Mathematical error analysis of normal map compression based on unity condition

Normal maps play an important role in realistic 3D image rendering to express pseudo roughness of the surface. In normal map compression, z components are often eliminated and calculated from x and y components based on the unity condition to achieve high compression rate. However, there is no theoretical background of the validity of eliminating z components so far. In this paper, a mathematical mean square error (MSE) model of such normal map compression based on the unity condition is proposed. In addition, the boundary condition whether to eliminate or include the z components in compression for the better efficient encoding is demonstrated based on our error analysis model.