An Efficient Calculation of Quaternion Correlation of Signals and Color Images

TL;DR

This paper introduces an efficient method for calculating quaternion correlation of signals and color images using a commutative quaternion algebra, simplifying the process and analyzing its computational complexity.

Contribution

It proposes a novel quaternion correlation method with commutative multiplication, enabling more efficient correlation computation for signals and color images.

Findings

Correlation calculation complexity is three times higher than in complex algebra.

The method simplifies quaternion correlation computation.

Effective for signal and color image processing.

Abstract

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 complexity of the correlation of color images is three times higher than in complex algebra.