Abstract: This paper presents a novel KPCA+Null Space method by integrating the kernel PCA method and the null space of the within-class scatter matrix. The kernel PCA method which extends to include fractional power polynomial models first derives nonlinear features of face samples, then this paper constructs the null space of the within-class scatter matrix, and calculates the optimal discriminating vectors by maximizing the between-class distribution, after the projection of the samples onto the optimal discriminating vectors, it can obtain the optimal discriminating feature vectors. The test results show that the KPCA+Null Space method is superior to Fisher face method in terms of recognition accuracy and stability to the variations between the images of the same face due to illumination, expression and viewing direction.

Key words: Face recognition, Fractional power polynomial models, Kernel principal component analysis(KPCA), Null space

摘要： 利用小指数多项式核主分量分析(KPCA)提取人脸样本的非线性特征，提高对光照、姿态及面部表情变化的鲁棒性，构造训练样本的类内散布矩阵零空间，在此零空间内找到令类间离散度最大的投影方向，往此方向投影得到人脸样本的最优分类特征矢量。实验结果表明；该方法的识别率和对光照、姿态及面部表情变化的鲁棒性比Fisher脸方法有显著提高。

关键词: 人脸识别, 小指数多项式, 核主分量分析, 零空间