Perspectives on color image processing by linear vector methods using projective geometric transformations

Advances in Imaging and Electron Physics

Volumn 175, Issue , 2013, Pages 283-307

  Sangwine, Stephen J ^a  

^a UNIVERSITY OF ESSEX   (United Kingdom)

Author keywords

Color image processing; homogeneous coordinates; linear vector processing; projective geometry; vector image processing

Indexed keywords

COLOR; GEOMETRY; LINEAR TRANSFORMATIONS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; PROCESSING; VECTORS;

DESIGN OF ALGORITHMS; GEOMETRIC OPERATIONS; GEOMETRIC TRANSFORMATIONS; HOMOGENEOUS COORDINATES; LINEAR VECTORS; PROJECTIVE GEOMETRY; PROJECTIVE TRANSFORMATION; VECTOR IMAGES;

COLOR IMAGE PROCESSING;

EID: 84872871571     PISSN: 10765670     EISSN: None     Source Type: Book Series    
DOI: 10.1016/B978-0-12-407670-9.00006-8     Document Type: Chapter

References (33)

1. T. Batard, M. Berthier, and C. Saint-Jean Clifford Fourier transform for color image processing E.J. Bayro-Corrochano, G. Scheuermann, Geometric Algebra Computing 2010 Springer Verlag London 135 161
2. Blanc-Talon, J., Philips, W., Popescu, D., Scheunders, P. (Eds.). 2009. Advanced concepts for intelligent vision systems. Proceedings 11th International Conference, ACIVS 2009. Vol. 5807 of Lecture Notes in Computer Science: Image Processing, Computer Vision, Pattern Recognition, and Graphics, Bordeaux, France.
3. P. Denis, P. Carré, and C. Fernandez-Maloigne Spatial and spectral quaternionic approaches for colour images Computer Vision and Image Understanding 107 1-2 2007 74 87 (Pubitemid 46830975)
4. T.A. Ell Hypercomplex spectral transformations. Ph.D. thesis 1992 University of Minnesota
5. T.A. Ell On systems of linear quaternion functions. Preprint 2007 http://www.arxiv.org/abs/math/0702084v1 2007
6. T.A. Ell, and S.J. Sangwine Hypercomplex Fourier transforms of color images IEEE Transactions on Image Processing 16 1 2007 22 35 (Pubitemid 46437466)
7. T.A. Ell, and S.J. Sangwine Linear quaternion systems toolbox for Matlab software library, licensed under the GNU General Public License 2007 http://lqstfm.sourceforge. net/
8. T.A. Ell, and S.J. Sangwine Quaternion involutions and anti-involutions Computers and Mathematics with Applications 53 1 2007 137 143 (Pubitemid 46551682)
9. T.A. Ell, and S.J. Sangwine Theory of vector filters based on linear quaternion functions Proceedings of EUSIPCO 2008, 16th European Signal Processing Conference 2008 European Association for Signal Processing Lausanne, Switzerland 5
10. C.J. Evans, T.A. Ell, and S.J. Sangwine Hypercomplex color-sensitive smoothing filters IEEE International Conference on Image Processing (ICIP 2000) Vol. I 2000 Institute of Electrical and Electronics Engineers Vancouver, Canada 541 544 (Pubitemid 32465923)
11. R. Goldman Rethinking Quaternions: Theory and Computation. No. 13 in Synthesis Lectures on Computer Graphics and Animation 2010 Morgan & Claypool San Rafael, CA
12. R. Goldman Understanding quaternions Graphical Models 73 2 2011 21 49
13. D. Hestenes, and G. Sobczyk Clifford Algebra to Geometric Calculus 1984 D. Reidel Publishing Company Dordrecht
14. B.P. Ickes A new method for performing digital control system attitude computations using quaternions AIAA Journal 8 1 1970 13 17
15. J.R. Koza Human-competitive results produced by genetic programming Genetic Programming and Evolvable Machines 11 3-4 2010 251 284
