Color-grayscale image registration using hypercomplex phase correlation

Phase correlation has been used for the registration of grayscale images for the past 25 years. A previously published hypercomplex generalization of phase correlation has been applied to the registration of vector, or color, images. This paper demonstrates phase-correlation between a grayscale and a color image using the two possibilities for encoding the grayscale image in a quaternion image format. By implementing both the scalar and vector forms of the grayscale image this paper compares, for the first time, vector-vector to scalar-vector hypercomplex correlation. While both are found to give a similar performance, for this application, the analysis of the hypercomplex response finds that the inherent geometry of the quaternionic encoding hides the underlying processing and the phase and axis information. The choice of which method to employ in such applications should therefore be considered with due respect to the encoding of the data in either case.