Fast Hypercomplex Polar Fourier Analysis

Zhuo YANG  Sei-ichiro KAMATA  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E95-D   No.4   pp.1166-1169
Publication Date: 2012/04/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E95.D.1166
Print ISSN: 0916-8532
Type of Manuscript: LETTER
Category: Image Processing and Video Processing
Keyword: 
fast hypercomplex polar Fourier analysis,  hypercomplex polar Fourier analysis,  Fourier analysis,  

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Summary: 
Hypercomplex polar Fourier analysis treats a signal as a vector field and generalizes the conventional polar Fourier analysis. It can handle signals represented by hypercomplex numbers such as color images. Hypercomplex polar Fourier analysis is reversible that means it can reconstruct image. Its coefficient has rotation invariance property that can be used for feature extraction. However in order to increase the computation speed, fast algorithm is needed especially for image processing applications like realtime systems and limited resource platforms. This paper presents fast hypercomplex polar Fourier analysis based on symmetric properties and mathematical properties of trigonometric functions. Proposed fast hypercomplex polar Fourier analysis computes symmetric points simultaneously, which significantly reduce the computation time.