超复数把彩色图像作为一个矢量整体进行处理,与传统算法相比,它能更好地描述图像的色彩关联,超复数互相关已广泛应用到彩色图像处理的各个领域.本文首先分析和介绍了目前的实现二维超复数傅氏变换和超复数互相关的快速方法,然后通过把超复数按实部和各个虚部展开,分别进行传统的快速傅氏变换,再把对应的单位虚向量还原,从而为超复数傅氏变换和超复数互相关提出了一种新的快速算法.分析表明:本文提出的方法比目前现有的方法更简单易行,且计算量更小.最后,本文介绍了我们把超复数互相关技术应用到彩色目标跟踪上获得的一些新结果.

Hypercomplexs encode the red,green and blue channels of a color image as a whole vector for the follow processing.Comparing with the traditional methods,the hypercomplex processing methods can better describe the intrinsic color relationships of images.Hypercomplex correlation techniques have been widely used in many applications of color image processing.This paper analyzes and introduces the fast algorithms of the 2-D hypercomplex Fourier transform and hypercomplex correlation by using the traditional complex fast Fourier transforms.And our novel algorithms are proposed,which respectively calculate each part Fourier transform by FFT algorithm by means of separating a hypercomplex into a real part and other imaginary parts.When reverting the corresponding unit imaginary operators and combining the results of the real and imaginary parts Fourier transforms,we can get the hypercomplex results.The analytical results show that our algorithms are easier to implement and have less computing complexity than the known fast algorithms.Finally some new results by applying hypercomplex correlation into object tracking are introduced.