IEICE TRANSACTIONS on Information
Hypercomplex Polar Fourier Analysis for Image Representation
Summary :
Fourier transform is a significant tool in image processing and pattern recognition. By introducing a hypercomplex number, hypercomplex Fourier transform treats a signal as a vector field and generalizes the conventional Fourier transform. Inspired from that, hypercomplex polar Fourier analysis that extends conventional polar Fourier analysis is proposed in this paper. The proposed method can handle signals represented by hypercomplex numbers as color images. The hypercomplex 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, color plate test and image retrieval are given to illustrate the usefulness of the proposed method as an image analysis tool.
- Publication
- IEICE TRANSACTIONS on Information Vol.E94-D No.8 pp.1663-1670
- Publication Date
- 2011/08/01
- Publicized
- Online ISSN
- 1745-1361
- DOI
- 10.1587/transinf.E94.D.1663
- Type of Manuscript
- PAPER
- Category
- Image Recognition, Computer Vision
Authors
Keyword
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Zhuo YANG, Sei-ichiro KAMATA, "Hypercomplex Polar Fourier Analysis for Image Representation" in IEICE TRANSACTIONS on Information,
vol. E94-D, no. 8, pp. 1663-1670, August 2011, doi: 10.1587/transinf.E94.D.1663.
Abstract: Fourier transform is a significant tool in image processing and pattern recognition. By introducing a hypercomplex number, hypercomplex Fourier transform treats a signal as a vector field and generalizes the conventional Fourier transform. Inspired from that, hypercomplex polar Fourier analysis that extends conventional polar Fourier analysis is proposed in this paper. The proposed method can handle signals represented by hypercomplex numbers as color images. The hypercomplex 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, color plate test and image retrieval are given to illustrate the usefulness of the proposed method as an image analysis tool.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E94.D.1663/_p
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@ARTICLE{e94-d_8_1663,
author={Zhuo YANG, Sei-ichiro KAMATA, },
journal={IEICE TRANSACTIONS on Information},
title={Hypercomplex Polar Fourier Analysis for Image Representation},
year={2011},
volume={E94-D},
number={8},
pages={1663-1670},
abstract={Fourier transform is a significant tool in image processing and pattern recognition. By introducing a hypercomplex number, hypercomplex Fourier transform treats a signal as a vector field and generalizes the conventional Fourier transform. Inspired from that, hypercomplex polar Fourier analysis that extends conventional polar Fourier analysis is proposed in this paper. The proposed method can handle signals represented by hypercomplex numbers as color images. The hypercomplex 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, color plate test and image retrieval are given to illustrate the usefulness of the proposed method as an image analysis tool.},
keywords={},
doi={10.1587/transinf.E94.D.1663},
ISSN={1745-1361},
month={August},}
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TY - JOUR
TI - Hypercomplex Polar Fourier Analysis for Image Representation
T2 - IEICE TRANSACTIONS on Information
SP - 1663
EP - 1670
AU - Zhuo YANG
AU - Sei-ichiro KAMATA
PY - 2011
DO - 10.1587/transinf.E94.D.1663
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E94-D
IS - 8
JA - IEICE TRANSACTIONS on Information
Y1 - August 2011
AB - Fourier transform is a significant tool in image processing and pattern recognition. By introducing a hypercomplex number, hypercomplex Fourier transform treats a signal as a vector field and generalizes the conventional Fourier transform. Inspired from that, hypercomplex polar Fourier analysis that extends conventional polar Fourier analysis is proposed in this paper. The proposed method can handle signals represented by hypercomplex numbers as color images. The hypercomplex 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, color plate test and image retrieval are given to illustrate the usefulness of the proposed method as an image analysis tool.
ER -
English
