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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 2 — Feb. 1, 2006
  • pp: 247–257

Processing halftone color images by vector space methods

Li Liu, Yongyi Yang, and Henry Stark  »View Author Affiliations

JOSA A, Vol. 23, Issue 2, pp. 247-257 (2006)

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The reproduction of color images by color halftoning can be characterized by the Neugebauer model/equation. However, the Neugebauer equation is not easy to solve because of the highly nonlinear relationship between the underlying Neugebauer primaries and the colorants. We attempt to solve the Neugebauer equation by vector space methods. The proposed method of solution is applicable to any number of colorants, although our experimental results are confined to the CMY and CMYK cases. Among the constraints we consider are those related to a bound on the permissible amount of total ink and a bound on the total cost of applying colorants to achieve a satisfactory level of color reproduction. Our results demonstrate that the vector space method is a feasible approach for solving for the required amounts of colorants in the constrained color halftoning problem.

© 2006 Optical Society of America

OCIS Codes
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(100.2810) Image processing : Halftone image reproduction
(330.1690) Vision, color, and visual optics : Color

ToC Category:
Image Processing

Original Manuscript: April 1, 2005
Revised Manuscript: June 16, 2005
Manuscript Accepted: June 18, 2005

Virtual Issues
Vol. 1, Iss. 3 Virtual Journal for Biomedical Optics

Li Liu, Yongyi Yang, and Henry Stark, "Processing halftone color images by vector space methods," J. Opt. Soc. Am. A 23, 247-257 (2006)

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  1. J. A. C. Yule, Principles of Color Reproduction (Wiley, 1967).
  2. H. R. Kang, Digital Color Halftoning (SPIE, 1999).
  3. H. E. J. Neugebauer, "Die Theoretischen Grundlagen des Mehrfarbenbuchdrucks (The theoretical foundation for multicolor printing)," Z. Wiss. Photogr. 36, 73-89 (1937).
  4. Adobe ICC Profiles (Adobe, 2003), http://www.adobe.com/support/downloads.
  5. E. J. Giorgianni and T. E. Madden, Digital Color Management (Addison-Wesley, 1998).
  6. L. Liu, Y. Yang, and H. Stark, "Spatial processing in color reproduction," J. Opt. Soc. Am. A 8, 1482-1491 (2005). [CrossRef]
  7. H. J. Trussell, "Application of set theoretic methods to color system," Color Res. Appl. 16, 31-64 (1991). [CrossRef]
  8. Y. Yang and H. Stark, "Solutions of several color-matching problems using projection theory," J. Opt. Soc. Am. A 11, 89-96 (1994). [CrossRef]
  9. G. Sharma and H. J. Trussell, "Set theoretic estimation in color scanner characterization," J. Electron. Imaging 5, 479-489 (1996). [CrossRef]
  10. G. Sharma, "Set theoretic estimation for problems in subtractive color," Color Res. Appl. 25, 333-348 (2000). [CrossRef]
  11. H. Stark and Y. Yang, Vector Space Projections: A Numerical Approach to Signal and Image Processing, Neural Nets, and Optics, Wiley Series in Telecommunications and Signal Processing (Wiley,1998). [PubMed]
  12. I. Pobboravsky and M. Pearson, "Computation of dot areas required to match a colorimetrically specified color using the modified Neugebauer equations," in Proceedings 1972 of Technical Association of Graphics Arts (Technical Association of Graphics Arts, 1972), pp. 65-77.
  13. M. Mahy, "Color separation method and apparatus for same," U.S. patent 5,878,195 (2 March 1999).
  14. R. K. Molla, Electronic Color Separation (R. K. Printing & Publishing, 1988).
  15. A. Levi and H. Stark, "Image restoration by the method of generalized projections with application to restoration from magnitude," J. Opt. Soc. Am. A 1, 932-943 (1984). [CrossRef]
  16. D. C. Youla, "Generalized image restoration by the method of alternating orthogonal projections," IEEE Trans. Circuits Syst. 25, 694-702 (1978). [CrossRef]
  17. D. C. Youla and H. Webb, "Image restoration by the method of convex projections: part 1--theory," IEEE Trans. Med. Imaging MI-1, 81-94 (1982). [CrossRef]
  18. M. I. Sezan and H. Stark, "Image restoration by the method of convex projections: part 2--applications," IEEE Trans. Med. Imaging MI-1, 95-101 (1982). [CrossRef]
  19. A. Levi and H. Stark, "Signal restoration from phase by projections onto convex sets," J. Opt. Soc. Am. 73, 810-822 (1983). [CrossRef]
  20. P. L. Combettes, "The foundations of set theoretic estimation," Proc. IEEE 81, 182-208 (1993). [CrossRef]
  21. H. J. Trussell and M. Civanlar, "The feasible solution in signal restoration," IEEE Trans. Acoust., Speech, Signal Process. 32, 201-212 (1984). [CrossRef]
  22. J. P. Allebach, "Reconstruction of continuous-tone from halftone by projections onto convex sets," in Proceedings of the 1988 International Conference on Advances in Communication and Control Systems (Optimization Software, 1988), pp. 469-478.
  23. Y. Yang and N. P. Galatsanos, "Removal of compression artifacts using projections onto convex sets and line process modeling," IEEE Trans. Image Process. 6, 1345-1357 (1997). [CrossRef] [PubMed]
  24. P. L. Combettes and J. C. Pesquet, "Image restoration subject to a total variation constraint," IEEE Trans. Image Process. 13, 1213-1222 (2004). [CrossRef] [PubMed]
  25. K. Sayanagi, "Black printer, UCR and UCA--gray component replacement," in Proceedings 1987 of Technical Association of Graphics Arts (Technical Association of Graphics Arts, 1987), pp. 711-724.
  26. ICC Specification ICC.1:2004-04 : Image Technology Colour Management--Architecture, Profile Format, and Data Structure (International Color Consortium, 2004). [PubMed]

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