Consistency of robust estimators in multi-structural visual data segmentation

A theoretical framework is presented to study the consistency of robust estimators used in vision problems involving extraction of fine details. A strong correlation between asymptotic performance of a robust estimator and the asymptotic bias of its scale estimate is mathematically demonstrated where the structures are assumed to be linear corrupted by Gaussian noise. A new measure for the inconsistency of scale estimators is defined and formulated by deriving the functional forms of four recent high-breakdown robust estimators. For each estimator, the inconsistency measures are numerically evaluated for a range of mutual distances between structures and inlier ratios, and the minimum mutual distance between the structures, for which each estimator returns a non-bridging fit, is calculated.