BIAS IN ROBUST ESTIMATION CAUSED BY DISCONTINUITIES AND MULTIPLE STRUCTURES

When fitting models to data containing multiple structures, such as wh en fitting surface patches to data taken from a neighborhood that incl udes a range discontinuity, robust estimators must tolerate both gross outliers and pseudo outliers. Pseudo outliers are outliers to the str ucture of interest, but inliers to a different structure. They differ from gross outliers because of their coherence. Such data occurs frequ ently in computer vision problems, including motion estimation, model fitting, and range data analysis. The focus in this paper is the probl em of fitting surfaces near discontinuities in range data. To characte rize the performance of least median of the squares, least trimmed squ ares, M-estimators, Hough transforms, RANSAC, and MINPRAN on this type of data, the ''pseudo outlier bias'' metric is developed using techni ques from the robust statistics literature, and it is used to study th e error in robust fits caused by distributions modeling various types of discontinuities. The results show each robust estimator to be biase d at small, but substantial, discontinuities. They also show the circu mstances under which different estimators are most effective. Most imp ortantly, the results imply present estimators should be used with car e, and new estimators should be developed.