Hypercomplex polar Fourier analysis for color image

Zhuo Yang*, Sei Ichiro Kamata

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

11 Citations (Scopus)


Fourier transform is a significant tool in image processing and pattern recognition. By introducing hypercomplex number, hypercomplex Fourier transform [1] treats signal as vector field and generalizes conventional Fourier transform. Inspired from that, hypercomplex polar Fourier analysis is proposed in this paper. This work extends conventional polar Fourier analysis [5]. The proposed method can handle hypercomplex number represented signals like color image. The hypercom-plex 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 and color plate test are given to illustrate the usefulness of the proposed method as an image analysis tool.

Original languageEnglish
Title of host publicationICIP 2011
Subtitle of host publication2011 18th IEEE International Conference on Image Processing
Number of pages4
Publication statusPublished - 2011 Dec 1
Event2011 18th IEEE International Conference on Image Processing, ICIP 2011 - Brussels, Belgium
Duration: 2011 Sept 112011 Sept 14

Publication series

NameProceedings - International Conference on Image Processing, ICIP
ISSN (Print)1522-4880


Conference2011 18th IEEE International Conference on Image Processing, ICIP 2011


  • hy-percomplex polar Fourier descriptor
  • hypercomplex polar Fourier analysis
  • rotation invariance

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Signal Processing


Dive into the research topics of 'Hypercomplex polar Fourier analysis for color image'. Together they form a unique fingerprint.

Cite this