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 brightness equations relative to various perspective shape-from-shading models allows us to make the corresponding differential problems well-posed. We propose a unified approach based on the theory of viscosity solutions 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.