从一维透视投影图恢复二维刚体运动和结构

Determining the Motion and Structure of a 2-D Rigid Object from 3 Images of 1-D Perspective Projection

研究从一维透视投影图恢复二维刚体运动和结构。证明利用 3幅一维透视投影图中最少 5组对应点可以完全得到二维刚体的旋转运动参数 ,一般情况下有 4个解。可以得到含一个未知比例因子的二维刚体平移运动参数和结构参数 ,能完全确定二维刚体的形状。

In this paper,we study the problem of determining the motion and structure of a 2-D rigid object from 3 images of its 1-D perspective projection. It is proved that the 2-D rotational motion parameters of a rigid object can be determined by using 5 corresponding points from 3 images of its 1-D perspective projection at least,and there are 4 solutions in general. The 2-D translation motion parameters with a scale factor can be obtained. The 2-D structure with a scale factor of the rigid object can be determined. The closed-form solutions are obtained on the 2-D rotational motion parameters,and the 2-D translation motion parameters and the 2-D structure with a scale factor of a rigid object. Some simulating experiments show that our method is simple and effective.