Novel Algorithm for Polar and Spherical Fourier Analysis on Two and Three Dimensional Images

Zhuo YANG  Sei-ichiro KAMATA  

IEICE TRANSACTIONS on Information and Systems   Vol.E95-D   No.5   pp.1248-1255
Publication Date: 2012/05/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E95.D.1248
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Section on Recent Advances in Multimedia Signal Processing Techniques and Applications)
Category: Image Processing
polar Fourier analysis,  spherical Fourier analysis,  rotation invariant,  relative prime number,  image retrieval,  

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Polar and Spherical Fourier analysis can be used to extract rotation invariant features for image retrieval and pattern recognition tasks. They are demonstrated to show superiorities comparing with other methods on describing rotation invariant features of two and three dimensional images. Based on mathematical properties of trigonometric functions and associated Legendre polynomials, fast algorithms are proposed for multimedia applications like real time systems and large multimedia databases in order to increase the computation speed. The symmetric points are computed simultaneously. Inspired by relative prime number theory, systematic analysis are given in this paper. Novel algorithm is deduced that provide even faster speed. Proposed method are 9–15% faster than previous work. The experimental results on two and three dimensional images are given to illustrate the effectiveness of the proposed method. Multimedia signal processing applications that need real time polar and spherical Fourier analysis can be benefit from this work.