A new finite difference method is proposed to solve the image irradiance equation of shape from shading.Firstly

the non-linear term in the reflectance map is approximated by a Taylor-expansion.Then the resulting linear partial difference equation is solved numerically by a semi-implicit cross difference scheme

combining with initial and boundary conditions.We prove its stability and convergence in detail.Surface height is obtained iteratively by successive over-relaxation method

and the method of selecting optimization factor is also given in the paper.Experimental results on synthetic images demonstrate the new algorithm suits for any light direction and the reconstruction results are better than the traditional ones.