Abstract

This paper exploits the monotonicity of general isotropic re- flectances for estimating elevation angles of surface normal given the az- imuth angles. With an assumption that the reflectance includes at least one lobe that is a monotonic function of the angle between the surface normal and half-vector (bisector of lighting and viewing directions), we prove that elevation angles can be uniquely determined when the surface is observed under varying directional lights densely and uniformly dis- tributed over the hemisphere. We evaluate our method by experiments using synthetic and real data to show its wide applicability, even when the assumption does not strictly hold. By combining an existing method for azimuth angle estimation, our method derives complete surface nor- mal estimates for general isotropic reflectances.