Abstract

We consider the reproduction of color subject to material and neighborhood constraints. By “material constraints,” we mean any constraints that are applied to the amount of ink, lights, voltages, and currents that are used in the generation of color. In the first instance we consider the problem of reproducing a target color constrained by maximum additive color signals, such as in the phosphorescence process in a cathode ray tube. In the second instance we consider the more difficult problem of reproducing color subject to constraints on the maximum primary color variations in a (spatial) neighborhood. We introduce the idea of adjacent color variance (ACV) and then attempt to reproduce colors subject to an upper bound on the ACV. An algorithm that is suitable for this task is the method of vector space projections (VSP). In order to use VSP for constrained color reproduction, we use a novel approach to linearize nonlinear CIE-Lab space constraints. Experimental results are furnished that demonstrate that using the ACV as a bound helps to reduce reproduction artifacts in a color image.

© 2005 Optical Society of America

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References

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  1. R. W.G. Hunt, Measuring Color (Wiley, 1987).
  2. G. Wyszecki, W. S. Sitles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, 2000).
  3. Colorimetry, CIE Publication No. 15.2 (Central Bureau of the CIE, 1986).
  4. R. Bala, “Inverse problems in color device characterization,” in Computational Imaging, C. A. Bouman and R. L. Stevenson, eds., Proc. SPIE5016, 185–195 (2003).
    [CrossRef]
  5. P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).
  6. H. E.J. Neugebauer, “Die Theoretischen Grundlagen des Mehrfarbenbuchdrucks (The theoretical foundation for multicolor printing),” Z. Wissenschaftliche Photogr. 36(4), pp. 73–89, 1937).
  7. ICC Profile Format Specification V3.4 (International Color Consortium, 1997).
  8. M. R. Gupta, “An information theory approach to supervised learning,” Ph.D. thesis (Stanford University, 2003).
  9. C-Y. Tsai, M.-J. Liaw, H.-P. D. Shieh, “Color reproduction of twist nematic LCD by polynomial regression applied in primary-invariance model,” in Proceedings of the 5th Asian Symposium on Information Display (IEEE, 1999), pp. 115–118).
  10. G. Sharma, Digital Color Imaging Handbook (CRC Press, 2002).
    [CrossRef]
  11. H. R. Kang, Digital Color Halftoning (SPIE, 1999).
  12. G. Sharma, H. J. Trussell, “Set theoretic estimation in color scanner characterization,” J. Electron. Imaging 5, 479–489 (1996).
    [CrossRef]
  13. G. Sharma, “Set theoretic estimation for problems in subtractive color,” Color Res. Appl. 25, 333–348 (2000).
    [CrossRef]
  14. M. D. Fairchild, “A simple printer calibration technique for ‘good enough’ color reproduction of CRT images,” Munsell Color Science Laboratory Technical Report (Munsell Laboratory, Rochester Institute of Technology, 1994).
  15. R. Bala, R. Eschbac, “Reducing multi-separation color moire by a variable under color removal and gray component replacement strategy,” J. Imaging Sci. Technol. 45(2), 152–160 (2001).
  16. S. Tominaga, “A color mapping method for CMYK printers and its evaluation,” in Proceeding of the 4th IS&T/SID Color Imaging Conference (Society for Imaging Science and Technology, 1995), pp. 172–176.
  17. T. J. Cholewo, “Printer model inversion by constrained optimization,” in Color Imaging: Device Independent Color, Color Hardcopy and Graphic Arts V, R. Eschbach and G. G. Marcu, eds., Proc. SPIE3963, pp. 349–357 (2000).
  18. J. A.C. Yule, Principles of Color Reproduction (Wiley, 1967).
  19. I. Pobboravsky, 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).
  20. M. Mahy, “Color separation method and apparatus for same,” U.S. Patent 5,878,195 (March 2, 1999).
  21. G. Sharma, M. J. Vrhel, H. J. Trussell, “Color imaging for multimedia,” in Proc. IEEE 86, 1088–1108 (1998).
    [CrossRef]
  22. A. Levi, H. Stark, “Signal restoration from phase by projections onto convex sets,” J. Opt. Soc. Am. 73, 810–822 (1983).
    [CrossRef]
  23. D. C. Youla, “Generalized image restoration by the method of alternating orthogonal projections,” IEEE Trans. Circuits Syst. 25, 694–702 (1978).
    [CrossRef]
  24. D. C. Youla, H. Webb, “Image restoration by the method of convex projections: part 1—theory,” IEEE Trans. Med. Imaging MI-1, 81–94 (1982).
    [CrossRef]
  25. M. I. Sezan, H. Stark, “Image restoration by the method of convex projections: part 2—applications,” IEEE Trans. Med. Imaging MI-1, 95–101 (1982).
    [CrossRef]
  26. A. Levi, “Image restoration by the method of projections with applications to the phase and magnitude retrieval problem,” Ph.D. thesis (Rensselaer Polytechnic Institute, 1983).
  27. H. Stark, 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).
  28. P. L. Combettes, “The foundations of set theoretic estimation,” Proc. IEEE 81, 182–208 (1993).
    [CrossRef]
  29. H. J. Trussell, M. Civanlar, “The feasible solution in signal restoration,” IEEE Trans. Acoust. Speech, Signal Process. 32, 201–212 (1984).
    [CrossRef]
  30. P. L. Combettes, J. C. Pesquet, “Image restoration subject to a total variation constraint,” IEEE Trans. Image Process. 13, 1213–1222 (2004).
    [CrossRef] [PubMed]
  31. 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 Inc., 1988), pp. 469–478.
  32. H. J. Trussell, “Application of set theoretic methods to color system,” Color Res. Appl. 16, 31–64 (1991).
    [CrossRef]
  33. Y. Yang, H. Stark, “Solutions of several color-matching problems using projection theory,” J. Opt. Soc. Am. A 11, 89–96 (1994).
    [CrossRef]
  34. M. C. Stone, W. B. Cowan, J. C. Beatty, “Color gamut mapping and the printing of digital color images,” ACM Trans. Graphics 7, 249–292 (1988).
    [CrossRef]
  35. S. Suzuki, M. Shimizu, S. Semba, “High-accuracy color reproduction (color management systems),” Fujitsu Sci. Tech. J. 35, 240–247 (1999).
  36. E. J. Stollnitz, V. Ostromoukhov, D. H. Salesin, “Reproducing color images using custom inks,” in Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 1998), pp. 267–274.
  37. Y. Yang, H. Stark, “Probability density function estimation using convex projections,” in Signal Processing Methods for Audio, Images and Telecommunications, P. Clarkson and H. Stark, eds. (Academic, 1994), Chap. 10.
  38. Y. Yang, 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]

