Abstract

Hue plane preserving color correction (HPPCC), introduced by Andersen and Hardeberg [Proceedings of the 13th Color and Imaging Conference (CIC) (2005), pp. 141–146], maps device-dependent color values (RGB) to colorimetric color values (XYZ) using a set of linear transforms, realized by white point preserving 3×3 matrices, where each transform is learned and applied in a subregion of color space, defined by two adjacent hue planes. The hue plane delimited subregions of camera RGB values are mapped to corresponding hue plane delimited subregions of estimated colorimetric XYZ values. Hue planes are geometrical half-planes, where each is defined by the neutral axis and a chromatic color in a linear color space. The key advantage of the HPPCC method is that, while offering an estimation accuracy of higher order methods, it maintains the linear colorimetric relations of colors in hue planes. As a significant result, it therefore also renders the colorimetric estimates invariant to exposure and shading of object reflection. In this paper, we present a new flexible and robust version of HPPCC using constrained least squares in the optimization, where the subregions can be chosen freely in number and position in order to optimize the results while constraining transform continuity at the subregion boundaries. The method is compared to a selection of other state-of-the-art characterization methods, and the results show that it outperforms the original HPPCC method.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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    [Crossref]
  8. H. Kang, “Colour scanner calibration,” J. Imaging Sci. Technol. 36, 162–170 (1992).
  9. R. S. Berns and M. J. Shyu, “Colorimetric characterization of a desktop drum scanner using a spectral model,” J. Electron. Imaging 4, 360–372 (1995).
    [Crossref]
  10. G. Hong, M. R. Luo, and P. A. Rhodes, “A study of digital camera characterisation based on polynomial modelling,” Color Res. Appl. 26, 76–84 (2001).
    [Crossref]
  11. T. Cheung and S. Westland, “Colour camera characterisation using artificial neural networks,” in 10th Color Imaging Conference (The Society for Information Display, 2002), vol. 4, pp. 117–120.
  12. H. Kang and P. Anderson, “Neural network application to the color scanner and printer calibration,” J. Electron. Imaging 1, 125–134 (1992).
    [Crossref]
  13. L. Xinwu, “A new color correction model based on bp neural network,” Adv. Inf. Sci. Serv. Sci. 3, 72–78 (2011).
  14. T. Cheung, S. Westland, D. Connah, and C. A. Ripamonti, “Comparative study of the characterization of colour cameras by means of neural networks and polynomial transforms,” J. Color. Technol. 120, 19–25 (2004).
  15. P. Hung, “Colorimetric calibration in electronic imaging devices using a look-up tables model and interpolations,” J. Electron. Imaging 2, 53–61 (1993).
    [Crossref]
  16. J. McElvain and W. Gish, “Camara color correction using two-dimensional transforms,” in Proceedings of the 21st Color and Imaging Conference (CIC) (2013).
  17. S. H. Lim and A. Silverstein, “Spatially varying colour correction matrices for reduced noise,” (Imaging Systems Laboratory, HP Laboratories, 2004).
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    [Crossref]
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  26. C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (SIAM, 1995).
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    [Crossref]
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2016 (1)

C. F. Andersen and D. Connah, “Weighted constrained hue plane preserving camera characterization,” IEEE Trans. Image Process. 25, 4329–4339 (2016).
[Crossref]

2015 (2)

G. Finlayson, M. Mackiewicz, and A. Hurlbert, “Colour correction using root-polynomial regression,” IEEE Trans. Image Process. 24, 1460–1470 (2015).
[Crossref]

M. M. Darrodi, G. Finlayson, T. Goodman, and M. Mackiewicz, “Reference data set for camera spectral sensitivity estimation,” J. Opt. Soc. Am. A 32, 381–391 (2015).
[Crossref]

2014 (1)

J. Vazquez-Corral, D. Connah, and M. Bertalmio, “Perceptual color characterization of cameras,” Sensors 14, 23205–23229 (2014).
[Crossref]

2012 (1)

E. Garcia, R. Arora, and M. R. Gupta, “Optimized regression for efficient function evaluation,” IEEE Trans. Image Process. 21, 4128–4140 (2012).

