Color Image Processing Using Reduced Biquaternions with Application to Face Recognition in a PCA Framework

In this paper, we present the theory of reduced biquaternion algebra to represent color images and to develop efficient vector processing methods. We apply this theory to the field of face recognition in a principal component analysis (PCA) framework. We develop a novel PCA method based on reduced biquaternion to make full use of the face color cues. Moreover, we derive new mathematical results on the computation of the eigenvalues/eigenvectors of the data scatter matrix. We also extend this method to two-dimensional color PCA to combine the face spatial and color information. Experiments on several public-domain color face benchmark datasets demonstrate the higher performance of the proposed methods compared to regular PCA and like methods.