Numerical schemes for advanced reflectance models for Shape from Shading

In recent years, Shape from Shading (SfS) research has been dominated by the rise of perspective models and advanced numerical schemes, which allowed for impressive results compared to previous methods in the field. Despite of these groundbreaking developments, researchers concentrated on Lambertian reflectance models. Recently, some researchers started to include more advanced reflectance models into the Lambertian state-of-the art model of Prados and Faugeras. Such methods include simple models for specular reflectance, which is of particular importance when reconstructing shiny objects. Other models replace Lambertian reflectance by more advanced types of diffuse reflectance like the Oren-Nayar model, which is of particular importance for the reconstruction of human skin. We review these reflectance models and discuss their compatibility with the state-of-the-art numerical solvers for SfS, both iterative and non-iterative.