Shape from Shading and Photometric Stereo are two fundamental problems in Computer Vision aimed at reconstructing surface depth given either a single image taken under a known light source or multiple images taken under different illuminations, respectively. Shape from shading with multiple light sources is an active research area, and a diverse range of approaches have been proposed in recent decades. However, devising a robust reconstruction technique still remains a challenging goal, as the image acquisition process is highly nonlinear. Recent Photometric Stereo variants rely on simplifying assumptions in order to make the problem solvable: light propagation is still commonly assumed to be uniform, and the Bidirectional Reflectance Distribution Function is assumed to be diffuse, with limited interest for specular materials. In this talk, a well-posed formulation based on PDEs for a unified reflectance function that can model both diffuse and specular reflections will be introduced as well as a new formulation of the problem dealing with additive bias. These derivations are based on ratio of images, which makes the model independent from photometric invariants and yields a well-posed system of quasi-linear PDEs with discontinuous coefficients.