Fast Quaternion Algorithm for Face Recognition

Anita Carević and Ivan Slapničar ()
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Anita Carević: Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Rudjera Boškovića 32, 21000 Split, Croatia
Ivan Slapničar: Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Rudjera Boškovića 32, 21000 Split, Croatia

Mathematics, 2025, vol. 13, issue 12, 1-18

Abstract: 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.

Keywords: quaternion matrices; quaternion eigenvalue problem; face recognition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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