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Background models have been widely used for video surveillance and other applications. Methods for constructing background models and associated application algorithms are mainly studied in the spatial domain (pixel level). Many video sources, however, are in a compressed format before processing. In this paper, we propose an approach to construct background models directly from compressed video. The proposed approach utilizes the information from DCT coefficients at block level to construct accurate background models at pixel level. We implemented three representative algorithms of background models in the compressed domain, and theoretically explored their properties and the relationship with their counterparts in the spatial domain. We also present some general technical improvements to make them more capable for a wide range of applications. The proposed method can achieve the same accuracy as the methods that construct background models from the spatial domain with much lower computational cost (50% on average) and more compact storages.