Orthogonal Illuminations in Two Light-Source Photometric Stereo

In this paper we investigate the case of ambiguous shape reconstruction from two light-source photometric stereo based on illuminating the unknown Lambertian surface. So-far this problem is merely well-understood for two linearly independent light-source directions with one illumination assumed as overhead. As already established, a necessary and sufficient condition to disambiguate the entire shape reconstruction process is controlled by the satisfaction of the corresponding second-order linear PDE with constant coefficients in two independent variables. This work extends the latter to an arbitrary pair of light-source directions transforming the above constraint into a special nonlinear PDE. In addition, a similar ambiguity analysis is also performed for a special configuration of two light-source directions assumed this time as orthogonal and contained in the vertical plane. Finally, this work is supplemented by illustrative examples exploiting symbolic computation used within a framework of continuous reflectance map model (i.e. an image irradiance equation) and applied to a genuine Lambertian surfaces.