2D quaternion Fourier spectral analysis and its applications

Author

Chang, Ja-Han ; Pei, Soo-Chang ; Ding, Jian-Jiun

Author_Institution

Dept. of Electr. Eng., National Taiwan Univ., Taipei, Taiwan

Volume

3

fYear

2004

fDate

23-26 May 2004

Abstract

Hypercomplex Fourier transforms based on quaternions have been used for gray and color image processing. In this paper, we present the relations between the quaternion Fourier spectral coefficients. Using these relations, we can separate the scalar and vector part of quaternion image for frequency domain and find the constraints of the Fourier spectral coefficients which the quaternion Fourier transform of these spectral coefficients will have zero scalar part. In addition, we can calculate the DQFT of four real images, or the DQFT of two complex images by only one DQFT and we can design a color cosine image from frequency domain. Finally, we discuss the property of the DQFT of a causal image.

Keywords

Fourier transforms; frequency-domain analysis; image processing; spectral analysis; 2D quaternion; DQFT; Fourier spectral analysis; Fourier spectral coefficients; causal image; color cosine image; color image processing; complex images; frequency domain; gray image processing; hypercomplex Fourier transforms; quaternion Fourier transform; quaternion image; real images; zero scalar; Acceleration; Color; Convolution; Fourier transforms; Frequency domain analysis; Image analysis; Image processing; Quaternions; Signal processing; Spectral analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 2004. ISCAS '04. Proceedings of the 2004 International Symposium on

Print_ISBN

0-7803-8251-X

Type

conf

DOI

10.1109/ISCAS.2004.1328728

Filename

1328728