2004 (1)

P. L. Combettes, J. C. Pesquet, “Image restoration subject to a total variation constraint,” IEEE Trans. Image Process. 13, 1213–1222 (2004).
[CrossRef] [PubMed]

2001 (1)

R. Bala, R. Eschbac, “Reducing multi-separation color moire by a variable under color removal and gray component replacement strategy,” J. Imaging Sci. Technol. 45(2), 152–160 (2001).

2000 (1)

G. Sharma, “Set theoretic estimation for problems in subtractive color,” Color Res. Appl. 25, 333–348 (2000).
[CrossRef]

1999 (1)

S. Suzuki, M. Shimizu, S. Semba, “High-accuracy color reproduction (color management systems),” Fujitsu Sci. Tech. J. 35, 240–247 (1999).

1998 (1)

G. Sharma, M. J. Vrhel, H. J. Trussell, “Color imaging for multimedia,” in Proc. IEEE 86, 1088–1108 (1998).
[CrossRef]

1997 (1)

Y. Yang, 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]

1996 (1)

G. Sharma, H. J. Trussell, “Set theoretic estimation in color scanner characterization,” J. Electron. Imaging 5, 479–489 (1996).
[CrossRef]

1994 (1)

1993 (1)

P. L. Combettes, “The foundations of set theoretic estimation,” Proc. IEEE 81, 182–208 (1993).
[CrossRef]

1991 (1)

H. J. Trussell, “Application of set theoretic methods to color system,” Color Res. Appl. 16, 31–64 (1991).
[CrossRef]

1988 (1)

M. C. Stone, W. B. Cowan, J. C. Beatty, “Color gamut mapping and the printing of digital color images,” ACM Trans. Graphics 7, 249–292 (1988).
[CrossRef]

1984 (1)

H. J. Trussell, M. Civanlar, “The feasible solution in signal restoration,” IEEE Trans. Acoust. Speech, Signal Process. 32, 201–212 (1984).
[CrossRef]

1983 (1)

1982 (2)

