Abstract: Previous work has demonstrated that the image variation of many objects（human faces in particular） under variable lighting can be effectively modeled by low-dimensional linear spaces.Lee has proved that there exists configuration of 9 point light source directions，such that，by taking 9 images of an object under these single sources，the resulting subspace is an effective representation for recognition under a wide range of lighting conditions.The method proposed by Lee achieves better recognition performance.However，it requires the 9 images of each object illuminated by lights from the universal configuration to act as training samples，which restricts its applications in face recognition.In addition，3-d subspace in quotient image method doesn’t suffice to represent all images of an object under varying illuminations.Therefore，an improved method based on image on 9-d linear subspace constructed using 9 images of object under the configuration is presented to overcome these deficiencies.And 9 images of another object under the configuration are generated.The suggested method can meet the theoretical prerequisites of quotient image method，and achieve better image synthesis and face recognition results.

Key words: illumination linear subspace, quotient image, face recognition, image synthesis

摘要： 以前的研究已经证明，在变化光照条件，甚至多个光源和阴影存在的情况下，对象（尤其是人脸）所形成的图像能够被低维线性子空间有效地表示。Lee证明了存在9个光源方向的统一配置，任一对象在这些统一配置光照方向下的9幅图像所组成的线性子空间，能够很好地表示该对象所有光照情况，并且达到了很好的识别性能。但它要求每一对象在统一配置光照方向下的9幅图像作为训练集，这一要求限制了它在实际中的应用。此外，商图像方法中简单的三维点光源模型无法很好地近似任意光照情况，因此，提出一种基于九维线性子空间的改进的商图像方法，并利用改进后的商图像方法合成对象在统一配置光源方向下的9幅图像，克服了Lee所提方法的不足。该文方法较好地满足了商图像方法的理论前提，从而达到了较好的图像合成和人脸识别性能。

关键词: 光照线性子空间, 商图像, 人脸识别, 图像合成