Robust Estimation of Multiple Inlier Structures

Xiang Yang, Peter Meer

Published 2016-09-20Version 1

In this paper we present a method to robustly estimate multiple inlier structures with different scales in the presence of noise.The estimation is done iteratively with the objective function transformed into a higher dimensional linear space by carrier vectors. An initial set consisting of a small number of points that has the minimum sum of Mahalanobis distances is detected from the trials based on elemental subsets. The region of interest is defined by applying an expansion criteria to an increasing sequence of sets of points which begins with the initial set and increases until the set cannot expand. The largest expansion in this region gives the scale estimate. The original mean shift is applied to all remaining input points to re-estimate the structure. After all data are processed, the segmented structures are sorted by strengths with the strongest inlier structures at the front. Several synthetic and real examples are presented to illustrate every aspect of the algorithm. This method is easy to implement and its limitations of robustness are clearly stated.