D. C. Youla, H. Webb, “Image restoration by the method of convex projections: part 1—theory,” IEEE Trans. Med. Imaging MI-1, 81–94 (1982).
[CrossRef]

M. I. Sezan, H. Stark, “Image restoration by the method of convex projections: part 2—applications,” IEEE Trans. Med. Imaging MI-1, 95–101 (1982).
[CrossRef]

1978 (1)

D. C. Youla, “Generalized image restoration by the method of alternating orthogonal projections,” IEEE Trans. Circuits Syst. 25, 694–702 (1978).
[CrossRef]

1937 (1)

H. E.J. Neugebauer, “Die Theoretischen Grundlagen des Mehrfarbenbuchdrucks (The theoretical foundation for multicolor printing),” Z. Wissenschaftliche Photogr. 36(4), pp. 73–89, 1937).

1931 (1)

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

Allebach, J. P.

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 Inc., 1988), pp. 469–478.

Bala, R.

R. Bala, R. Eschbac, “Reducing multi-separation color moire by a variable under color removal and gray component replacement strategy,” J. Imaging Sci. Technol. 45(2), 152–160 (2001).

R. Bala, “Inverse problems in color device characterization,” in Computational Imaging, C. A. Bouman and R. L. Stevenson, eds., Proc. SPIE5016, 185–195 (2003).
[CrossRef]

Beatty, J. C.

M. C. Stone, W. B. Cowan, J. C. Beatty, “Color gamut mapping and the printing of digital color images,” ACM Trans. Graphics 7, 249–292 (1988).
[CrossRef]

Cholewo, T. J.

T. J. Cholewo, “Printer model inversion by constrained optimization,” in Color Imaging: Device Independent Color, Color Hardcopy and Graphic Arts V, R. Eschbach and G. G. Marcu, eds., Proc. SPIE3963, pp. 349–357 (2000).

Civanlar, M.

H. J. Trussell, M. Civanlar, “The feasible solution in signal restoration,” IEEE Trans. Acoust. Speech, Signal Process. 32, 201–212 (1984).
[CrossRef]

Combettes, P. L.

P. L. Combettes, J. C. Pesquet, “Image restoration subject to a total variation constraint,” IEEE Trans. Image Process. 13, 1213–1222 (2004).
[CrossRef] [PubMed]

P. L. Combettes, “The foundations of set theoretic estimation,” Proc. IEEE 81, 182–208 (1993).
[CrossRef]

Cowan, W. B.

M. C. Stone, W. B. Cowan, J. C. Beatty, “Color gamut mapping and the printing of digital color images,” ACM Trans. Graphics 7, 249–292 (1988).
[CrossRef]

Eschbac, R.

R. Bala, R. Eschbac, “Reducing multi-separation color moire by a variable under color removal and gray component replacement strategy,” J. Imaging Sci. Technol. 45(2), 152–160 (2001).

Fairchild, M. D.

M. D. Fairchild, “A simple printer calibration technique for ‘good enough’ color reproduction of CRT images,” Munsell Color Science Laboratory Technical Report (Munsell Laboratory, Rochester Institute of Technology, 1994).

Galatsanos, N. P.

Y. Yang, 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]

Gupta, M. R.

M. R. Gupta, “An information theory approach to supervised learning,” Ph.D. thesis (Stanford University, 2003).

Hunt, R. W.G.

R. W.G. Hunt, Measuring Color (Wiley, 1987).

Kang, H. R.

H. R. Kang, Digital Color Halftoning (SPIE, 1999).

Kubelka, P.

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

Levi, A.

A. Levi, H. Stark, “Signal restoration from phase by projections onto convex sets,” J. Opt. Soc. Am. 73, 810–822 (1983).
[CrossRef]

A. Levi, “Image restoration by the method of projections with applications to the phase and magnitude retrieval problem,” Ph.D. thesis (Rensselaer Polytechnic Institute, 1983).

Liaw, M.-J.

C-Y. Tsai, M.-J. Liaw, H.-P. D. Shieh, “Color reproduction of twist nematic LCD by polynomial regression applied in primary-invariance model,” in Proceedings of the 5th Asian Symposium on Information Display (IEEE, 1999), pp. 115–118).

Mahy, M.

M. Mahy, “Color separation method and apparatus for same,” U.S. Patent 5,878,195 (March 2, 1999).

Munk, F.

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

Neugebauer, H. E.J.

