An Efficient Calculation of Quaternion Correlation of Signals and Color Images. (arXiv:2205.05113v1 [math.AC])

Web: http://arxiv.org/abs/2205.05113

Over the past century, a correlation has been an essential mathematical
technique utilized in engineering sciences, including practically every
signal/image processing field. This paper describes an effective method of
calculating the correlation function of signals and color images in quaternion
algebra. We propose using the quaternions with a commutative multiplication
operation and defining the corresponding correlation function in this
arithmetic. The correlation between quaternion signals and images can be
calculated by multiplying two quaternion DFTs of signals and images. The …

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