Robust regression methods for computer vision: A review

Regression analysis (fitting a model to noisy data) is a basic technique in computer vision, Robust regression methods that remain reliable in the presence of various types of noise are therefore of considerable importance. We review several robust estimation techniques and describe in detail the least-median-of-squares (LMedS) method. The method yields the correct result even when half of the data is severely corrupted. Its efficiency in the presence of Gaussian noise can be improved by complementing it with a weighted least-squares-based procedure. The high time-complexity of the LMedS algorithm can be reduced by a Monte Carlo type speed-up technique. We discuss the relationship of LMedS with the RANSAC paradigm and its limitations in the presence of noise corrupting all the data, and we compare its performance with the class of robust M-estimators. References to published applications of robust techniques in computer vision are also given.