The theoretical investigation of the use of a long straight-line light source and a camera to determine the profiles of reflecting surfaces, started by Gilbert and Scott [1], is continued. In the earlier paper, expressions were found describing the observed image in terms of the configuration of the apparatus and the surface shape for surfaces whose cross-section is uniform in a fixed direction. In this paper, these expressions are inverted, so that the surface profile may be deduced from the observed image. The inversion process is shown to be equivalent to the problem of solving a certain ordinary differential equation with appropriate boundary data, but it is found that the problem does not have a unique solution. The use of a second photograph yields a problem which does admit a unique solution, and for some configurations of the apparatus, a solution in closed form is found. Numerical experiments to test the ordinary differential equation and the closed form of solution, and practical experiments to check the prediction of non-uniqueness are described.