A Novel High Breakdown M-estimator for Visual Data Segmentation

Abstract

Most robust estimators, designed to solve computer vision problems, use random sampling to optimize their objective functions. Since the random sampling process is patently blind and computationally cumbersome, other searches of parameter space using techniques such as Nelder Meade simplex or gradient search techniques have been also proposed (particularly in combination with PbM-estimators). In this paper, we introduce a novel high breakdown M-estimator having a differentiable objective function for which a closed form updating formula is mathematically derived (similar to redescending M-estimators) and used to search the parameter space. The resulting M-estimator has a high breakdown point and is called high breakdown M-estimator (HBM). We show that this objective function can be optimized using an iterative reweighted least squares regression similar to redescending M-estimators. The closed mathematical form of HBM and its guaranteed stability combined with its high breakdown point and fast convergence speed make this estimator an outstanding choice for segmentation of multi-structural data. A number of experiments, using both synthetic and real data have been conducted to show and benchmark the performance of the proposed estimator both in terms of accurate segmentation of numerous structures in the data and also the convergence speed. Moreover, the computational time of HBM, ASSC, MSSE and PbM are compared using the same computing platform and the results show that HBM significantly outperforms aforementioned techniques.