H. E.J. Neugebauer, “Die Theoretischen Grundlagen des Mehrfarbenbuchdrucks (The theoretical foundation for multicolor printing),” Z. Wissenschaftliche Photogr. 36(4), pp. 73–89, 1937).

Ostromoukhov, V.

E. J. Stollnitz, V. Ostromoukhov, D. H. Salesin, “Reproducing color images using custom inks,” in Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 1998), pp. 267–274.

Pearson, M.

I. Pobboravsky, 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).

Pesquet, J. C.

P. L. Combettes, J. C. Pesquet, “Image restoration subject to a total variation constraint,” IEEE Trans. Image Process. 13, 1213–1222 (2004).
[CrossRef] [PubMed]

Pobboravsky, I.

I. Pobboravsky, 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).

Salesin, D. H.

E. J. Stollnitz, V. Ostromoukhov, D. H. Salesin, “Reproducing color images using custom inks,” in Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 1998), pp. 267–274.

Semba, S.

S. Suzuki, M. Shimizu, S. Semba, “High-accuracy color reproduction (color management systems),” Fujitsu Sci. Tech. J. 35, 240–247 (1999).

Sezan, M. I.

M. I. Sezan, H. Stark, “Image restoration by the method of convex projections: part 2—applications,” IEEE Trans. Med. Imaging MI-1, 95–101 (1982).
[CrossRef]

Sharma, G.

G. Sharma, “Set theoretic estimation for problems in subtractive color,” Color Res. Appl. 25, 333–348 (2000).
[CrossRef]

G. Sharma, M. J. Vrhel, H. J. Trussell, “Color imaging for multimedia,” in Proc. IEEE 86, 1088–1108 (1998).
[CrossRef]

G. Sharma, H. J. Trussell, “Set theoretic estimation in color scanner characterization,” J. Electron. Imaging 5, 479–489 (1996).
[CrossRef]

G. Sharma, Digital Color Imaging Handbook (CRC Press, 2002).
[CrossRef]

Shieh, H.-P. D.

C-Y. Tsai, M.-J. Liaw, H.-P. D. Shieh, “Color reproduction of twist nematic LCD by polynomial regression applied in primary-invariance model,” in Proceedings of the 5th Asian Symposium on Information Display (IEEE, 1999), pp. 115–118).

Shimizu, M.

S. Suzuki, M. Shimizu, S. Semba, “High-accuracy color reproduction (color management systems),” Fujitsu Sci. Tech. J. 35, 240–247 (1999).

Sitles, W. S.

G. Wyszecki, W. S. Sitles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, 2000).

Stark, H.

Y. Yang, H. Stark, “Solutions of several color-matching problems using projection theory,” J. Opt. Soc. Am. A 11, 89–96 (1994).
[CrossRef]

A. Levi, H. Stark, “Signal restoration from phase by projections onto convex sets,” J. Opt. Soc. Am. 73, 810–822 (1983).
[CrossRef]

M. I. Sezan, H. Stark, “Image restoration by the method of convex projections: part 2—applications,” IEEE Trans. Med. Imaging MI-1, 95–101 (1982).
[CrossRef]

H. Stark, 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).

Y. Yang, H. Stark, “Probability density function estimation using convex projections,” in Signal Processing Methods for Audio, Images and Telecommunications, P. Clarkson and H. Stark, eds. (Academic, 1994), Chap. 10.

Stollnitz, E. J.

E. J. Stollnitz, V. Ostromoukhov, D. H. Salesin, “Reproducing color images using custom inks,” in Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 1998), pp. 267–274.

Stone, M. C.

M. C. Stone, W. B. Cowan, J. C. Beatty, “Color gamut mapping and the printing of digital color images,” ACM Trans. Graphics 7, 249–292 (1988).
[CrossRef]

Suzuki, S.

S. Suzuki, M. Shimizu, S. Semba, “High-accuracy color reproduction (color management systems),” Fujitsu Sci. Tech. J. 35, 240–247 (1999).

Tominaga, S.

S. Tominaga, “A color mapping method for CMYK printers and its evaluation,” in Proceeding of the 4th IS&T/SID Color Imaging Conference (Society for Imaging Science and Technology, 1995), pp. 172–176.

Trussell, H. J.

