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Robust and accurate segmentation of the oil slick from SAR imagery is a key step for the detection and monitoring of oil spills, whose observation is very important for protecting the marine environments. However, intensity inhomogeneity, noise, and weak boundary often exist in the oil slick region in SAR imagery, making the accurate segmentation of oil slick very challenging. In this paper, we propose a novel statistical active contour model for oil slick segmentation. First, we fit the distributions of the inhomogeneous intensity with Gaussian distributions of different means and variances. Then, a moving window is used to map the original image intensity into another domain, where the intensity distributions of inhomogeneous objects are still Gaussian but are better separated. In the transformed domain, the means of the Gaussian distributions can be adaptively estimated by multiplying a smooth function with the signal within the window. Thereafter, for each local region, we define a statistical energy function, which combines the smooth function, the level set function, and the constant approximating the true signal from the corresponding object. In addition, in order to make the final segmentation robust to the initialization of level set function, we present a new energy function which is convex with respect to the level set function, thereby avoiding the local minima. An efficient iterative algorithm is then proposed to minimize the energy function that makes the segmentation robust. Experiments undertaken using some challenging SAR oil slick images demonstrate the superiority of our proposed algorithm with respect to the state-of-the-art representative methods.