Novel Algorithms for Fast Hypercomplex Fourier Transform and Hypercomplex Correlation with Applications

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.