PFMM(perspective fast marching method) is a successful approach to shape from shading (SFS) technique

but it is restricted by some conditions and sensitive to the precision of the initialization. In this paper

we have studied the characteristics of the coefficients in the Eikonal equation and proposed an improved perspective fast marching method based on adaptive Eikonal equation. This algorithm depends much less on the initialization which may have error from the real surface. Moreover we have proved that PFMM is a particular case of our algorithm. Experiments on synthetical pictures demonstrate that our algorithm can obtain higher accuracy than PFMM does and yield good performance for perspective SFS problem.