Novel algorithm for polar and spherical fourier analysis on two and three dimensional images

Zhuo Yang*, Sei Ichiro Kamata

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1248-1255
Number of pages8
JournalIEICE Transactions on Information and Systems
Issue number5
Publication statusPublished - 2012 May


  • Image retrieval
  • Polar Fourier analysis
  • Relative prime number
  • Rotation invariant
  • Spherical Fourier analysis

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering
  • Artificial Intelligence


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