不变性

They include:collinearity--an invariance under the projective transformation group;Parallelisminvariance under the affine transformation group;the direction of angles--aninvariance under the rotation transformation group.

这些几何不变性质包括共线性——在射影变换群下的不变性；平行性——在仿射变换群下的不变性；角的方向——在欧氏平移变换群下的不变性。

Thus, when Van Til goes on to discuss God's immutability, he bases that doctrine upon the divine aseity:"Naturally God does not and cannot change since there is nothingbesides his own eternal Being upon which he depends (Mal. 3:6, James 1:7)."(DF2, 9.) IST = Introduction to Systematic Theology

IST， 206。因此，当范泰尔讨论上帝的不变性时，他将上帝不变性的教义建立在上帝的自存上﹕「显然的，上帝不会改变，祂不能改变；因为除了祂自己永恒的存有之外，祂不靠任何其他的事物。

Thus, when Van Til goes on to discuss God's immutability, he bases that doctrine upon the divine aseity:"Naturally God does not and cannot change since there is nothing besides his own eternal Being upon which he depends (Mal. 3:6, James 1:7)."(DF2, 9.) IST = Introduction to Systematic Theology

IST， 206。因此，当范泰尔讨论上帝的不变性时，他将上帝不变性的教义建立在上帝的自存上﹕「显然的，上帝不会改变，祂不能改变；因为除了祂自己永恒的存有之外，祂不靠任何其他的事物。

For Hu invariant moment having no scale invariance, two modified algorithms are proposed: one is based on the normalized central moment coming from the concept of image square and the other is based on constructing a new invariant moment.

主要贡献如下： 1。针对离散情况下Hu不变矩特征仅仅具有平移、旋转不变性，不具有比例不变性的问题，提出了两种改进算法：一种是从图像正方形概念演变而来的归一化中心矩的修正；另一种是重新构造新的不变矩特征。

In order to recognize the 2D shapes, we proposed a set of perspective invariants of a pair of coplanar conics in this paper, we suggest a perspective invariant representation of general planar curve based on ellipse, and give an algorithm using the invariants and the representation to recognize 2D shapes.

为了实现二维形状的透视投影不变性识别，本文推导出了一种共面二次曲线对的透视投影不变量，提出了一种基于椭圆的平面曲线的透视不变性表示方法，并且给出了用该不变量和不变性表示方法实现二维形状识别的算法。

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。

Invariant theorem of the operator series multiplier convergent. Using operator series multiplier convergent,AK-space of concept ,we obtained the theorem of operator series multiplier convergent invariant and the old theorem of general series multiplier convergent invariant is looked as special case.

第三章 算子级数乘数收敛的不变性：利用算子级数乘数收敛、AK—空间的定义，得到了算子级数乘数收敛的不变性定理，从而将以往的普通级数乘数收敛的不变性定理作为特殊情况。

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。

A new method based on the Maximum Effective Circle is presented using the characteristic of the palmprint that the uniqueness and the invariance to the rotation can be obtained by obtain the datum point.

因此，本文在学习掌纹识别主要技术的基础上，重点分析研究了掌纹识别技术中的不变性特征提取技术，并利用掌纹识别技术具有可通过基准点对掌纹进行定义从而获得旋转不变性和唯一性的特点，在掌纹图像的不变性特征提取方面提出了一种基于最大有效圆的定位方法。

An image can be better described by a small set of its pseudo-Zernike moments than any other types of moments such as geometric moments, Legendre moments, rotational moments, and complex moments in terms of mean-square error.

为了能使伪Zernike矩得到更广泛的应用，在详细分析伪 Zernike矩不变性的基础上，提出了伪 Zernike矩的改进方法，使改进后的伪 Zernike矩在保持旋转不变性的同时，还具有真正意义上的比例不变性，同时给出了部分的实验分析结果。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。