1. A computing device to estimate head motion between two images of a face, the computing device comprising: a processor; and a memory coupled to the processor, the memory comprising computer-program instructions executable by the processor for: identifying locations of a plurality of distinct facial features in the two images, the locations corresponding to a number of unknowns determined upon estimation of head motion, the number of unknowns being determined by a number of equations; converting the identified locations into a set of physical face parameters based on the symmetry of the distinct facial features, the set of physical face parameters reducing the number of unknowns as compared to the number of equations used to determine the unknowns; adding an inequality constraint on a particular face parameter of the physical face parameters, such that the particular face parameter is constrained within a predetermined minimum and maximum value; converting the inequality constraint to an equality constraint using a penalty function; and estimating head motion from identified points in the two images, the identified points being based on the set of physical face parameters.