Existence and uniqueness of solutions of surface reconstruction problem

Surface reconstruction from scattered data is an important problem in such areas as reverse engineering and computer aided design. In solving partial differential equations derived from surface reconstruction problems, level-set method has been successfully used. We present in this paper a theoretical analysis on the existence and uniqueness of the solution of a partial differential equation derived from a model of surface reconstruction using the level-set approach. We give the uniqueness analysis of the classical solution. Results on the existence and uniqueness of the viscosity solution are also established.