G. Sharma, M. J. Vrhel, H. J. Trussell, “Color imaging for multimedia,” in Proc. IEEE 86, 1088–1108 (1998).
[CrossRef]

G. Sharma, H. J. Trussell, “Set theoretic estimation in color scanner characterization,” J. Electron. Imaging 5, 479–489 (1996).
[CrossRef]

H. J. Trussell, “Application of set theoretic methods to color system,” Color Res. Appl. 16, 31–64 (1991).
[CrossRef]

H. J. Trussell, M. Civanlar, “The feasible solution in signal restoration,” IEEE Trans. Acoust. Speech, Signal Process. 32, 201–212 (1984).
[CrossRef]

Tsai, C-Y.

C-Y. Tsai, M.-J. Liaw, H.-P. D. Shieh, “Color reproduction of twist nematic LCD by polynomial regression applied in primary-invariance model,” in Proceedings of the 5th Asian Symposium on Information Display (IEEE, 1999), pp. 115–118).

Vrhel, M. J.

G. Sharma, M. J. Vrhel, H. J. Trussell, “Color imaging for multimedia,” in Proc. IEEE 86, 1088–1108 (1998).
[CrossRef]

Webb, H.

D. C. Youla, H. Webb, “Image restoration by the method of convex projections: part 1—theory,” IEEE Trans. Med. Imaging MI-1, 81–94 (1982).
[CrossRef]

Wyszecki, G.

G. Wyszecki, W. S. Sitles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, 2000).

Yang, Y.

Y. Yang, 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]

Y. Yang, H. Stark, “Solutions of several color-matching problems using projection theory,” J. Opt. Soc. Am. A 11, 89–96 (1994).
[CrossRef]

Y. Yang, H. Stark, “Probability density function estimation using convex projections,” in Signal Processing Methods for Audio, Images and Telecommunications, P. Clarkson and H. Stark, eds. (Academic, 1994), Chap. 10.

H. Stark, 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).

Youla, D. C.

D. C. Youla, H. Webb, “Image restoration by the method of convex projections: part 1—theory,” IEEE Trans. Med. Imaging MI-1, 81–94 (1982).
[CrossRef]

D. C. Youla, “Generalized image restoration by the method of alternating orthogonal projections,” IEEE Trans. Circuits Syst. 25, 694–702 (1978).
[CrossRef]

Yule, J. A.C.

J. A.C. Yule, Principles of Color Reproduction (Wiley, 1967).

ACM Trans. Graphics (1)

M. C. Stone, W. B. Cowan, J. C. Beatty, “Color gamut mapping and the printing of digital color images,” ACM Trans. Graphics 7, 249–292 (1988).
[CrossRef]

Color Res. Appl. (2)

H. J. Trussell, “Application of set theoretic methods to color system,” Color Res. Appl. 16, 31–64 (1991).
[CrossRef]

G. Sharma, “Set theoretic estimation for problems in subtractive color,” Color Res. Appl. 25, 333–348 (2000).
[CrossRef]

Fujitsu Sci. Tech. J. (1)

S. Suzuki, M. Shimizu, S. Semba, “High-accuracy color reproduction (color management systems),” Fujitsu Sci. Tech. J. 35, 240–247 (1999).

IEEE Trans. Acoust. Speech, Signal Process. (1)

H. J. Trussell, M. Civanlar, “The feasible solution in signal restoration,” IEEE Trans. Acoust. Speech, Signal Process. 32, 201–212 (1984).
[CrossRef]

IEEE Trans. Circuits Syst. (1)

D. C. Youla, “Generalized image restoration by the method of alternating orthogonal projections,” IEEE Trans. Circuits Syst. 25, 694–702 (1978).
[CrossRef]

IEEE Trans. Image Process. (2)

P. L. Combettes, J. C. Pesquet, “Image restoration subject to a total variation constraint,” IEEE Trans. Image Process. 13, 1213–1222 (2004).
[CrossRef] [PubMed]

Y. Yang, 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]

IEEE Trans. Med. Imaging (2)

D. C. Youla, H. Webb, “Image restoration by the method of convex projections: part 1—theory,” IEEE Trans. Med. Imaging MI-1, 81–94 (1982).
[CrossRef]

M. I. Sezan, H. Stark, “Image restoration by the method of convex projections: part 2—applications,” IEEE Trans. Med. Imaging MI-1, 95–101 (1982).
[CrossRef]

J. Electron. Imaging (1)

G. Sharma, H. J. Trussell, “Set theoretic estimation in color scanner characterization,” J. Electron. Imaging 5, 479–489 (1996).
[CrossRef]

