Multiple light sources and reflectance property estimation based on a mixture of spherical distributions

In tins paper we propose a new method for simultaneously estimating the illumination of the scene and the reflectance property of an object from a single image. We assume that the illumination consists of multiple point sources and the shape of the object is known. Unlike previous methods, we will recover not only the direction and intensity of the light sources, but also the number of light sources and the specular reflection parameter of the object. First, we represent the illumination on the surface of a unit sphere as a finite mixture of von Mises-Fisher distributions by deriving a spherical specular reflection model. Next, we estimate this mixture and the number of distributions. Finally, using this result as initial estimates, we refine the estimates using the original specular reflection model. We can use the results to render the object under novel lighting conditions