2011 (1)

L. Xinwu, “A new color correction model based on bp neural network,” Adv. Inf. Sci. Serv. Sci. 3, 72–78 (2011).

2004 (1)

T. Cheung, S. Westland, D. Connah, and C. A. Ripamonti, “Comparative study of the characterization of colour cameras by means of neural networks and polynomial transforms,” J. Color. Technol. 120, 19–25 (2004).

2002 (1)

K. Barnard, L. Martin, B. Funt, and A. Coath, “A dataset for color research,” Color Res. Appl. 27, 147–151 (2002).
[Crossref]

2001 (2)

A. Laratta and F. Zironi, “Computation of lagrange multipliers for linear least squares problems with equality constraints,” Computing 67, 335–350 (2001).

G. Hong, M. R. Luo, and P. A. Rhodes, “A study of digital camera characterisation based on polynomial modelling,” Color Res. Appl. 26, 76–84 (2001).
[Crossref]

1997 (1)

G. D. Finlayson and M. Drew, “Constrained least-squares regression in color spaces,” J. Electron. Imaging 6, 484-493 (1997).
[Crossref]

1995 (1)

R. S. Berns and M. J. Shyu, “Colorimetric characterization of a desktop drum scanner using a spectral model,” J. Electron. Imaging 4, 360–372 (1995).
[Crossref]

1993 (1)

P. Hung, “Colorimetric calibration in electronic imaging devices using a look-up tables model and interpolations,” J. Electron. Imaging 2, 53–61 (1993).
[Crossref]

1992 (2)

H. Kang, “Colour scanner calibration,” J. Imaging Sci. Technol. 36, 162–170 (1992).

H. Kang and P. Anderson, “Neural network application to the color scanner and printer calibration,” J. Electron. Imaging 1, 125–134 (1992).
[Crossref]

1976 (1)

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1976).
[Crossref]

1927 (1)

R. T. D. Luther, “Aus dem Gebiet der Farbreizmetric,” Z. Tech. Phys. 8, 540–555 (1927).

1915 (1)

H. E. Ives, “The transformation of color-mixture equations from one system to another,” J. Franklin Inst. 180, 673–701 (1915).
[Crossref]

Andersen, C.

M. Mackiewicz, C. Andersen, and G. Finlayson, “Hue plane preserving colour correction using constrained least squares regression,” in Proceedings of the 22nd Color and Imaging Conference (CIC) (2015).

Andersen, C. F.

C. F. Andersen and D. Connah, “Weighted constrained hue plane preserving camera characterization,” IEEE Trans. Image Process. 25, 4329–4339 (2016).
[Crossref]

C. F. Andersen and J. Y. Hardeberg, “Colorimetric characterization of digital cameras preserving hue planes,” in Proceedings of the 13th Color and Imaging Conference (CIC) (2005), pp. 141–146.

Anderson, M.

M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A standard default color space for the internet—sRGB,” (Hewlett-Packard, Microsoft, 1996).

Anderson, P.

H. Kang and P. Anderson, “Neural network application to the color scanner and printer calibration,” J. Electron. Imaging 1, 125–134 (1992).
[Crossref]

Arora, R.

E. Garcia, R. Arora, and M. R. Gupta, “Optimized regression for efficient function evaluation,” IEEE Trans. Image Process. 21, 4128–4140 (2012).

Barnard, K.

K. Barnard, L. Martin, B. Funt, and A. Coath, “A dataset for color research,” Color Res. Appl. 27, 147–151 (2002).
[Crossref]

Berns, R. S.

R. S. Berns and M. J. Shyu, “Colorimetric characterization of a desktop drum scanner using a spectral model,” J. Electron. Imaging 4, 360–372 (1995).
[Crossref]

Bertalmio, M.

J. Vazquez-Corral, D. Connah, and M. Bertalmio, “Perceptual color characterization of cameras,” Sensors 14, 23205–23229 (2014).
[Crossref]

Chandrasekar, S.

