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This letter proposes a generalized-likelihood ratio test-based edge detector to be fed by possibly polarimetric synthetic aperture radar (SAR) data. It can be used to detect dark spots on the sea surface and, hence, as the first stage of a system for identification and monitoring of oil spills. The proposed constant false alarm rate (CFAR) detector does not require secondary data (namely pixels from a slick-free area); remarkably, a preliminary performance assessment, carried out by resorting to real SAR recordings, shows that it guarantees detection capabilities comparable to those of previously proposed polarimetric CFAR detectors (which though make use of secondary data). The preliminary performance assessment also seems to indicate that processing polarimetric data does not ensure improved detection capabilities.