J. Imaging Sci. Technol. (1)

R. Bala, R. Eschbac, “Reducing multi-separation color moire by a variable under color removal and gray component replacement strategy,” J. Imaging Sci. Technol. 45(2), 152–160 (2001).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Proc. IEEE (2)

P. L. Combettes, “The foundations of set theoretic estimation,” Proc. IEEE 81, 182–208 (1993).
[CrossRef]

G. Sharma, M. J. Vrhel, H. J. Trussell, “Color imaging for multimedia,” in Proc. IEEE 86, 1088–1108 (1998).
[CrossRef]

Z. Tech. Phys. (Leipzig) (1)

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

Z. Wissenschaftliche Photogr. (1)

H. E.J. Neugebauer, “Die Theoretischen Grundlagen des Mehrfarbenbuchdrucks (The theoretical foundation for multicolor printing),” Z. Wissenschaftliche Photogr. 36(4), pp. 73–89, 1937).

Other (20)

ICC Profile Format Specification V3.4 (International Color Consortium, 1997).

M. R. Gupta, “An information theory approach to supervised learning,” Ph.D. thesis (Stanford University, 2003).

C-Y. Tsai, M.-J. Liaw, H.-P. D. Shieh, “Color reproduction of twist nematic LCD by polynomial regression applied in primary-invariance model,” in Proceedings of the 5th Asian Symposium on Information Display (IEEE, 1999), pp. 115–118).

G. Sharma, Digital Color Imaging Handbook (CRC Press, 2002).
[CrossRef]

H. R. Kang, Digital Color Halftoning (SPIE, 1999).

R. W.G. Hunt, Measuring Color (Wiley, 1987).

G. Wyszecki, W. S. Sitles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, 2000).

Colorimetry, CIE Publication No. 15.2 (Central Bureau of the CIE, 1986).

R. Bala, “Inverse problems in color device characterization,” in Computational Imaging, C. A. Bouman and R. L. Stevenson, eds., Proc. SPIE5016, 185–195 (2003).
[CrossRef]

M. D. Fairchild, “A simple printer calibration technique for ‘good enough’ color reproduction of CRT images,” Munsell Color Science Laboratory Technical Report (Munsell Laboratory, Rochester Institute of Technology, 1994).

S. Tominaga, “A color mapping method for CMYK printers and its evaluation,” in Proceeding of the 4th IS&T/SID Color Imaging Conference (Society for Imaging Science and Technology, 1995), pp. 172–176.

T. J. Cholewo, “Printer model inversion by constrained optimization,” in Color Imaging: Device Independent Color, Color Hardcopy and Graphic Arts V, R. Eschbach and G. G. Marcu, eds., Proc. SPIE3963, pp. 349–357 (2000).

J. A.C. Yule, Principles of Color Reproduction (Wiley, 1967).

I. Pobboravsky, 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).

M. Mahy, “Color separation method and apparatus for same,” U.S. Patent 5,878,195 (March 2, 1999).

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 Inc., 1988), pp. 469–478.

A. Levi, “Image restoration by the method of projections with applications to the phase and magnitude retrieval problem,” Ph.D. thesis (Rensselaer Polytechnic Institute, 1983).

H. Stark, 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).

E. J. Stollnitz, V. Ostromoukhov, D. H. Salesin, “Reproducing color images using custom inks,” in Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 1998), pp. 267–274.

Y. Yang, H. Stark, “Probability density function estimation using convex projections,” in Signal Processing Methods for Audio, Images and Telecommunications, P. Clarkson and H. Stark, eds. (Academic, 1994), Chap. 10.

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Figures (2)

Fig. 1
Fig. 1

Standard observer configuration.

Fig. 2
Fig. 2

Reproductions of the color image channels. Left column, target image; center column, image reproduced with material constraints only; right column, image reproduced with material and ACV constraints.

Equations (73)