M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A standard default color space for the internet—sRGB,” (Hewlett-Packard, Microsoft, 1996).

Cheung, T.

T. Cheung, S. Westland, D. Connah, and C. A. Ripamonti, “Comparative study of the characterization of colour cameras by means of neural networks and polynomial transforms,” J. Color. Technol. 120, 19–25 (2004).

T. Cheung and S. Westland, “Colour camera characterisation using artificial neural networks,” in 10th Color Imaging Conference (The Society for Information Display, 2002), vol. 4, pp. 117–120.

Coath, A.

K. Barnard, L. Martin, B. Funt, and A. Coath, “A dataset for color research,” Color Res. Appl. 27, 147–151 (2002).
[Crossref]

Connah, D.

C. F. Andersen and D. Connah, “Weighted constrained hue plane preserving camera characterization,” IEEE Trans. Image Process. 25, 4329–4339 (2016).
[Crossref]

J. Vazquez-Corral, D. Connah, and M. Bertalmio, “Perceptual color characterization of cameras,” Sensors 14, 23205–23229 (2014).
[Crossref]

T. Cheung, S. Westland, D. Connah, and C. A. Ripamonti, “Comparative study of the characterization of colour cameras by means of neural networks and polynomial transforms,” J. Color. Technol. 120, 19–25 (2004).

Crichton, S.

M. Mackiewicz, S. Crichton, S. Newsome, R. Gazerro, G. Finlayson, and A. Hurlbert, “Spectrally tunable led illuminator for vision research,” in Proceedings of the 6th Colour in Graphics, Imaging and Vision (CGIV) (2012), Vol. 6, pp. 372–377.

Darrodi, M. M.

Drew, M.

G. D. Finlayson and M. Drew, “Constrained least-squares regression in color spaces,” J. Electron. Imaging 6, 484-493 (1997).
[Crossref]

P. Hubel, J. Holm, G. Finlayson, and M. Drew, “Matrix calculations for digital photography,” in Proceedings of the 5th Color and Imaging Conference (CIC) (1997).

Finlayson, G.

M. M. Darrodi, G. Finlayson, T. Goodman, and M. Mackiewicz, “Reference data set for camera spectral sensitivity estimation,” J. Opt. Soc. Am. A 32, 381–391 (2015).
[Crossref]

G. Finlayson, M. Mackiewicz, and A. Hurlbert, “Colour correction using root-polynomial regression,” IEEE Trans. Image Process. 24, 1460–1470 (2015).
[Crossref]

M. Mackiewicz, C. Andersen, and G. Finlayson, “Hue plane preserving colour correction using constrained least squares regression,” in Proceedings of the 22nd Color and Imaging Conference (CIC) (2015).

P. Hubel, J. Holm, G. Finlayson, and M. Drew, “Matrix calculations for digital photography,” in Proceedings of the 5th Color and Imaging Conference (CIC) (1997).

M. Mackiewicz, S. Crichton, S. Newsome, R. Gazerro, G. Finlayson, and A. Hurlbert, “Spectrally tunable led illuminator for vision research,” in Proceedings of the 6th Colour in Graphics, Imaging and Vision (CGIV) (2012), Vol. 6, pp. 372–377.

Finlayson, G. D.

G. D. Finlayson and M. Drew, “Constrained least-squares regression in color spaces,” J. Electron. Imaging 6, 484-493 (1997).
[Crossref]

Funt, B.

K. Barnard, L. Martin, B. Funt, and A. Coath, “A dataset for color research,” Color Res. Appl. 27, 147–151 (2002).
[Crossref]

Garcia, E.

E. Garcia, R. Arora, and M. R. Gupta, “Optimized regression for efficient function evaluation,” IEEE Trans. Image Process. 21, 4128–4140 (2012).

Gazerro, R.

M. Mackiewicz, S. Crichton, S. Newsome, R. Gazerro, G. Finlayson, and A. Hurlbert, “Spectrally tunable led illuminator for vision research,” in Proceedings of the 6th Colour in Graphics, Imaging and Vision (CGIV) (2012), Vol. 6, pp. 372–377.

