Fast Quaternion Algorithm for Face Recognition

Quaternions extend the concept of complex numbers and have significant applications in image processing, as they provide an efficient way to represent RGB images. One interesting application is face recognition, which aims to identify a person in a given image. In this paper, we propose an algorithm for face recognition that models images using quaternion matrices. To manage the large size of these matrices, our method projects them onto a carefully chosen subspace, reducing their dimensionality while preserving relevant information. An essential part of our algorithm is the novel Jacobi method we developed to solve the quaternion Hermitian eigenproblem. The algorithm’s effectiveness is demonstrated through numerical tests on a widely used database for face recognition. The results demonstrate that our approach, utilizing only a few eigenfaces, achieves comparable recognition accuracy. This not only enhances execution speed but also enables the processing of larger images. All algorithms are implemented in the Julia programming language, which allows for low execution times and the capability to handle larger image dimensions.