1. A computer program product comprising one or more non-transient computer-readable mediums having encoded thereon executable instructions that, when executed by at least one processor, cause the at least one processor to carry out a process of producing a face image, the process comprising: causing capture of an electronic image of the user with a camera; creating a three-dimensional mesh from at least a portion of the electronic image that includes an eye area of the user; identifying a viewing angle of the user by assessing surface features about the eye area; estimating an angle of rotation for gaze correction; rotating the three-dimensional mesh, based on the angle of rotation, to produce a rotated image of at least the eye area of the user; and updating the electronic image of the user with the rotated image.