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In this paper, we address the problem of estimating the 3D structure and motion of a non-rigid object based on feature points throughout a image sequence. The main limitation of existing factorization methods is that they are difficult to provide correct structure and motion estimates: the motion matrix has a repetitive structure which is not represented by these methods. In order to cope with this problem, we formulate the 3D non-rigid shape as a linear combination of basis trajectories which are represented by the Discrete Cosine Transform (DCT). Based on this, a framework of Markov random field (MRF) with constraints is proposed. By incorporating the motion prior constraints into the MRF, the motion smoothness features between consecutive image frames and local regions are reflected. Finally, the motion and shape estimates are achieved by a non-linear optimization method. Experimental results from a talking face image sequence demonstrate the feasibility of the proposed approach.