Abstract: Under the condition that the projecting light is perpendicular to the image plane, and from a study on the geometric and boundary properties of the imaged object, this paper discusses the uniqueness of the conditions for solving SFS problem form the image of a general object. Two theorems are established, the uniqueness of SFS for the global area and the non-uniqueness in some local regions, both of them extend the research results in this field. The proofs are based on differential geometry and geometric theory of ordinary differential equations and are constructive. The proof itself provides a possible way to uniquely recover the surface of a monocular-imaged object with the absence of regularization technique.