Finite sample bias of robust estimators in segmentation of closely spaced structures: A comparative study

This paper presents the design and implementation of a new comparative analytical framework for studying the usability of modern high breakdown robust estimators. The emphasis is on finding the intrinsic limits, in terms of size and relative spatial accuracy, of such techniques in solving the emerging challenges of the segmentation of fine structures. A minimum threshold for the distance between separable structures is shown to depend mainly on the scale estimation error. A scale invariant performance measure is introduced to quantify the finite sample bias of the scale estimate of a robust estimator and the measure is evaluated for some state-of-the-art high breakdown robust estimators using datasets containing at least two close but distinct structures with varying distances and inlier ratios. The results show that the new generation of density-based robust estimators (such as pbM-estimator and TSSE) have a poorer performance in problems with datasets containing only a small number of samples in each structure compared with ones based on direct processing of the residuals (such as MSSE). An important message of this paper is that an estimator that performs best in some circumstances, may not be competitive in others: particularly performance on data structures that are relatively large and/or well-separated vs closely spaced fine structures