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Quaternion correlation filters for color face recognition

Face recognition has been an active research topic, and many algorithms have been proposed for grayscale face images. However, only a few methods take advantage of color in face images, even though most cameras produce color images and color can be beneficial for face recognition. Among the proposed color face recognition methods, most treat the three color channels separately and apply some grayscale face recognition methods to each of the channels and combine the results. In this paper we propose the quaternion correlation filter technique for color face recognition that processes all color channels jointly. Quaternion numbers are the generalization of the complex numbers and can be considered as a number with a real part and three orthogonal imaginary parts. A color image (e.g., in RGB) may be represented using quaternion representation by encoding the three color components in the imaginary parts of the quaternion number. The quaternion correlation filter is extended from the standard correlation filter based on the recently developed concepts of quaternion Fourier transform (QFT), quaternion convolution (QCV), and quaternion correlation (QC). Face recognition is performed by cross-correlating (QC) an input face image with a designed filter. Numerical results show that quaternion correlation filters can improve the recognition performance over conventional face recognition methods.