Hypercomplex Polar Fourier Analysis for Image Representation

Zhuo YANG  Sei-ichiro KAMATA  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E94-D   No.8   pp.1663-1670
Publication Date: 2011/08/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E94.D.1663
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Image Recognition, Computer Vision
Keyword: 
hypercomplex polar Fourier analysis,  hypercomplex polar Fourier descriptor,  rotation invariance,  image representation,  

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Summary: 
Fourier transform is a significant tool in image processing and pattern recognition. By introducing a hypercomplex number, hypercomplex Fourier transform treats a signal as a vector field and generalizes the conventional Fourier transform. Inspired from that, hypercomplex polar Fourier analysis that extends conventional polar Fourier analysis is proposed in this paper. The proposed method can handle signals represented by hypercomplex numbers as color images. The hypercomplex 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, color plate test and image retrieval are given to illustrate the usefulness of the proposed method as an image analysis tool.