论文标题
有效计算信号和颜色图像的四个相关性
An Efficient Calculation of Quaternion Correlation of Signals and Color Images
论文作者
论文摘要
在过去的一个世纪中，相关性是工程科学中使用的必不可少的数学技术，包括几乎每个信号/图像处理领域。本文介绍了一种计算四元素代数中信号和颜色图像的相关函数的有效方法。我们建议使用以交换性乘法操作的四元素，并在此算术中定义相应的相关函数。四元信号和图像之间的相关性可以通过乘以两个信号和图像的Quaternion DFT来计算。颜色图像的相关性的复杂性比复杂代数高三倍。
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.
