改进的从运动中恢复目标结构的因子分解法

因子分解法是从图像序列中恢复刚体目标几何结构的重要方法。介绍了传统因子分解法的基本过程，分析了该方法存在的不足，并针对该方法容易失效的缺点，提出一种改进的因子分解法。该方法避开传统方法中求解修正矩阵的复杂过程，利用旋转矩阵的特性，直接修正由传统方法SVD分解得到的每帧图像的旋转矩阵，然后根据观测矩阵和得到旋转矩阵直接利用线性最小二乘法求解目标的结构矩阵。仿真和实测数据的实验结果表明，本文方法能够有效地从序列图像中恢复目标的几何结构，相比传统的因子分解法而言，在稳定性上有较大的提升。

An improved factorization method for structure from motion

The factorization method is an important method for recovering the geometric structure of a rigid object from image sequences. Firstly, the conventional factorization method is introduced, as well as the analysis of its shortage. In order to avoid the invalidation, an improved factorization method is then proposed. Meanwhile, the complex process of solving for the corrective matrix in conventional way is avoided. The rotation matrix of each frame is directly corrected according to the property of a rotation matrix, which has been decomposed by the conventional method using Singular Value Decomposition (SVD). Then we calculate the structure matrix using linear least squares method which directly combining the watching matrix with the solved rotation matrix. The experiments using synthetic and real images illustrate that the proposed method can recover the geometric structure from image streams very efficiently, and it also improves the stability, compared with the conventional method.