摄像机自标定的线性理论与算法

文中提出一种新的摄像机线性自标定的算法和理论。与文献中已有的方法相比，该文方法的主要优点是对摄像机的运动要求不苛刻，如不要求摄像机的运动为正交运动。该方法的关键步骤是确定无穷远平面的单应性矩阵（Homography)。文中从理论上严格证明了下述结论：摄像机作两组运动参数未知的运动M1＝{（R1，t^11)，(R1，t^12)},M2={(R2,t^21),(R2,t^22)},若下述两个条件满足：（1）T1＝{t^11,t^12},T2={t^21,t^22}是两个线性无关组（即本组内的两个平移向量线性无关）；（2）R1，R2的旋转轴不同，则可线性地唯一确定摄像机的内参矩阵和运动参数。另外，在四参数摄像机模型下，严格证明了一组运动可线性地唯一确定摄像机的内参数矩阵和运动参数。模拟实验和实际图像实验验证了本文方法的正确性和可行性。

A New Theory and Algorithm of Linear Camera Self Calibration

Active vision based camera calibration is one of the major research directions in 3D computer vision. A new theory and algorithm of linear camera calibration is proposed in this paper. Compared with the related techniques reported in the literature, the main advantage of our method is that it is less stringent to the camera's motion, for example, it does not require the camera to undertake orthogonal motions which are difficult to be done without special hardware support. Our method can be easily done with a hand-held camera. The key step in our new method is to determine linearly the homography of the plane at infinity. In this paper, we prove rigorously the following conclusion: Assume the camera undertakes two such sets of motions with unknown parameters M 1={(R 1,t 11),(R 1,t 12)} and M 2={(R 2,t 21),(R 2,t 22)}, and if the following two conditions are satisfied, then the camera's 5 intrinsic parameters, two rotations matrices R 1, R 2, as well as the directions of the four translation vectors can be linearly and uniquely determined: (1) t 11 and t 12 are linearly independent, and t 21 and t 22 are linearly independent; (2) The two rotation axes of the two matrices R 1,R 2 are not parallel. In addition, suppose the camera's skew parameter is zero, we prove additionally that the camera matrix and the rotation matrix can be uniquely factorized from the homography of the plane at infinity. Simulations and experiments validate our new method.