Fast Polar and Spherical Fourier Descriptors for Feature Extraction

Zhuo YANG  Sei-ichiro KAMATA  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E93-D   No.7   pp.1708-1715
Publication Date: 2010/07/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E93.D.1708
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Section on Machine Vision and its Applications)
Category: 
Keyword: 
polar fourier descriptor,  spherical Fourier descriptor,  rotation invariant,  image retrieval,  fast algorithm,  

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Summary: 
Polar Fourier Descriptor(PFD) and Spherical Fourier Descriptor(SFD) are rotation invariant feature descriptors for two dimensional(2D) and three dimensional(3D) image retrieval and pattern recognition tasks. They are demonstrated to show superiorities compared with other methods on describing rotation invariant features of 2D and 3D images. However in order to increase the computation speed, fast computation method is needed especially for machine vision applications like realtime systems, limited computing environments and large image databases. This paper presents fast computation method for PFD and SFD that are deduced based on mathematical properties of trigonometric functions and associated Legendre polynomials. Proposed fast PFD and SFD are 8 and 16 times faster than direct calculation that significantly boost computation process. Furthermore, the proposed methods are also compact for memory requirements for storing PFD and SFD basis in lookup tables. The experimental results on both synthetic and real data are given to illustrate the efficiency of the proposed method.