Shape and Reflectance from Natural Illumination

We introduce a method to jointly estimate the BRDF and geometry of an object from a single image under known, but uncontrolled, natural illumination. We show that this previously unexplored problem becomes tractable when one exploits the orientation clues embedded in the lighting environment. Intuitively, unique regions in the lighting environment act analogously to the point light sources of traditional photometric stereo; they strongly constrain the orientation of the surface patches that reflect them. The reflectance, which acts as a bandpass filter on the lighting environment, determines the necessary scale of such regions. Accurate reflectance estimation, however, relies on accurate surface orientation information. Thus, these two factors must be estimated jointly. To do so, we derive a probabilistic formulation and introduce priors to address situations where the reflectance and lighting environment do not sufficiently constrain the geometry of the object. Through extensive experimentation we show what this space looks like, and offer insights into what problems become solvable in various categories of real-world natural illumination environments.