八点算法的降维EVD技术

传统的应用于双视图三维复原的八点算法使用标准特征值分析(EVD)算法。通过统计分析可知,该技术存在估计偏差大和均方误差都大的缺点。其产生原因是数据噪声的有色性和自相关函数矩阵的条件数过大,因此白化数据噪声和正则化变换是提高性能的有效措施。通过理论分析和计算机仿真实验,表明文中所给出的降维EVD技术固有地同时具备噪声预白化功能和数据正则化功能,因此它能给出均方误差相当小的无偏估计。由于它无须进行预白化变换或正则化变换,并把最优化过程的维数从9降为4,所以它还具有计算快速、实现简单方便的优点。

Dimension-reduced EVD Technique of Eight-point Algorithm

The traditional eight-point algorithm applied to two-view 3D reconstruction utilizes the standard Eigen Value Decomposition (EVD) algorithm. By means of the statistical analysis, we know that, it has the disadvantages of very big estimation bias and mse. The reason is that the data noise is not white and the condition number of the ACF matrix of the data observation is extremely big. Thus, the effective measure to improve the reconstruction performance is whitening the data noise and regularizing the condition number of the ACF matrix of the data observation. This theoretic analysis has strongly supported the regularized EVD algorithm developed by Hartley. Then, we develop a dimension-reduced EVD algorithm. The theoretical analysis and computer simulations have demonstrated that the technique has the advantages of intrinsical ability to whiten the data noise and to regularize the condition number of the ACF matrix of the data observation so that it can give an unbiased estimation of essential matrix parameter with very small mse. Furthermore, neither whitening transformation nor regulation transformation is needed and the dimension number of the optimization procedure is reduced from 9 to 4. Therefore the computation complex is largely simplified.