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-known that when such constraint is imposed, a solution can be identified 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, efficient 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.

In this paper we propose a novel solution to uncalibrated photometric stereo. Our approach is to eliminate the so-called generalized bas relief (GBR) ambiguity by exploiting points where the Lambertian reflection is maximal. We demonstrate several noteworthy properties of these maxima: 1) Closed-form solution: A single diffuse maximum constrains the GBR ambiguity to a semi-circle in 3D space; 2) Efficiency: As few as two diffuse maxima in different images identify a unique solution; 3) GBR-invariance: The estimation error of the GBR parameters is completely independent of the true parameters. Furthermore, our algorithm is remarkably robust: It can obtain an accurate estimate of the GBR parameters even with extremely high levels of outliers in the detected maxima (up to 80% of the observations). The method is validated on real data and achieves state-of-the-art results.