关键词: 光照线性子空间, 商图像, 人脸识别, 图像合成

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