Shape from shading for multiple light sources

Abstract

Many shape recovery algorithms—in particular, shape from shading (SFS)—are based on a point source at infinity or a uniform hemispheric source. It will be convenient and useful if we can perform SFS under indoor lights that may be spherical, cylindrical, or flat (ceiling lights) in shape in an uncontrolled environment. As a first step toward this goal we propose a light source model for each of the above shapes for performing SFS. In this study we give the derivation of the rectangular, spherical, and cylindrical light source models. In indoor environments the positions (usually on the ceiling or walls) of the light sources are known. Assuming that the target object is small relative to the distances from the sources, we have derived a reflectance map for the Lambertian surface of an object under a mixture of light sources of the above shapes. Hence the shape recovery can be performed by using the SFS technique. This is a significant step toward the application of SFS in uncontrolled practical environments under household or office lighting. This technique of shape recovery is verified by many examples of simulations and real experiments, and the results are good.