中文摘要：

基于摄像机的正交运动对摄像机进行标定是基于主动视觉摄像机标定的一种重要方法．一般来说，5组这样的正交运动就可以线性标定摄像机的5个内参数．然而，关于这5组摄像机运动应满足什么条件才可以保证所产生的5个线性约束方程是独立的，文献中对这个问题至今没有定论．一种流行的猜测是只要这5组正交运动下的平移向量任意3个不共面，则对应的5个摄像机内参数约束方程必然独立．本文对这个问题进行了进一步讨论，汪明了当5组正交运动中其中的3组构成一个三正交运动时，此时尽管构成5组正交运动的7个平移向量没有任意3个共面，但产生的5个约束方程却可能不独立，并给出了一个不独立的具体例子．

英文摘要：

The orthogonal-motion based camera calibration is an important approach in active-vision based calibration. In general, each pair of orthogonal movings of a camera can generate a linear constraint on the camera＇s five intrinsic parameters, and five such motion pairs are sufficient to linearly calibrate the camera. However an open question is that under what conditions of such five pairs of orthogonal movings the resulting constraints can be independent. A common view is that if no three motions out of the five motion pairs are coplanar, the corresponding five constraints can be independent. In the paper, this problem is further investigated. In particular, we show that if three sets out of the five orthogonal motion sets happen to form a threeorthogonal motion set （i.e., three motions are mutually orthogonal）, then even if no three motions among the total seven ones are coplanar, the resulting five constraints are not necessarily independent, and a concrete non-independent example is also provided.