Fast estimation of epipolar geometry using high breakdown M-estimators

The high breakdown M-estimator (HBM) is introduced in this paper as an outstanding choice compared to modern high breakdown estimators for epipolar geometry estimation and motion segmentation problems. It is mathematically demonstrated that since HBM automatically guides its cost optimization using an iterative reweighted least square regression (instead of using random sampling like high breakdown RANSAC-based techniques), its computational cost is substantially cheaper than that of modern high breakdown estimators. In a number of experiments involving both synthetic and real image pairs, the performance of HBM, MSSE and pbM-estimator to solve fundamental matrix estimation problems are compared. The results verify that in terms of computational cost, HBM significantly outperforms the modern RANSAC-based high breakdown estimator and the pbM-estimator, while the estimation accuracies of HBM and its tolerances to high fractions of gross or pseudo outliers are similar to the other estimators. For real-time epipolar geometry estimation and multiple motion segmentation problems that involve multi-structured data segmentation (large fractions of outliers), application of the HBM-estimator for fast computation is highly recommended.