中文摘要：

为了缓解线性判别分析（linear discriminant analysis,LDA）方法在小样本情况下出现的矩阵奇异性问题,针对彩色人脸图像,利用其四元数矩阵表示模式,在人脸识别中引入基于四元数表示的二维LDA、双向LDA方法.这些方法充分利用了彩色图像的空间分布信息,通过在行、列方向降维提取图像的2DLDA、BDLDA特征,缓解了类内散度矩阵的奇异性问题.在FERET彩色人脸数据库及AR彩色人脸数据库上的大量实验证明,本文方法与基于四元数矩阵表示的2DPCA、BDPCA算法相比,识别性能均有提高.

英文摘要：

To ease the singularity of within-class scatter matrix due to the small sample size problem for linear discriminant analysis （LDA） method, the modified 2D linear diseriminant analysis and bi- directional linear discriminant analysis method based on quaternion matrix were proposed to recognize a color face. These methods made full use of the information of the spatial distribution of color images, and extracted the 2DLDA or BDLDA feature by reducing the dimensionality in both column and row directions, and smoothed the singularity of the within-class scatter matrix. By using the FERET color face database and AR color face database, experimental results show that this approach has better recognition performance than the 2DPCA or BDPCA method based on quaternion matrix.