Geometric–photometric approach to monocular shape estimation

Abstract

Monocular, reflectance map-based shape estimation has traditionally relied exclusively on photometric data, but the recently introduced disparity-based photometric stereo (DBPS) and Green's function shape from shading (GSFS) have brought more geometry into it by incorporating a matching equation, and can appropriately be termed a geometric–photometric approach. In DBPS, the matching equation is used for obtaining disparities from the input image pair, while in GSFS it is used for generating the matching image, a uniform disparity field being considered. In both cases, depth can be recovered if one assumes the disparities to result from the displacement of the irradiance pattern over the imaged surface. Starting from the analysis of such displacement under perspective projection, we show that the original DBPS/GSFS formulation must be amended: reconstructions with no free parameters are no longer feasible, but we are able to propose an approximate procedure which yields higher quality estimates, up to a multiplicative factor.