Face is a perceptually symmetric object; however, it often appears not so in captured image due to the rotation in depth within the 3D space. In this paper, we explore the invariant of the symmetry point pair when the pose and symmetry radius are changed. Under the general perspective camera model, we present an invariant, called perspective symmetry invariant (PSI), which only depends on the focus length and the rotation angle in depth when the angle is relatively small. PSI is discriminating for pose estimation; meanwhile, it can be used to synthesize face shape in novel views with different PSI values. Encouraging experiments on these two contributions of PSI are presented.