Statistical approaches to ill-posed image processing problems such as restoration, segmentation and edge-detection have been proposed previously that were based on Markov random fields (MRFs). MRFs provide a regularization framework where a-priori knowledge expressed in a probabilistic way can be used together with available data for obtaining solutions characterized by a "good" global behaviour. A-priori knowledge and evidential knowledge can be used to specify constraints on the solution within a probabilistic functional. Observation models are necessary to capture evidential knowledge, i.e., the relations between the solution and data acquired either by a physical or a logical device. The present paper is based on a multilevel MRF approach introduced in Regazzoni (1994) and Regazzoni and Venetsanopoulos aiming at three different tasks: 1) to detect straight lines, 2) to restore the original image, and 3) to detect edge points. In particular, a new line detection approach is introduced, consisting in a progressive relaxation of the threshold used to establish the line presence in an appropriate parameter space. The method is applied to SAR remote sensing.
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