Coordinated Science Laboratory and the Department of Electrical Engineering, University of Illinois, Urbana, IL 61801; IBM T. J. Watson Research Center, Yorktown Heights, NY 10598.
IEEE Trans Pattern Anal Mach Intell. 1984 Jan;6(1):13-27. doi: 10.1109/tpami.1984.4767471.
Two main results are established in this paper. First, we show that seven point correspondences are sufficient to uniquely determine from two perspective views the three-dimensional motion parameters (within a scale factor for the translations) of a rigid object with curved surfaces. The seven points should not be traversed by two planes with one plane containing the origin, nor by a cone containing the origin. Second, a set of ``essential parameters'' are introduced which uniquely determine the motion parameters up to a scale factor for the translations, and can be estimated by solving a set of linear equations which are derived from the correspondences of eight image points. The actual motion parameters can subsequently be determined by computing the singular value decomposition (SVD) of a 3×3 matrix containing the essential parameters.
本文主要得到两个结果。首先，我们证明了在不共面且不共线的七个点的情况下，从两个视角可以唯一地确定具有曲面的刚体的三维运动参数（平移尺度因子）。这七个点不能在两个包含原点的平面上通过，也不能在包含原点的圆锥面上通过。其次，本文引入了一组“本质参数”，它们在平移尺度因子的范围内唯一确定了运动参数，可以通过求解由八个图像点对应关系导出的一组线性方程组来估计。然后，可以通过计算包含本质参数的 3×3 矩阵的奇异值分解（SVD）来确定实际的运动参数。
