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The aim of building edge detection is to obtain a map of man-made structure edges of the investigated scene. Different detectors have been developed exploiting synthetic aperture radar (SAR) data, based on the use of the reflectivity difference (working with SAR amplitude images) or of the phase difference (working with SAR interferometric images) between neighboring pixels. In this letter, a novel approach using jointly both the amplitudes and the interferometric phase of two complex SAR images is proposed, based on the hypothesis that information related to building edges can be retrieved in the two data domains. The technique is based on stochastic estimation theory, exploiting, in particular, Markov random fields. Compared to classical amplitude-based edge detectors and to phase-based ones, the proposed method shows an improvement in terms of detection accuracy, false alarm rate, and building shape recovery. The algorithm has been tested and analyzed using simulated data and validated on L-band and X-band real data sets.