Linear Discriminant Analysis and its Application to Face Identification.

In this thesis, we study and develop a linear discriminant analysis (LDA) feature based face identification approach that is fast, simple, and can be used in practical Personal Identity Recognition and Verification systems. This was achieved by combining face image geometric alignment, photometric normalisation, extraction of the reliable LDA subspace and a distinct matching strategy in the LDA subspace. Face image geometric normalisation employs a simple geometrical alignment based on the coordinates of two eyes. A template based eye detector was developed to localise the centre of two eyes automatically. The algorithmic techniques for the implementation of the LDA subspace in the context of face recognition and verification are investigated experimentally on four publicly available face databases (M2VTS, YALE, XM2VTS, HARVARD) using the Euclidean distance classifier. Three main algorithmic techniques: matrix transformation, the Cholesky factorisation and QR algorithm, the Kronecker canonical form and QZ algorithm are proposed and tested. The results consistently support that the implementation of LDA using the Kronecker canonical form and the QZ algorithm accomplishes the best performance in all experiments, confirming the theoretic advantage of the LDA features comparing with the PCA features in the capability of classification. Novel matching scores in the LDA subspace are proposed and tested on the XM2VTS database using the Lausanne protocol. The normalised correlation which is widely used in image processing and pattern recognition is applied in the LDA subspace for computing the matching score. It achieved satisfactory performance as compared with the Euclidean distance classifier. A detailed analysis of the reasons behind the success of the normalised correlation led to improved understanding of the role of metric in decision making and in turn that naturally resulted in a novel way of measuring the distance between a probe image and a model. By extensive experimental studies, this innovate metric is shown to be consistently superior to both the Euclidean distance and normalised correlation matching scores. Another novelty of this research work is the proposed one-dimensional client-specific linear discriminant analysis (CS-LDA) representation for face identification. The proposed approach provides two measures for authentication and the two decision scores are combined to achieve significant performance gains. Experimental results obtained on the XM2VTS database using the Lausanne protocol showed the superiority of this approach over any matching schemes in the conventional LDA subspace.