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C ( λ ) = α min α max C ( α ) δ ( α λ ) d α ,
L { C ( λ ) } = α min α max C ( α ) L { δ ( α λ ) } d α = α min α max C ( α ) [ f 1 ( c ) ( α ) f 2 ( c ) ( α ) f 3 ( c ) ( α ) ] t d α ,
R α min α max C ( α ) f 1 ( c ) ( α ) d α ,
G α min α max C ( α ) f 2 ( c ) ( α ) d α ,
B α min α max C ( α ) f 3 ( c ) ( α ) d α ,
L { C ( λ ) } = ( R G B ) v .
R = α min α max i = 1 3 m i P i ( α ) f 1 ( c ) ( α ) d α ,
G = α min α max i = 1 3 m i P i ( α ) f 2 ( c ) ( α ) d α ,
B = α min α max i = 1 3 m i P i ( α ) f 3 ( c ) ( α ) d α .
a i j α min α max f i ( c ) ( λ ) P j ( λ ) d λ , i = 1 , 2 , 3 ; j = 1 , 2 , 3 ,
A m = v ,
( X Y Z ) = [ 0.49 0.31 0.20 1.7697 0.8124 0.010 0 0.01 0.99 ] ( R G B ) ,
D m = w ,
d X Y Z ( C 1 , C 2 ) ( X 1 X 2 ) 2 + ( Y 1 Y 2 ) 2 + ( Z 1 Z 2 ) 2 .
L = 116 ( Y Y 0 ) 1 3 16 ,
a = 500 [ ( X X 0 ) 1 3 ( Y Y 0 ) 1 3 ] ,
b = 200 [ ( Y Y 0 ) 1 3 ( Z Z 0 ) 1 3 ] ,
x k + 1 = P n P n 1 P 1 x k , x 0 arbitrary ,
d Lab ( C R , C T ) = Δ L 2 + Δ a 2 + Δ b 2 ,
C 3 = { m R 3 : d 2 t m = Y T }
a R b R = a T b T ,
sgn ( b R ) = sgn ( b T ) .
[ Δ a ( m ) ] 2 + [ Δ b ( m ) ] 2 δ Lab 2 .
C 4 = { m R 3 : x 1 d 1 t m x 2 } ,
C 5 = { m R 3 : z 1 d 3 t m z 2 } .
C 6 = { m R 3 : d 3 t m z 3 if b T > 0 , d 3 t m z 3 if b T < 0 } .
m k + 1 = P 1 P 2 P 3 P 4 P 5 P 6 m k ,
σ i 2 ( j ) k = 1 M 1 [ m i ( j , k ) m i ( j , k + 1 ) ] 2
C S i ( j ) { m i R M × M : σ i 2 ( j ) δ i ( j ) } i = 1 , 2 , 3 ; j = 1 , , M .
σ i 2 R I { [ m i ( j , k ) m i ( j + 1 , k ) ] 2 + [ m i ( j , k ) m i ( j , k + 1 ) ] 2 } ,
σ i 2 R I { [ m i ( i , k ) m i ( j + 1 , k + 1 ) ] 2 + [ m i ( j + 1 , k ) m i ( j , k + 1 ) ] 2 } ,
C S ( δ ) { m R M : k = 1 M 1 [ m ( k ) m ( k + 1 ) ] 2 δ } .
L ( γ ) = k = 1 M m ( k ) z ( k ) 2 + γ ( { k = 1 M 1 [ m ( k ) m ( k + 1 ) ] 2 } δ ) .
C S { m R M : k = 1 M 2 [ m ( 2 k ) m ( 2 k 1 ) ] 2 δ 1 , k = 1 ( M 2 ) 1 [ m ( 2 k + 1 ) m ( 2 k ) ] 2 δ 2 , δ 1 + δ 2 = δ } .
C S ( 1 ) { m R M : k = 1 M 2 [ m ( 2 k ) m ( 2 k 1 ) ] 2 δ 1 } ,
C S ( 2 ) { m R M : k = 1 ( M 2 ) 1 [ m ( 2 k + 1 ) m ( 2 k ) ] 2 δ 2 } ,
C 1 { m R 3 : 0 m i 1 , i = 1 , 2 , 3 } .
P 1 x [ y 1 y 2 y 3 ] , where y i = { 1 if x i > 1 0 if x i < 0 , i = 1 , 2 , 3 x i else } .
C 2 ( ϵ ) { m R 3 : i = 1 3 m i ϵ } .