Gish, W.

J. McElvain and W. Gish, “Camara color correction using two-dimensional transforms,” in Proceedings of the 21st Color and Imaging Conference (CIC) (2013).

Goodman, T.

Gu, J.

J. Jiang, D. Liu, J. Gu, and S. Susstrunk, “What is the space of spectral sensitivity functions for digital color cameras?” in Proceedings of the IEEE Workshop on Applications of Computer Vision (WACV) (IEEE Computer Society, 2013), pp. 168–179.

Gupta, M. R.

E. Garcia, R. Arora, and M. R. Gupta, “Optimized regression for efficient function evaluation,” IEEE Trans. Image Process. 21, 4128–4140 (2012).

Hanson, R. J.

C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (SIAM, 1995).

Hardeberg, J. Y.

C. F. Andersen and J. Y. Hardeberg, “Colorimetric characterization of digital cameras preserving hue planes,” in Proceedings of the 13th Color and Imaging Conference (CIC) (2005), pp. 141–146.

Holm, J.

P. Hubel, J. Holm, G. Finlayson, and M. Drew, “Matrix calculations for digital photography,” in Proceedings of the 5th Color and Imaging Conference (CIC) (1997).

Hong, G.

G. Hong, M. R. Luo, and P. A. Rhodes, “A study of digital camera characterisation based on polynomial modelling,” Color Res. Appl. 26, 76–84 (2001).
[Crossref]

Hubel, P.

P. Hubel, J. Holm, G. Finlayson, and M. Drew, “Matrix calculations for digital photography,” in Proceedings of the 5th Color and Imaging Conference (CIC) (1997).

P. Hubel, “Foveon technology and the changing landscape of digital cameras,” in Proceedings of the 13th Color and Imaging Conference (CIC) (2005), pp. 314–317.

Hung, P.

P. Hung, “Colorimetric calibration in electronic imaging devices using a look-up tables model and interpolations,” J. Electron. Imaging 2, 53–61 (1993).
[Crossref]

Hunt, R.

R. Hunt and M. R. Pointer, Measuring Colour, 4th ed. (Wiley, 2011).

Hurlbert, A.

G. Finlayson, M. Mackiewicz, and A. Hurlbert, “Colour correction using root-polynomial regression,” IEEE Trans. Image Process. 24, 1460–1470 (2015).
[Crossref]

M. Mackiewicz, S. Crichton, S. Newsome, R. Gazerro, G. Finlayson, and A. Hurlbert, “Spectrally tunable led illuminator for vision research,” in Proceedings of the 6th Colour in Graphics, Imaging and Vision (CGIV) (2012), Vol. 6, pp. 372–377.

Ives, H. E.

H. E. Ives, “The transformation of color-mixture equations from one system to another,” J. Franklin Inst. 180, 673–701 (1915).
[Crossref]

Jiang, J.

J. Jiang, D. Liu, J. Gu, and S. Susstrunk, “What is the space of spectral sensitivity functions for digital color cameras?” in Proceedings of the IEEE Workshop on Applications of Computer Vision (WACV) (IEEE Computer Society, 2013), pp. 168–179.

Kang, H.

H. Kang and P. Anderson, “Neural network application to the color scanner and printer calibration,” J. Electron. Imaging 1, 125–134 (1992).
[Crossref]

H. Kang, “Colour scanner calibration,” J. Imaging Sci. Technol. 36, 162–170 (1992).

Laratta, A.

A. Laratta and F. Zironi, “Computation of lagrange multipliers for linear least squares problems with equality constraints,” Computing 67, 335–350 (2001).

Lawson, C. L.

C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (SIAM, 1995).

Lim, S. H.

S. H. Lim and A. Silverstein, “Spatially varying colour correction matrices for reduced noise,” (Imaging Systems Laboratory, HP Laboratories, 2004).

Liu, D.

J. Jiang, D. Liu, J. Gu, and S. Susstrunk, “What is the space of spectral sensitivity functions for digital color cameras?” in Proceedings of the IEEE Workshop on Applications of Computer Vision (WACV) (IEEE Computer Society, 2013), pp. 168–179.

