An M-estimator for High Breakdown Robust Estimation in Computer Vision

Several high breakdown robust estimators have been developed to solve computer vision problems involving parametric modeling and segmentation of multi-structured data. Since the cost functions of these estimators are not differentiable functions of parameters, they are commonly optimized by random sampling. This random search can be computationally cumbersome in cases involving segmentation of multiple structures. This paper introduces a high breakdown M-estimator (called HBM for short) with a differentiable cost function that can be directly optimized by iteratively reweighted least squares regression. The fast convergence and high breakdown point of HBM make this estimator an outstanding choice for segmentation of multi-structured data. The results of a number of experiments on range image segmentation and fundamental matrix estimation problems are presented. Those experiments involve both synthetic and real image data and benchmark the performance of HBM estimator both in terms of accurate segmentation of numerous structures in the data and convergence speed in comparison against a number of modern robust estimators developed for computer vision applications (e.g. pbM and ASKC). The results show that HBM outperforms other estimators in terms of computation time while exhibiting similar or better accuracy of estimation and segmentation.