研究几何学

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 investigates the converse theorem of rectangular projection theorem in descriptive geometry,and furthermore supplements and confirms another converse theorem,If the projection of two lines intersecting vertically fo rms a rectangle on a certain projecting plane,at least one line of the two lines is parallel to the projecting plane.

通过对《画法几何学》中直角投影定理的逆定理的研究，得出："若垂直相交的两直线在某一投影面上投影成直角，则该两直线至少有一条直线平行于该投影面"的推论。

Thus, to determine the curvature of a surface it is necessary to study the geometry on this surface.

所以，要决定一个面的曲率就必须要研究它表面的几何学。

And Monge, continuing his researches, arrived at that general method of the application of geometry to the arts of construction which is now called descriptive geometry.

而蒙日继续进行研究，发现了应用几何学到建筑设计的一般方法，也就是今天所谓的画法几何。

The study of curves and surfaces forms an important part of classical differential geometry.

曲线和表面的研究形成一个古典不同几何学的重要的部分。

The paper researches the geometric base of the 3D garment CAD and the technology of digitized draping cutting of ...

本文研究了三维服装CAD的几何学基础与服装数字化立体裁剪技术。

The paper researches the geometric base of the 3D garment CAD and the technology of digitized draping cutting of garment.

本文研究了三维服装CAD的几何学基础与服装数字化立体裁剪技术。

By the use of the principles and methods of fractal geometry, the morphological character and biomass of?

应用分形几何学的原理和方法对木榄幼苗的形态特征和生物量进行了研究。

Based on image generative model, in combination with independent component analysis model and wavelet model, the basis function representation of image information as well as its key problem are studied in this thesis.

基于基函数的图像信息表示方法研究是目前图像处理技术的前沿课题，涉及到统计学、几何学、图像处理与分析、模式识别、视觉生理学等众多学科。

Remarkable is that this more than a century ago almost directly with the achievement of modern mathematics, the following methods, the general flow is concepts, algebra to geometry closely linked, he and his successors -- Beiertelami, Christopher Tuofeier, Lee Puxici developed differential Zhang volume analysis has gradually become more research on the flow geometry and analysis of an important tool.

令人赞叹的是，这一个多世纪前的成就几乎直接同现代数学中的拓扑方法、一般流形概念、代数几何学等紧密相连，他和他的接班人——贝尔特拉米、克里斯托费尔、李普希茨所发展的微分张量分析逐渐成为研究流形上几何结构和分析的一个重要工具。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。