MDPE: A very robust estimator for model fitting and range image segmentation

Abstract

In this paper, we propose a novel and highly robust estimator, called MDPE (Maximum Density Power Estimator). This estimator applies nonparametric density estimation and density gradient estimation techniques in parametric estimation. MPDE optimizes an objective function that measures more than just the residuals. Both the density distribution of data points and the size of the residual corresponding to the local maximum of the density distribution, are considered as important characteristics in our objective function. MDPE can tolerate more than 85% outliers. Compared with several other recently proposed similar estimators, MDPE has a higher breakdown point and less error variance. We also present a new range image segmentation algorithm, based on a modified version of the MDPE (Quick-MDPE), and its performance is compared to several other segmentation methods. Segmentation requires more than a simple minded application of an estimator, no matter how good that estimator is: our segmentation algorithm overcomes several difficulties faced with applying a statistical estimator to this task. Keywords: robust estimation, breakdown point, model fitting, range image segmentation, least median of squares, residual consensus, adaptive least kth order squares, mean shift.