Shape from shading is a central, difficult problem of machine vision. Although its formulation is precise, its solution has usually been considered ill-posed, possible only with additional assumptions. In recent papers, however, the PIs gave the first proof that shape form shading is not only well-posed but solvable uniquely, for general objects, when the illumination is from the direction of the camera. For general illumination direction, it was shown that the solution is determined effectively up to a finite ambiguity. Thus, regularization the standard technique for selecting a single `physically reasonable' surface solution by imposing additional requirements such as smoothness is generally unnecessary. The aim of the proposed research is to develop and implement algorithms for surface reconstruction without regularization, which, unlike previous algorithms, will explicitly utilize the strong constraints on the surface solutions that make shape from shading well posed. Through exploiting these constraints, the algorithms may be fast and robust. Two of the four algorithms proposed are non-variational unlike most previous ones, and are based on the novel mathematical techniques of the viscosity solution, and dynamical systems theory. The long term aim is to combine shape from shading algorithms with techniques using other information, such as sparse depth data, for robust surface reconstruction from shaded images.//
