目前,人脸光照建模方法总是假设人脸满足朗伯凸模型、已知人脸表面法向量和反射率等条件，这与实际情况不符，建立的人脸光照模型也存在较大的偏差。为了解决这一问题，提出了一种新的人脸光照建模方法。该方法首先采用黎曼张量人脸图像多模态分解，建立人脸光照模型；然后基于改进的广义拉格朗日算法对人脸光照模型进行优化。理论分析和实验结果表明，该方法比光度立体学、球谐函数方法具有较高的精度和较强的实用性。

The present face illumination modeling methods always suppose that the faces meet convex Lambertian and the surface normals and albedos must be known. However, these restrictions are different from the facts and the constructed illumination model also has bigger difference. In order to solve the problem, a novel method of face illumination modeling is proposed. Firstly，the multi-mode decomposition of Riemannian tensor is adopted and the face illumination is modeled. Then, the illumination model is optimized based on the improved generalized Lagrange algorithm. Theoretical analysis and experimental results both show that our method has higher precision and better practicability compared with photometric stereo harmonic image method.