针对传统 SFS(Shap from Shading)的不足，提出了一种新的基于 BP神经网络的明暗恢复形状的方法，该方法是基于兰伯特 (L am bertian)反射模型的改进算法，利用了 BP神经网络强的非线性映射能力，将 L ambertian表面反射模型与光滑表面模型相结合，然后再利用一些已知条件，构成 SFS问题的正则化模型 ;变换不同的照明条件，将模型平移或旋转获得多幅图象，以增加约束条件 ;计算出误差补偿参数去修正邻域内的三维误差.由于考虑了邻域的平均值，使算法的稳定性和精确性都得到了加强.实例表明，该算法较传统的算法更快和更精确

Shape from shading(SFS) is one of the critical techniques to recover three-dimensional shape in computer vision, which obtains 3D of the visible surface of an object from only one images of its using the shading knowledge in the given picture. The former methods are ill-posed.. In this paper, the algorithm of shape from shading based on BP neural networks is proposed, which is based on Lambertian reflection model. The suggest method has error compensation. We demonstrate the robustness of our approach to strong illumination variations and with significant pose variations. The recovered face shape is then shown along with the original surface .In comparison with the traditional methods, examples show that the algorithm is verified to be accurate and applicable.