2DPCA plus LDA: A novel fisher discriminant framework for feature extraction and face recognition

The extraction of discriminant features is the most fundamental and important problem in face recognition. This paper presents a novel method, 2D-FPCA, to extract optimal discriminant features and representation for face images by applying the two dimensional Fisherface method in the two dimensional principal component analysis (2DPCA) subspace. As 2DPCA is based on 2D image matrices rather than 1D vectors so the image matrix does not need to be transformed into a vector prior to feature extraction. The total image covariance matrix S_t is constructed directly using the original image matrices and its eigenvectors are derived for image feature extraction. Similarly, the betweens S_B and the within image covariance S_W matrices are constructed and transformed to the 2DPCA subspace, S_BB and S_WW, using the selected set of eigenvectors from S_t. Therefore, the dimensions of S_BB and S_WW are reduced significantly. Since the eigenvectors are statistically determined by S_BB and S_WW in the Fisherface method, are evaluated more accurately. As a result, 2D-FPCA is more suitable for small sample size problems (like face recognition) since S_BB and S_WW are quite small. The result is that 2D-FPCA is faster and yields greater recognition accuracy. The ORL database is used as a benchmark. The new algorithm achieves a recognition rate of 95.50% compared to the recognition rate of 90.00% for the Fisherface method.