Abstract: Based on local Lax-Friedrichs flux splitting scheme, this paper proposes a fast sweeping method for the problem of perspective shape from shading.First we model this problem as a static Hamilton-Jacobi equation. To solve this equation, an algorithm which combines Local Lax-Friedrichs flux splitting scheme and the fast sweeping method is presented.Then the surface of the object can be reconstructed. The method can be applied on non-convex Hamiltonian, and can improve the results of local places. Moreover, it doesn’t need estimated initialization of the surface, and is simple to realize.Experiments on synthetic and real images demonstrate that our algorithm can obtain much accurate results for perspective SFS problem