P 2 x = { x if 1 , x ϵ x + ϵ x , 1 3 1 else } ,
C 3 { m R 3 : d 2 t m = Y T } .
P 3 x = { x if x , d 2 = Y T x + Y T x , d 2 d 2 t 2 d 2 t else } .
C 4 { m R 3 : x 1 d 1 t m x 2 }
C 5 { m R 3 : z 1 d 3 t m z 2 }
C 6 { m R 3 : d 3 t m z 3 if b T > 0 , d 3 t m z 3 if b T < 0 }
x 1 = [ ( μ 1 μ 2 + μ 3 μ 4 + 2 μ 1 μ 2 μ 3 μ 4 + δ Lab 2 ( μ 1 2 + μ 4 2 ) ) ( μ 1 2 + μ 4 2 ) ] 3 ,
x 2 = [ ( μ 1 μ 2 + μ 3 μ 4 2 μ 1 μ 2 μ 3 μ 4 + δ Lab 2 ( μ 1 2 + μ 4 2 ) ) ( μ 1 2 + μ 4 2 ) ] 3 ,
z 1 = [ ( μ 5 μ 6 + μ 7 μ 8 + 2 μ 5 μ 6 μ 7 μ 8 + δ Lab 2 ( μ 5 2 + μ 8 2 ) ) ( μ 5 2 + μ 8 2 ) ] 3 ,
z 2 = [ ( μ 5 μ 6 + μ 7 μ 8 2 μ 5 μ 6 μ 7 μ 8 + δ Lab 2 ( μ 5 2 + μ 8 2 ) ) ( μ 5 2 + μ 8 2 ) ] 3 ,
z 3 = Z 0 Y R Y 0 ,
μ 1 200 ( a T b T ) ( Y T Y 0 ) 1 3 ,
μ 2 200 ( a T b T ) ( Z 0 1 3 ) ,
μ 3 200 ( Y T Y 0 ) 1 3 b T ,
μ 4 200 ( Z 0 1 3 ) ,
μ 5 500 ( X 0 1 3 ) ,
μ 6 500 ( Y T Y 0 ) 1 3 + a T ,
μ 7 500 ( b T a T ) ( Y T Y 0 ) 1 3 + b T ,
μ 8 500 ( b T a T ) X 0 1 3 ,
P 4 x = { x + x 1 x , d 1 d 1 t 2 d 1 t x , d 1 x 1 x + x 2 x , d 1 d 1 t 2 d 1 t x , d 1 x 2 x else } .
( 1 + k 2 ) ( a R a T ) 2 δ Lab 2 .
δ Lab 1 + k 2 + a T 500 [ ( X R X 0 ) 1 3 ( Y R Y 0 ) 1 3 ] δ Lab 1 + k 2 + a T .
( Y T Y 0 ) 1 3 + [ ( δ Lab 1 + k 2 + a T ) 500 ] ( X R X 0 ) 1 3 ( Y T Y 0 ) 1 3 + [ ( δ Lab 1 + k 2 + a T ) 500 ] .
x 1 d 1 t m x 2 ,
C S ( 1 ) { m R M : k = 1 M 2 [ m ( 2 k ) m ( 2 k 1 ) ] 2 δ 1 } ,
C S ( 2 ) { m R M : k = 1 ( M 2 ) 1 [ m ( 2 k + 1 ) m ( 2 k ) ] 2 δ 2 } .
L ( γ ) = k = 1 M [ m ( k ) z ( k ) ] 2 + γ { k = 1 M 2 [ m ( 2 k ) m ( 2 k 1 ) ] 2 δ 1 } .
L m ( k ) = 2 [ m ( k ) z ( k ) ] + 2 γ [ m ( k ) m ( k 1 ) ] = 0 , k even ,
L m ( k ) = 2 [ m ( k ) z ( k ) ] + 2 γ [ m ( k ) m ( k + 1 ) ] = 0 , k odd .
k = 1 M 2 [ m ( 2 k ) m ( 2 k 1 ) ] 2 = k = 1 M 2 [ z ( 2 k ) z ( 2 k 1 ) 1 + 2 γ ] 2 = δ 1 .
γ = 1 2 [ ( { k = 1 M 2 [ z ( 2 k ) z ( 2 k 1 ) ] 2 } δ 1 ) 1 2 1 ] ,
P S ( 1 ) Z = { ( 1 + γ ) z ( k ) + γ z ( k + 1 ) 1 + 2 γ k odd ( 1 + γ ) z ( k ) + γ z ( k 1 ) 1 + 2 γ k even } .
P S ( 2 ) Z = { z ( 1 ) k = 1 ( 1 + γ ) z ( k ) + γ z ( k 1 ) 1 + 2 γ k odd and k > 1 ( 1 + γ ) z ( k ) + γ z ( k + 1 ) 1 + 2 γ k even and k M z ( M ) k = M } ,
γ = 1 2 [ ( { k = 1 ( M 2 ) 1 [ z ( 2 k + 1 ) z ( 2 k ) ] 2 } δ 2 ) 1 2 1 ] .

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