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We deal with the inverse problem of reconstructing a surface with photometric stereo technique, i.e. using two or more pictures of the surface lighted under different light sources. The new model studied in this paper allows us to extend previous results [1, 2] obtaining a uniqueness result and to solve the classical convex/concave ambiguity of the Shape from Shading (SfS) problem. Finally, we propose an approximation scheme for the solution of the problem testing it on real and synthetic images.