3D object and its 2D image could overcome the problem caused by viewpoint, calibration and feature correspondence effectively, it has been attracting more and more attention and research efforts over the last 20 years. For more comprehension to this field, firstly, the main research contents of the invariance-based 3D object recognition is discussed, including geometry frames and their invariance, as well as the way to apply the geometric invariance.

为使人们了解该领域的研究现状，以对该领域的研究有所启发，首先讨论了基于几何不变性的3D物体识别方法的研究内容，包括研究的几何框架和其不变性以及几何不变性在3D物体识别中的主要应用；其次，总结性地评述了该领域的研究现状；最后，提出了研究的发展方向。

Through analyzing the research result of four series studies, we conclude that the description about toplogical perception that is prior to the perception of local featural properties does not fit to the visual perception, and the figure visual perception is not affected by the different geometrical levels, and the relative perceptual salience of different geometrical properities is not consistent with the hierarchy of geometries according to Kleins Erlangen Program.

四个系列研究的研究结果表明，陈霖的拓扑性质知觉理论对视觉系统具有早期抽取图形拓扑性质的描述欠妥当，图形视知觉的加工过程并不受图形几何变换功能层次的制约，不同几何性质的相对知觉显著性与克莱茵的埃尔朗根纲领所描述的几何层次不一致。

A new 3D human face model is put forward in this paper after some characters of the human face and the muscle tissues on the face are researched and some actions of the facial expression are analyzed. In this model we divide the whole face into some parts according to its structure. To each part, we apply the principle of elastomer metamorphosing to our face model, so a specific face model can be easily gotten by modifying a common face model.

本文在分析和总结了前人工作的基础上，深入研究了人脸的生理特征、面部肌肉组织结构，分析了人脸面部表情的基本动作，提出了将人脸整体分解为若干个小块的三维人脸几何模型，并根据力学中的弹性体形变原理，将弹性体的形变应用于上述基于面分块的三维人脸几何模型，使特定人脸几何模型的建立变得简单、效率高。

In the third chapter,We study some geometric properties and spectral propertiesof the Jacobi operator on a solvable extension G of Heisenberg groups H.In the firstsection,we give the definition of G and some fundamental geometric properties on G.Inthe second section,we discuss the Integrability of certain subbundles and the geometricstructure of the induced foliations in case of integrability.In the third section,we studythe spectral properties of the Jacobi operator of G.

可解李群与类对称空间亦密切相关，Damcek-Ricci空间即是广义Heisenberg的一可解扩张李群，在第三章中，我们构造且研究了Heisenberg群的一可解扩张李群G的几何性质，第一节讨论了G的曲率，李指数映射，整体坐标等基本几何性质；第二章研究了TG的某些子丛的可积性及可积时诱导叶片的几何结构；第三节给出了G的Jacobi算子的特征值和相应的特征子空间。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。