交比投影不变原理在结构光平面拟合中的应用

文中简介了机器视觉研究中的一种编码结构光投影系统，在它的编码模板上具有很多的编码特征点，它们在模板的水平和垂直方向上分别构成多组共线的点，经投影后，这些点分别形成了纵向和横向的若干光平面，而这些光平面相对于投影系统三维坐标系的位置关系需要事先标定。在标定过程中需要若干组位于各光平面上的三维空间特征点，将这些点与光平面共同成像于CCD像平面上，再从图像中提取出它们的图像坐标，由共线投影不变性可知，三维特征点所在的直线与光平面所在的直线在CCD像平面上相交于若干点，然后利用代数射影几何中的交比不变原理就可将结构光平面与三维空间点建立对应关系，从而标定出各光平面的参数。文中给出了详细的实验步骤，列出了一些数据及图表，并对实验结果进行了说明。

The principle of cross-ratio and its application in fitting structured light planes

The paper introduces a kind of projector with encoding structured light used in machine vision. The projector has a pattern on which are many groups of encoded interest points. These points are collinear along the horizontal and vertical directions respectively. After they are projected into 3D space,they can be fitted to longitudinal and latitudinal spatial light planes. Our purpose is to discover three parameters for each plane up to the projector coordinate frame. To get high precision calibration result,many groups of accurate 3D points coordinates must be known as datum mark. In order to get a lot of strict 3D points,we make use of a one-dimensional worktable and a glass flat on which there are numerous standard circles. During the test,the glass flat will move along the orbit of the worktable and keep perpendicular to moving orientation. It is necessary that two positions at least of the flat on the worktable must be sure. In this way,some explicit coordinates of spatial points may be established. Afterwards,all of the 3D points and light planes are captured by a CCD camera. There are many cross points intersected by the lines in CCD image and these points are lying not only on the light planes,but also on the feature lines in 3D space. Then,the principle of cross-ratio in algebraic projective geometry is described. We can find out some 3D points lying on the light plane. Therefore,by fitting these points,the equations of spatial planes will be presented. Subsequently,the detailed experiment steps are introduced. Some important datum and figures are also offered to verify the efficiency and accuracy of our method.