Mixture of Spherical Distributions for Single-View Relighting

We present a method for simultaneously estimating the illumination of a scene and the reflectance property of an object from single view images – a single image or a small number of images taken from the same viewpoint. We assume that the illumination consists of multiple point light sources and the shape of the object is known. First, we represent the illumination on the surface of a unit sphere as a finite mixture of von Mises-Fisher distributions based on a novel spherical specular reflection model that well approximates the Torrance-Sparrow reflection model. Next, we estimate the parameters of this mixture model including the number of its component distributions and the standard deviation of them, which correspond to the number of light sources and the surface roughness, respectively. Finally, using these results as the initial estimates, we iteratively refine the estimates based on the original Torrance-Sparrow reflection model. The final estimates can be used to relight single-view images such as altering the intensities and directions of the individual light sources. The proposed method provides a unified framework based on directional statistics for simultaneously estimating the intensities and directions of an unknown number of light sources as well as the specular reflection parameter of the object in the scene.