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In this paper, the problem of building edge detection in synthetic aperture radar images is addressed. A new stochastic approach based on local Gaussian Markov random field (LGMRF) is proposed. The algorithm finds the edges of buildings starting from the estimation of the hyperparameters of the LGMRF model. The hyperparameters are seen as an indicator of the spatial correlation between adjacent pixels. The procedure is applied on interferometric data, using single-channel and multichannel configurations. The algorithm has been tested on simulated and real data, providing good results in both cases.