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Background subtraction (BS) is an efficient technique for detecting moving objects in video sequences. A simple BS process involves building a model of the background and extracting regions of the foreground (moving objects) with the assumptions that the camera remains stationary and there exist no movements in the background. These assumptions restrict the applicability of BS methods to real-time object detection in video. In this letter, we propose an extended cluster BS technique with a mixture of symmetric alpha-stable (SαS) distributions. An online self-adaptive mechanism is presented that allows automated estimation of the model parameters using the log moment method. Results over real video sequences from indoor and outdoor environments, with data from static and moving video cameras are presented. The SαS mixture model is shown to improve the detection performance compared with a cluster BS method using a Gaussian mixture model and the method of Li et al.