This paper presents a segmentation algorithm for marine synthetic aperture radar (SAR) images. The proposed approach is based on the analysis of image sublooks along azimuth direction and exploits a novel indicator, called incoherent entropy, to divide the input targets into three classes, namely, ship, sea, and ambiguity. A global threshold detector is then implemented to discriminate between stable targets (ships), providing low incoherent entropy amplitude, and ambiguity or sea, implying very high and high values of the indicator, respectively. An integration of the segmentation algorithm into maritime surveillance systems is investigated, proposing its use as a discrimination tool to limit the false alarm rate of traditional prescreening algorithms. The main steps of a standard SAR-based ship detection system are thus implemented to provide a first screening of the candidate targets, which are, then, processed by sublook analysis using incoherent entropy to identify false detections. The proposed technique is tested on stripmap SAR images collected by the TerraSAR-X mission, over the Gulf of Naples, Italy. Algorithm detections are validated using ground-truth data, provided by automatic identification system. The results confirm the capability of the proposed discrimination approach to reject the vast majority of the false detections resulting from the prescreening algorithm.