Quaternion principal component analysis of color images

IEEE International Conference on Image Processing

Volumn 1, Issue , 2003, Pages 809-812

  Le Bihan, Nicolas ^a   Sangwine, Stephen J ^b  

^a ENSIEG   (France)

^b UNIVERSITY OF ESSEX   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; EIGENVALUES AND EIGENFUNCTIONS; FOURIER TRANSFORMS; MATRIX ALGEBRA; PRINCIPAL COMPONENT ANALYSIS;

EIGENVALUE DECOMPOSITION (EVD); QUATERNION FIELDS;

COLOR IMAGE PROCESSING;

EID: 0344666580     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (13)

1. Hamilton W.R., "On quaternions," Proceeding of the Royal Irish Academy, Nov. 11, 1844.
2. Kantor I.L. and Solodovnikov A.S., Hypercomplex numbers, an elementary introduction to algebras, Springer-Verlag, 1989.
3. Pei S.-C. and Cheng C.-M., "A novel block truncation coding of color images by using quaternion-moment preserving principle," IEEE International Symposium on Circuits and systems, Atlanta, GA. 12-15 May, 1996, vol. 2, pp. 684-687.
4. Sangwine S.J., "Fourier transforms of colour images using quaternions, or hypercomplex, numbers," Electronics letters, vol. 32, no. 21, pp. 1979-1980, 1996.
5. Sangwine S.J. and Ell T.A., "Hypercomplex auto- and cross-correlation of color images," IEEE International Conference on Image Processing (ICIP'99), Kobe, Japan, 1999, number IV, pp. 319-322.
6. Sangwine S.J. Evans C.J. and Ell T.A., "Colour-sensitive edge detection using hypercomplex filters," Proceedings of the tenth European Signal Processing Conference (EUSIPCO), Tampere, Finland, 2000, vol. I, pp. 107-110.
7. S.J. Moxey E., Sangwine and T.A. Ell, "Hypercomplex operators and vector correlation," Proceedings of the eleventh European Signal Processing Conference (EUSIPCO), Toulouse, France, 2002, vol. III, pp. 247-250.
8. Zhang F., "Quaternions and matrices of quaternions," Linear algebra and its applications, vol. 251, pp. 21-57, 1997.
9. Le Bihan N. and Mars J., "Quaternion subspace method for vector-sensor wave separation," XI European Signal and Image Processing Conference (EUSIPCO), 2002.
10. Wolf L.A., "Similarity of matrices in which elements are real quaternions," Bull. Amer. Math. Soc., vol. 42, pp. 737-743, 1936.
11. Scharf L.L., Statistical Signal Processing, Détection, Estimation and Time Series Analysis, Electrical and computer engineering: digital signal processing. Addison Wesley, 1991.
12. Huang L. and So W., "On left eigenvalues of a quaternionic matrix," Linear algebra and its applications, vol. 323, pp. 105-116, 2001.
13. Liu L.-S, A study of polynomials, determinants, eigenvalues and numerical ranges over real quaternions. Phd thesis, university of hong-kong, 1997.