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The research context of this paper is dynamic texture analysis and characterization. Many dynamic textures can be modeled as large scale propagating wavefronts and local oscillating phenomena. After introducing a formal model for dynamic textures, the morphological component analysis (MCA) approach with a well-chosen dictionary is used to retrieve the components of dynamic textures. We define two new strategies for adaptive thresholding in the MCA framework, which greatly reduce the computation time when applied on videos. Tests on real image sequences illustrate the efficiency of the proposed method. An application to global motion estimation is proposed and future prospects are finally exposed.