Photometric Stereo with Nearby Planar Distributed Illuminants

This paper considers the problem of shape-from-shading using nearby planar distributed illuminants. It is shown that a rectangular planar nearby distributed uniform isotropic illuminant shining on a small Lambertian surface patch is equivalent to a single isotropic point light source at infinity. A closed-form solution is given for the equivalent point light source direction in terms of the illuminant corner locations. Equivalent point light sources can be obtained for multiple rectangular illuminants allowing standard photometric stereo algorithms to be used. An extension is given to the case of a rectangular planar illuminant with arbitrary radiance distribution. It is shown that a Walsh function approximation to the arbitrary illuminant distribution leads to an efficient computation of the equivalent point light source directions. A search technique employing a solution consistency measure is presented to handle the case of unknown depths. Applications of the theory presented in this paper include visual user-interfaces using shape-from-shading algorithms making use of the illumination from computer monitors, or movie screens.