Luo, M. R.

G. Hong, M. R. Luo, and P. A. Rhodes, “A study of digital camera characterisation based on polynomial modelling,” Color Res. Appl. 26, 76–84 (2001).
[Crossref]

Luther, R. T. D.

R. T. D. Luther, “Aus dem Gebiet der Farbreizmetric,” Z. Tech. Phys. 8, 540–555 (1927).

Mackiewicz, M.

M. M. Darrodi, G. Finlayson, T. Goodman, and M. Mackiewicz, “Reference data set for camera spectral sensitivity estimation,” J. Opt. Soc. Am. A 32, 381–391 (2015).
[Crossref]

G. Finlayson, M. Mackiewicz, and A. Hurlbert, “Colour correction using root-polynomial regression,” IEEE Trans. Image Process. 24, 1460–1470 (2015).
[Crossref]

M. Mackiewicz, C. Andersen, and G. Finlayson, “Hue plane preserving colour correction using constrained least squares regression,” in Proceedings of the 22nd Color and Imaging Conference (CIC) (2015).

M. Mackiewicz, S. Crichton, S. Newsome, R. Gazerro, G. Finlayson, and A. Hurlbert, “Spectrally tunable led illuminator for vision research,” in Proceedings of the 6th Colour in Graphics, Imaging and Vision (CGIV) (2012), Vol. 6, pp. 372–377.

Martin, L.

K. Barnard, L. Martin, B. Funt, and A. Coath, “A dataset for color research,” Color Res. Appl. 27, 147–151 (2002).
[Crossref]

McElvain, J.

J. McElvain and W. Gish, “Camara color correction using two-dimensional transforms,” in Proceedings of the 21st Color and Imaging Conference (CIC) (2013).

Motta, R.

M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A standard default color space for the internet—sRGB,” (Hewlett-Packard, Microsoft, 1996).

Newsome, S.

M. Mackiewicz, S. Crichton, S. Newsome, R. Gazerro, G. Finlayson, and A. Hurlbert, “Spectrally tunable led illuminator for vision research,” in Proceedings of the 6th Colour in Graphics, Imaging and Vision (CGIV) (2012), Vol. 6, pp. 372–377.

Phong, B. T.

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1976).
[Crossref]

Pointer, M. R.

R. Hunt and M. R. Pointer, Measuring Colour, 4th ed. (Wiley, 2011).

Rhodes, P. A.

G. Hong, M. R. Luo, and P. A. Rhodes, “A study of digital camera characterisation based on polynomial modelling,” Color Res. Appl. 26, 76–84 (2001).
[Crossref]

Ripamonti, C. A.

T. Cheung, S. Westland, D. Connah, and C. A. Ripamonti, “Comparative study of the characterization of colour cameras by means of neural networks and polynomial transforms,” J. Color. Technol. 120, 19–25 (2004).

Shyu, M. J.

R. S. Berns and M. J. Shyu, “Colorimetric characterization of a desktop drum scanner using a spectral model,” J. Electron. Imaging 4, 360–372 (1995).
[Crossref]

Silverstein, A.

S. H. Lim and A. Silverstein, “Spatially varying colour correction matrices for reduced noise,” (Imaging Systems Laboratory, HP Laboratories, 2004).

Stokes, M.

M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A standard default color space for the internet—sRGB,” (Hewlett-Packard, Microsoft, 1996).

Styles, W.

G. Wyszecki and W. Styles, Color Science: Concepts and Methods, Quantative Data and Formulae (Wiley, 1982).

Susstrunk, S.

J. Jiang, D. Liu, J. Gu, and S. Susstrunk, “What is the space of spectral sensitivity functions for digital color cameras?” in Proceedings of the IEEE Workshop on Applications of Computer Vision (WACV) (IEEE Computer Society, 2013), pp. 168–179.

Vazquez-Corral, J.

J. Vazquez-Corral, D. Connah, and M. Bertalmio, “Perceptual color characterization of cameras,” Sensors 14, 23205–23229 (2014).
[Crossref]

Westland, S.

