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 recon- struction 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.
