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Reconstructing a 3D model of a human face from a video sequence is an important problem in computer vision, with applications to recognition, surveillance, multimedia etc. However, the quality of 3D reconstructions using structure from motion (SfM) algorithms is often not satisfactory. One common method of overcoming this problem is to use a generic model of a face. Existing work using this approach initializes the reconstruction algorithm with this generic model. The problem with this approach is that the algorithm can converge to a solution very close to this initial value, resulting in a reconstruction which resembles the generic model rather than the particular face in the video which needs to be modeled. We propose a method of 3D reconstruction of a human face from video in which the 3D reconstruction algorithm and the generic model are handled separately. A 3D estimate is obtained purely from the video sequence using SfM algorithms without use of the generic model. The final 3D model is obtained after combining the SfM estimate and the generic model using an energy function that corrects for the errors in the estimate by comparing local regions in the two models. The optimization is done using a Markov chain Monte Carlo (MCMC) sampling strategy. The main advantage of our algorithm over others is that it is able to retain the specific features of the face in the video sequence even when these features are different from those of the generic model. The evolution of the 3D model through the various stages of the algorithm is presented.