T. Cheung, S. Westland, D. Connah, and C. A. Ripamonti, “Comparative study of the characterization of colour cameras by means of neural networks and polynomial transforms,” J. Color. Technol. 120, 19–25 (2004).

T. Cheung and S. Westland, “Colour camera characterisation using artificial neural networks,” in 10th Color Imaging Conference (The Society for Information Display, 2002), vol. 4, pp. 117–120.

Wyszecki, G.

G. Wyszecki and W. Styles, Color Science: Concepts and Methods, Quantative Data and Formulae (Wiley, 1982).

Xinwu, L.

L. Xinwu, “A new color correction model based on bp neural network,” Adv. Inf. Sci. Serv. Sci. 3, 72–78 (2011).

Zironi, F.

A. Laratta and F. Zironi, “Computation of lagrange multipliers for linear least squares problems with equality constraints,” Computing 67, 335–350 (2001).

Adv. Inf. Sci. Serv. Sci. (1)

L. Xinwu, “A new color correction model based on bp neural network,” Adv. Inf. Sci. Serv. Sci. 3, 72–78 (2011).

Color Res. Appl. (2)

G. Hong, M. R. Luo, and P. A. Rhodes, “A study of digital camera characterisation based on polynomial modelling,” Color Res. Appl. 26, 76–84 (2001).
[Crossref]

K. Barnard, L. Martin, B. Funt, and A. Coath, “A dataset for color research,” Color Res. Appl. 27, 147–151 (2002).
[Crossref]

Commun. ACM (1)

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1976).
[Crossref]

Computing (1)

A. Laratta and F. Zironi, “Computation of lagrange multipliers for linear least squares problems with equality constraints,” Computing 67, 335–350 (2001).

IEEE Trans. Image Process. (3)

C. F. Andersen and D. Connah, “Weighted constrained hue plane preserving camera characterization,” IEEE Trans. Image Process. 25, 4329–4339 (2016).
[Crossref]

E. Garcia, R. Arora, and M. R. Gupta, “Optimized regression for efficient function evaluation,” IEEE Trans. Image Process. 21, 4128–4140 (2012).

G. Finlayson, M. Mackiewicz, and A. Hurlbert, “Colour correction using root-polynomial regression,” IEEE Trans. Image Process. 24, 1460–1470 (2015).
[Crossref]

J. Color. Technol. (1)

T. Cheung, S. Westland, D. Connah, and C. A. Ripamonti, “Comparative study of the characterization of colour cameras by means of neural networks and polynomial transforms,” J. Color. Technol. 120, 19–25 (2004).

J. Electron. Imaging (4)

P. Hung, “Colorimetric calibration in electronic imaging devices using a look-up tables model and interpolations,” J. Electron. Imaging 2, 53–61 (1993).
[Crossref]

R. S. Berns and M. J. Shyu, “Colorimetric characterization of a desktop drum scanner using a spectral model,” J. Electron. Imaging 4, 360–372 (1995).
[Crossref]

H. Kang and P. Anderson, “Neural network application to the color scanner and printer calibration,” J. Electron. Imaging 1, 125–134 (1992).
[Crossref]

G. D. Finlayson and M. Drew, “Constrained least-squares regression in color spaces,” J. Electron. Imaging 6, 484-493 (1997).
[Crossref]

J. Franklin Inst. (1)

H. E. Ives, “The transformation of color-mixture equations from one system to another,” J. Franklin Inst. 180, 673–701 (1915).
[Crossref]

J. Imaging Sci. Technol. (1)

H. Kang, “Colour scanner calibration,” J. Imaging Sci. Technol. 36, 162–170 (1992).

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

Sensors (1)

J. Vazquez-Corral, D. Connah, and M. Bertalmio, “Perceptual color characterization of cameras,” Sensors 14, 23205–23229 (2014).
[Crossref]

Z. Tech. Phys. (1)

R. T. D. Luther, “Aus dem Gebiet der Farbreizmetric,” Z. Tech. Phys. 8, 540–555 (1927).

Other (18)

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Figures (13)

Fig. 1.
Fig. 1.

