Photometric Stereo under Low Frequency Environment Illumination

Abstract

The well-studied problem of photometric stereo has almost exclusively made the assumption that illumination is provided by distant point light sources. In this paper, we consider for the first time the problem of photometric shape recovery from images in which an object is illuminated by environment lighting, i.e. where the illumination is modelled as a function over the incident sphere. To tackle this difficult problem, we restrict ourselves to low frequency illumination environments in which the lighting is known and can be well modelled using spherical harmonics. Under these conditions we show that shape recovery from one or more colour images requires only the solution of a system of linear equations. For the single image case we make use of the properties of spherical harmonics under rotations. We assume homogeneous Lambertian reflectance (with possibly unknown albedo) but discuss how the method could be extended to other reflectance models. We show that our method allows accurate shape recovery under complex illumination, even when our assumptions are breached, and that accuracy increases with the number of input images.