PFMM（perspective fast marching method）是一种有效解决透视投影下从明暗恢复形状（SFS）问题的方法，但是适应条件受限，且对初始数据的精度较为敏感。本文通过对Eikonal方程系数的分析，提出了在透视投影下基于自适应Eikonal方程的PFMM，解决了PFMM对初始数据过于依赖的问题，是PFMM的推广。对合成图像的实验表明本文算法比PFMM精度更高,对透视投影下SFS问题可以得到比较好的结果。

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.