Abstract We investigate the problem of reconstructing normals, albedo and lights of Lambertian surfaces in uncalibrated photometric stereo under the perspective projection model. Our analysis is based on establishing the integrability constraint. In the orthographic projection case, it is well-know that when such constraint is imposed, a solution can be identi?ed only up to 3 parameters, the so-called generalized bas-relief (GBR) ambiguity. We show that in the perspective projection case the solution is unique. We also propose a closed-form solution which is simple, ef?cient and robust. We test our algorithm on synthetic data and publicly available real data. Our quantitative tests show that our method outperforms all prior work of uncalibrated photometric stereo under orthographic projection.