Abstract: By analyzing the shortcoming of existing robust algorithms based on random sampling employed in estimating the fundamental matrix, combining the advantages of LMedS and M-estimators, a new L-M algorithm is proposed with high accuracy for estimating fundamental matrix. The algorithm uses the idea of LMedS method to construct an inliers set of matching points, in general, the inliers set does not contain false matches, but also exists bad locations. It uses Torr-M-estimators to compute fundamental matrix. M-estimators can get a accurate fundamental matrix when the inliers set only contains bad locations. Experimental results on a mass of synthetic data and real images show that the proposed algorithm has higher robustness and estimating accuracy in the case of Gaussian noise and mismatching.

Key words: fundamental matrix, Least Median of Squares（LMedS）, M-estimators

摘要： 分析了基于随机抽样检测思想的现有鲁棒算法在基本矩阵估计中存在的不足，结合LMedS和M估计法各自的优点，提出一种新的高精度的L-M基本矩阵估计算法。利用LMedS思想方法获得内点集，此时内点集通常情况下不包含误匹配，但仍存在位置误差，用Torr-M估计法计算基本矩阵，因为当匹配点只存在位置误差时，用M估计法得到的基本矩阵非常精确。大量的模拟实验和真实图像实验数据表明，在高斯噪声和误匹配存在的情况下，该算法具有更高的鲁棒性和精确度。

关键词: 基本矩阵, 最小平方中值法, M估计法