OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 15234The contribution was presented at SSVM 2015 :http://ssvm2015.math.u-bordeaux.fr/ Abstract. We tackle the problem of perspective 3D-reconstruction of Lambertian surfaces through photometric stereo, in the presence of outliers to Lambert's law, depth discontinuities, and unknown spatiallyvarying lightings. To this purpose, we introduce a robust L 1 -TV variational formulation of the recovery problem where the shape itself is the main unknown, which naturally enforces integrability and permits to avoid integrating the normal field.