16. B.E. Meserve Fundamental Concepts of Geometry 1983 Dover New York corrected reprint of 1959 edition
17. S.-C. Pei, J.-H. Chang, and J.-J. Ding Commutative reduced biquaternions and their Fourier transform for signal and image processing applications IEEE Transactions on Signal Processing 52 7 2004 2012 2031
18. S.-C. Pei, and C.M. Cheng Color image processing by using binary quaternion moment-preserving thresholding technique IEEE Transactions on Image Processing 8 5 1999 614 628
19. S.-C. Pei, J.-J. Ding, and J.-H. Chang Efficient implementation of quaternion Fourier transform, convolution, and correlation by 2-D complex FFT IEEE Transactions on Signal Processing 49 11 2001 2783 2797 (Pubitemid 33048447)
20. S. Said, N. Le Bihan, and S.J. Sangwine Fast complexified quaternion Fourier transform IEEE Transactions on Signal Processing 56 4 2008 1522 1531 (Pubitemid 351493846)
21. S.J. Sangwine Fourier transforms of colour images using quaternion, or hypercomplex, numbers Electronics Letters 32 21 1996 1979 1980 (Pubitemid 126606045)
22. S.J. Sangwine Colour image edge detector based on quaternion convolution Electronics Letters 34 10 1998 969 971 (Pubitemid 128560946)
23. S.J. Sangwine Canonic form of linear quaternion functions. Preprint 2008 http://arxiv.org/abs/arXiv:0801.2887
24. S.J. Sangwine, and T.A. Ell Colour image filters based on hypercomplex convolution IEE Proceedings-Vision, Image and Signal Processing 147 2 2000 89 93
25. S.J. Sangwine, and T.A. Ell The discrete Fourier transform of a colour image J.M. Blackledge, M.J. Turner, Image Processing II Mathematical Methods, Algorithms and Applications 2000 Horwood Publishing for Institute of Mathematics and its Applications Chichester 430 441 Proceedings of the Second IMA Conference on Image Processing, De Montfort University, Leicester, UK, September 1998.
26. S.J. Sangwine, and T.A. Ell Gray-centered RGB color space. In Second European Conference on Color in Graphics, Imaging and Vision (CGIV 2004) 2004 The Society for Imaging Science and Technology, Technology Center AGIT Aachen, Germany pp. 183-186
27. S.J. Sangwine, T.A. Ell, and B.N. Gatsheni Colour-dependent linear vector image filtering Proceedings of EUSIPCO 2004, XII European Signal Processing Conference Vol. I 2004 European Association for Signal Processing Vienna, Austria 585 588
28. S.J. Sangwine, B.N. Gatsheni, and T.A. Ell Linear colour-dependent image filtering based on vector decomposition Proceedings of EUSIPCO 2002, XI European Signal Processing Conference Vol. II 2002 European Association for Signal Processing Toulouse, France 274 277
29. S.J. Sangwine, B.N. Gatsheni, and T.A. Ell Vector amplification for color-dependent image filtering IEEE International Conference on Image Processing (ICIP 2003) Vol. 2 2003 Institute of Electrical and Electronics Engineers Barcelona, Spain 129 132
30. S.J. Sangwine, and N. Le Bihan Quaternion toolbox for Matlab. software library, licensed under the GNU General Public License 2005 http://qtfm. sourceforge.net/
31. L. Shi, and B. Funt Quaternion color texture segmentation Computer Vision and Image Understanding 107 1-2 2007 88 96 (Pubitemid 46829951)
32. University of Waterloo, Fractal Coding and Analysis Group Image repository digital image collection 2009 http://links.uwaterloo.ca/Repository. html
33. J.P. Ward Quaternions and Cayley Numbers: Algebra and Applications Vol. 403 of Mathematics and Its Applications 1997 Kluwer Dordrecht