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We describe an approach for segmenting a moving image into regions that correspond to surfaces in the scene that are partially surrounded by the medium. It integrates both appearance and motion statistics into a cost functional that is seeded with occluded regions and minimized efficiently by solving a linear programming problem. Where a short observation time is insufficient to determine whether the object is detachable, the results of the minimization can be used to seed a more costly optimization based on a longer sequence of video data. The result is an entirely unsupervised scheme to detect and segment an arbitrary and unknown number of objects. We test our scheme to highlight the potential, as well as limitations, of our approach.