Nikon D70 raw camera response to the scene containing a color checker, before (a) and after (b) correction to the sRGB color space by means of a 3×3 color correction matrix. Both images have a gamma of 0.5 applied.

Fig. 2.
Fig. 2.

(a) Example of real camera (Nikon 5100) sensors [7]; (b) XYZ color matching functions; and (c) their estimate using the best linear transform (least squares).

Fig. 3.
Fig. 3.

Visualization of the convex cone spanned by the two hue planes in the RGB unit cube. A hue plane is spanned by the neutral vector w¯ and a chromatic color (u¯ or v¯). These three vectors intersect the chromaticity plane (dotted triangle) at w¯, u¯, and v¯. The hue planes intersect the chromaticity plane in hue lines (dashed lines).

Fig. 4.
Fig. 4.

CIE xy chromaticity diagram and a sample hue plane distortion resulting from the root-polynomial color correction of degree two (red) [21] and nonmodified hue line (black).

Fig. 5.
Fig. 5.

Construction of hue regions in the rg chromaticity space.

Fig. 6.
Fig. 6.

Cross sections along the rg chromaticity plane of the XYZ=f(RGB) color correction hypersurface. Left: different colors representing ten hue regions used in this example. Right: the same figure with coloring proportional to X (top), Y (middle), and Z (bottom).

Fig. 7.
Fig. 7.

Estimated ten sets of color matching functions. The colors of the plots correspond to the colors of the hue regions in Fig. 6.

Fig. 8.
Fig. 8.

Mean, median, and 95 percentile ΔE errors for the increasing number of hue partitions for the SG chart dataset.

Fig. 9.
Fig. 9.

As in Fig. 8 but for the DC chart.

Fig. 10.
Fig. 10.

As in Figs. 8 and 9 but for the SFU dataset.

Fig. 11.
Fig. 11.

Color correction errors shown in the CIELUV chromaticity diagram. The errors plotted were calculated for the Nikon sensor, DC chart reflectance set, and four different color correction methods.

Fig. 12.
Fig. 12.

Spectra of three illuminants: D65, A, and F11.

Fig. 13.
Fig. 13.

Color correction results for the set of 37 sensors. SFU reflectance dataset. (a) Illuminant D65, (b) A, and (c) F11.

Tables (3)

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Table 1. Synthetic Data Characterization Resultsa

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Table 2. Average Results for 37 Sensors and Three Illuminants

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Table 3. Nikon D70 and Sigma SD15 Characterization Resultsa

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

θi={0if  ri=gi=13,π2if  ri=13gi>13,3π2if  ri=13gi<13,arctangi13ri13+mπotherwise,
m={0if  ri13gi13,1if  gi<13,2otherwise,
ri=Ri/(Ri+Gi+Bi),gi=Gi/(Ri+Gi+Bi).
[q¯kTq¯k+1Tw¯T]Tk=[p¯kTp¯k+1Tp¯wT]for  k=1k1[q¯kTq¯1Tw¯T]Tk=[p¯kTp¯1Tp¯wT]for  k=k,
minimizet¯  Qt¯x¯,
minimizet¯1t¯Kk=1KQkt¯kx¯k.
minimizeT¯  |AT¯X¯,
A=[Q1000Q2000QK],
q¯kTt¯k=q¯kTt¯k+1,k=1,,K1,q¯kTt¯k=q¯kTt¯1,k=K,w¯Tt¯1=w¯Tt¯2==w¯Tt¯K=xw,
CT¯=b¯,
C=[q¯1Tq¯1T000q¯2Tq¯2T000q¯K1Tq¯K1Tq¯KT00q¯KTw¯Tw¯T000w¯Tw¯T000w¯Tw¯Tw¯T00],
b¯=[0¯xw].
minimizeT¯  AT¯X¯subjecttoCT¯=b¯.
minimizeT  ATXsubjecttoCT=B,
B=[0p¯wT],
[TZ]=[2ATACTC0]1[2ATXB],

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