Well-posedness of linear shape-from-shading problem

Abstract

We continue to study here a global shape recovery of a smooth surface for which the reflectance map is linear. It was recently proved that under special conditions the corresponding finite difference based algorithms are stable and thus convergent to the ideal solution. The whole analysis was based on the assumption that the problem related to the linear image irradiance equation is well-posed. Indeed, we show in this paper that under certain conditions there exists a unique global C ² solution (depending continuously on the initial data) to the corresponding Cauchy problem defined over the entire image domain (with non-smooth boundary).