Hypercomplex polar Fourier analysis for color image

Fourier transform is a significant tool in image processing and pattern recognition. By introducing hypercomplex number, hypercomplex Fourier transform [1] treats signal as vector field and generalizes conventional Fourier transform. Inspired from that, hypercomplex polar Fourier analysis is proposed in this paper. This work extends conventional polar Fourier analysis [5]. The proposed method can handle hypercomplex number represented signals like color image. The hypercom-plex polar Fourier analysis is reversible that means it can be used to reconstruct image. The hypercomplex polar Fourier descriptor has rotation invariance property that can be used for feature extraction. Due to the noncommutative property of quaternion multiplication, both left-side and right-side hypercomplex polar Fourier analysis are discussed and their relationships are also established in this paper. The experimental results on image reconstruction, rotation invariance and color plate test are given to illustrate the usefulness of the proposed method as an image analysis tool.