Discontinuity-Adaptivity Model and Robust Estimation

Abstract

Robust methods (Tukey 1977; Huber 1981; Rousseeuw 1984) are tools for statistics problems in which outliers are an issue. It is well known that the least squares (LS) error estimates can be arbitrarily wrong when outliers are present in the data. A robust procedure is aimed to make solutions insensitive to the influence caused by outliers. That is, its performance should be good with all-inlier data and deteriorates gracefully with increasing number of outliers. The mechanism of robust estimators in dealing with outliers is similar to that of the discontinuity adaptive MRF prior model studied in the previous chapter. This chapter provides a comparative study (Li 1995a) of the two kinds of models based on the results about the DA model and presents an algorithm (Li 1995e) to improve the stability of the robust M-estimator to the initialization.