Simple consistent cluster methods based on redescending M-estimators with an application to edge identification in images

We use the local maxima of a redescending M-estimator to identify cluster, a method proposed already by Morgenthaler (in: H.D. Lawrence, S. Arthur (Eds.), Robust Regression, Dekker, New York, 1990, pp. 105–128) for finding regression clusters. We work out the method not only for classical regression but also for orthogonal regression and multivariate location and show that all three approaches are special cases of a general approach which includes also other cluster problems. For the general case we show consistency for an asymptotic objective function which generalizes the density in the multivariate case. The approach of orthogonal regression is applied to the identification of edges in noisy images.