Robust Estimation in the Presence of Spatially Coherent Outliers

We present a generative model based approach to deal with spatially coherent outliers. The model assumes that image pixels are generated by either one of two distinct processes: an inlier process which is responsible for the generation of the majority of the data, and an outlier process which generates pixels not adhering to the inlier model. The partitioning into inlier and outlier regions is made explicit by the introduction of a hidden binary map. To account for the coherent nature of outliers this map is modelled as a Markov Random Field, and inference is made tractable by a mean field EM-algorithm. We make a connection with classical robust estimation theory, and derive the analytic expressions of the equivalent M-estimator for two limiting cases of our model. The effectiveness of the proposed method is demonstrated with two examples. First, in a synthetic linear regression problem, we compare our approach with different M-estimators. Next, in a 2D-face recognition experiment, we try to identify people from partially occluded facial images.