交比

The cross ratio he called anharmonic ratio.

他把交比叫作非调和比。

Since cross ratio is an invariant of the group of all Mbius transformations,and a Mbius transformation maps a circle into another circle, it is convenient to represent a segment of circular arc with a parametric complex rational function.

利用Mbius变换的保交比性质和保圆性质，给出了一种快速、简便地生成平面上的一段精确圆弧曲线的新方法。

In this paper, cross ratios of the four collinear points and five coplanar points were analyzed first, then some affecting factors were concluded, and some constraints were proposed on constructing model-based object recognition system.

首先对共线4点和共面5点构成的交比不变量的稳定性进行了分析，得出了影响稳定性的因素，然后提出在构造目标识别系统的模型时应注意的约束条件，实验表明：在这些条件下构造模型的抗噪声能力大大提高。

To discover intrinsic properties of a scene by using the computation of cross ratio invariance has been one of the most hot research areas in computer vision fields.

交比是和射影变换有关的一个基本不变量，利用交比不变性的计算来揭示场景的本质特征也是计算机视觉研究的一个热点。

Based on the former chapter, one method based on fundamental matrix and crossrate is proposed in this chapter to render novel image considering the character of fundamental and cross-rate invariant in the perspective project, which utilized the correspondence relationship between the given two images and projective invariant between images to render novel image.

该方法通过将基本矩阵的稳定性求解问题转化为一个有条件的极值求解问题，结合遗传算法良好的全局寻优特点，将该方法很好地引入到基本矩阵的求解中，并取得了良好的实验结果。（5）第五章在上一章的基础上，综合基本矩阵和透视投影中的交比不变性的特点，提出了一种基于基本矩阵和交比的生成新图象的方法，这种利用已知两幅图象之间存在的匹配关系和新图象和已知图象存在的透视不变量，来生成新图象。

Two pairs of vanishing points of orthogonal directions from each image are obtained by using the concept of cross ratio and harmonic conjugate in projective geometry and the orthogonal property of the two diagonals on a square. All intrinsic parameters are calculated linearly after capturing the template from at least three shooting angles. Errors of edge detection and line fitting are avoided because the method does not require image matching.

充分利用了射影几何中交比和调和共轭的知识以及正方形模板对角线相互垂直的性质，根据一幅模板图像可以得到两组相互正交的消失点连线，在至少三个不同方向拍摄的图像上线性求解出摄像机的所有内部参数。

In this dissertation, applications of cross-ratio in shadow generation and identity verification are investigated.

在本篇论文中，我们应用交比发展了产生线光源影子的方法，以及利用交比进行脸孔辨识的系统。

That is, for every circle the cross-ratio of its four intersection points with neighboring circles is equal to a negative constant.

给出交比为负常数的SG圆模式的定义，即其中每一个圆与它相邻圆的四个交点的交比等于一个给定的负常数。

We also proved that it is relatively easier to obtain addition lines in the selfing population than to obtain double-monosomic additions.

根据BC2F3代自交品系来源的不同，初步认为由双单体附加自交比单体附加自交选择异附加系的效率高。

As the contour of a wheel rim is easier to detect than the contour of a wheel, and the contour of a wheel rim and the contour of a wheel are approximately concentric circles on the same plane, we first detect the contour of the wheel rim, the center of the wheel rim and the contacting point between the wheel and the ground, then we detect the contour of the wheel via the invariance of cross ratio under projective transformation.

由于提取钢圈轮廓比提取车轮橡胶轮廓容易，而且钢圈轮廓和车轮轮廓可以近似看作同一平面上的两个同心圆，所以在本文中，我们首先提取钢圈轮廓、钢圈圆心和车轮与地面接触点在图像上的投影，然后利用射影变换保持交比不变的性质求出车轮轮廓。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