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This paper describes a novel technique for decoupling two of the main sources of variation in 3-D facial structure, the subject's identity and expression. Decoupling and controlling independently these factors is a key step in many practical applications and in this work it is achieved by modeling the face manifold with a bilinear model. Bilinear modeling, however, can only be applied to vectors, and therefore a vector representation for each face is established first. To this end, we use a generic face model that is fitted to each face under the constraint that anatomical points get aligned. The effectiveness and applicability of the proposed method is demonstrated with an application to facial expression recognition.