Surface Determination by Photometric Ranging

We describe a method for recovering the three dimensional shape of a surface, using multiple images from a single camera, closely related to "light field reconstruction" described by Magda et al. A volume array of switchable illuminators is used to obtain a set of images that are used for the reconstruction. Unlike photometric stereo, where the illumination is assumed to be homogeneous, we exploit the inverse-square-law falloff of intensity with the distance between the illuminator and the surface. By placing illuminators at a variety of distances from the measurement volume, a direct estimate of surface range can be obtained, in addition to surface normal estimates obtained as in photometric stereo. We discuss solution methods and present simulation results for a few simple geometries. Aspects of illuminator design and calibration are also considered.