考虑图像投影鉴别分析问题,为提高特征抽取的速度和识别率,利用图像矩阵直接构造图像散布矩阵,在具有统计不相关的条件下将Foley-Sammon鉴别分析(FSLDA)转化为两目标约束优化问题,并给出了有效投影向量的概念;根据多目标优化的最优性条件可将求取有效投影向量的问题归结为求广义特征方程的最大特征值对应的特征向量,并据此进行特征抽取,进而提出了两目标最优图像投影鉴别分析方法。与其他鉴别投影分析方法相比,该方法具有以下特点:(1)可直接由图像矩阵构建散布矩阵;(2)有效投影向量具有统计不相关性;(3)训练样本的类内散布矩阵不必为可逆的,也不需要求某种形式矩阵的逆。在ORL标准人脸库和NUST603人脸库上的试验结果表明,上述图像投影鉴别分析方法在识别性能上较以往的方法有一定的提高,尤其是特征抽取的速度有明显的提高。

This paper addressed the image discriminant analysis problem.By constructing the scattering matrices of the image matrices,Foley-Sammon discriminant analysis(FSLDA)are transformed into a bi-objective optimization problem with uncorrelated constraint for improving the speed of feature extraction and the recognition rate.The efficient projection vector is defined and the efficient projection vector can be obtained from deciding the eigenvector corresponding to the eigenvalue of maximum of a generalized eigen-equation.Compared with the other image projection analysis methods,the proposed method has the following properties:(1)the scattering matrices are directly based on image matrices;(2)the efficient projection vectors are statistically uncorrelated;(3)the within scattering matrix is not necessarily invertible and some matrix inversions are not performed.Finally,the proposed method is tested on ORL and NUST603 face databases.The experimental results indicate that the recognition performance of the proposed method is prior to the other methods,and its speed for feature extraction is faster than the above methods.