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We address the issue of image sequence analysis jointly in space and time. While typical approaches to such an analysis consider two image frames at a time, we propose to perform this analysis jointly over multiple frames. We concentrate on spatiotemporal segmentation of image sequences and on analysis of occlusion effects therein. The segmentation process is three-dimensional (3-D); we search for a volume carved out by each moving object in the image sequence domain, or "object tunnel", a new space-time concept. We pose the problem in variational framework by using only motion information (no intensity edges). The resulting formulation can be viewed as volume competition, a 3-D generalization of region competition. We parameterize the unknown surface to be estimated, but rather than using an active-surface approach, we embed it into a higher dimensional function and apply the level-set methodology. We first develop simple models for the detection of moving objects over static background; no motion models are needed. Then, in order to improve segmentation accuracy, we incorporate motion models for objects and background. We further extend the method by including explicit models for occluded and newly exposed areas that lead to "occlusion volumes," another new space-time concept. Since, in this case, multiple volumes are sought, we apply a multiphase variant of the level-set method. We present various experimental results for synthetic and natural image sequences.