Mathematical error analysis of normal map compression based on unity condition

Toshihiko Yamasaki, Kazuya Hayase, Kiyoharu Aizawa

Abstract: 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.