This thesis presents a new solution to photometric stereo and its application to the automatic inspection of metallic surfaces. Four images are acquired with one camera and four light sources with different positions. This enables the reduction or elimination of undesirable effects associated with specular reflection. Three cases are considered: without specular reflection, the use of pseudo-inverse in obtaining a least squares approximation for the surface normal vectors; in the case where one image pixel is subject to specular reflection then the three remaining pixels are used, enabling complete reconstruction; when more than one pixel is affected then the normal vector is assumed to be vertical. Surface reconstruction from the surface normal vectors is performed using a new technique based on global discrete polynomial moments. This is a new general solution to surface reconstruction from gradient fields. The equation needing to be solved is a partitioned Lyapunov equation commonly encountered in control engineering. This reconstruction method is numerically more efficient than past solutions and delivers better reconstruction performance.This solution enables the reconstruction of the surface geometry independent of the surface albedo. This is important for surface inspection.