A unified approach to the well-posedness of some non-Lambertian models in Shape-from-Shading theory

In this paper we show that the introduction of an attenuation factor in the %image irradiance brightness equations relative to various perspective Shape from Shading models allows to make the corresponding differential problems well-posed. We propose a unified approach based on the theory of viscosity solution and we show that the brightness equations with the attenuation term admit a unique viscosity solution. We also discuss in detail the possible boundary conditions that we can use for the Hamilton-Jacobi equations associated to these models.