基于空间透视不变量的摄象机标定方法

GEOMETRIC INVARIANTS BASED CAMERA CALIBRATION

本文给出了一种以空间不变量的数据来计算摄象机外部参数的方法．空间透视不变量是指在几何变换中如投影或改变观察点时保持不变的形状描述．由于它可以得到一个相对于外界来讲独立的物体景物的特征描述，故可以很广泛的应用到计算机视觉等方面．摄象机标定是确定摄象机摄取的２Ｄ图象信息及其３Ｄ实际景物的信息之间的变换关系，它包括内部参数和外部参数两个部分．内部参数表征的是摄象机的内部特征和光学特征参数，包括图象中心（Ｃｘ，Ｃｙ）坐标、图象尺度因子Ｓｘ、有效的焦距长度ｆ和透镜的畸变失真系数Ｋ；外部参数表示的是摄象机的位置和方向在世界坐标中的坐标参数，它包括平移矩阵Ｔ和旋转矩阵Ｒ３×３，一般情况下可以写成一个扩展矩阵［ＲＴ］３×４．本文基于空间透视不变量的计算数据，给出了一种标定摄象机外部参数的方法，实验结果表明该方法具有很强的鲁棒性．

A new approach to camera calibration based on geometric invariants is proposed. Geometric invariants are shape descriptors that remain unchanged under geometric transformations such as projection or viewpoint change. They are widely used in computer vision because they can charaterize a object which is independent of external factors. Camera calibration is the problem of determining the relationship between the 2D image a camera perceives and the 3D information of the imaged object, including the extrinsic parameters and the intrinsic parameters. The intrinsic parameters characterize the inherent properties of the camera optics, including the focal length, the image center, the image scaling factor and the lens distortion coefficients; the extrinsic parameters of a camera indicate the position and the orientation of the camera with respect to a world coordinate system. In this paper, we propose a new method for computing the extrinsic parameters basing on the results of geometric invariants. Experimental results show that this method is simpler and more robust to noise.