Existence and uniqueness in photometric stereo

摘要

We analyze the problem of recovering the shape of a smooth Lambertian surface from two images obtained by consecutive illumination of the surface by distant point light sources from two different directions. We discuss the issues of existence and uniqueness for the corresponding system of two first-order nonlinear partial differential equations. We show that generically this system has, up to a constant, a unique solution. We also examine exceptional cases for which there is no such uniqueness.