This paper introduces a novel deformable model for face mapping and its application to automatic person identification. While most face recognition techniques directly model the face, our goal is to model the transformation between face images of the same person. As a global face transformation may be too complex to be modeled in its entirety, it is approximated by a set of local transformations with the constraint that neighboring transformations must be consistent with each other. Local transformations and neighboring constraints are embedded within the probabilistic framework of a two-dimensional Hidden Markov Model (2-D HMM). Experimental results on a face identification task show that the new approach compares favorably to the popular Fisherfaces algorithm.