1. A method for transferring a facial expression from a subject to a computer-generated character, the method comprising: receiving an input image capturing a facial expression of a subject; matching a first facial model to the facial expression in the input image; generating a displacement map representing finer-scale details not present in the first facial model using a regression function, wherein the regression function estimates the finer-scale details with one or more shapes using shading information determined from the input image, and wherein the one or more shapes correspond to the facial expression in the input image; combining the displacement map with the first facial model to create a second facial model that includes the finer-scale details; and rendering the second facial model to create a computer-generated image of the facial expression of the subject that includes the finer-scale details, wherein the computer-generated image is used for a computer-generated animation.