Abstract

In order to accurately predict a digital camera response to spectral stimuli, the spectral sensitivity functions of its sensor need to be known. These functions can be determined by direct measurement in the lab—a difficult and lengthy procedure—or through simple statistical inference. Statistical inference methods are based on the observation that when a camera responds linearly to spectral stimuli, the device spectral sensitivities are linearly related to the camera rgb response values, and so can be found through regression. However, for rendered images, such as the JPEG images taken by a mobile phone, this assumption of linearity is violated. Even small departures from linearity can negatively impact the accuracy of the recovered spectral sensitivities, when a regression method is used. In our work, we develop a novel camera spectral sensitivity estimation technique that can recover the linear device spectral sensitivities from linear images and the effective linear sensitivities from rendered images. According to our method, the rank order of a pair of responses imposes a constraint on the shape of the underlying spectral sensitivity curve (of the sensor). Technically, each rank-pair splits the space where the underlying sensor might lie in two parts (a feasible region and an infeasible region). By intersecting the feasible regions from all the ranked-pairs, we can find a feasible region of sensor space. Experiments demonstrate that using rank orders delivers equal estimation to the prior art. However, the Rank-based method delivers a step-change in estimation performance when the data is not linear and, for the first time, allows for the estimation of the effective sensitivities of devices that may not even have “raw mode.” Experiments validate our method.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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  1. N. Shimano, K. Terai, and M. Hironaga, “Recovery of spectral reflectances of objects being imaged by multi-spectral cameras,” J. Opt. Soc. Am. A. 24, 3211–3219 (2007).
    [Crossref]
  2. F. H. Imai and R. Berns, “Spectral estimation using trichromatic digital cameras,” in Proceedings of International Symposium on Multispectral Imaging and Colour Reproduction for Digital Archives (Society of Multispectral Imaging, 1999), pp. 42–49.
  3. S. Han, I. Sato, T. Okabe, and Y. Sato, “Fast spectral reflectance recovery using dlp projector,” in Proceedings of the Asian Conference on Computer Vision (Springer, 2010).
  4. G. D. Finlayson, P. M. Hubel, and S. Hordley, “Colour by correction,” in Proceedings of the Fifth Colour Imaging Conference: Colour Standards and Colour Measurements (IS & T, 1997), pp. 6–11.
  5. J. Park, M. Lee, M. D. Grossberg, and S. K. Nayar, “Multispectral imaging using multiplexed illumination,” in International Conference on Computer Vision (IEEE, 2007).
  6. G. D. Finlayson and M. S. Drew, “White-point preserving colour correction,” in Proceedings of the Fifth Colour Imaging Conference: Colour Standards and Colour Measurements (IS & T, 1997), pp. 258–261.
  7. G. D. Finlayson and M. S. Drew, “Constrained least-squares regression in colour space,” J. Electron. Imaging 6, 484–493 (1997).
    [Crossref]
  8. A. Forsyth, “A novel algorithm for colour constancy,” Int. J. Comput. Vis. 5, 5–35 (1990).
    [Crossref]
  9. G. Finlayson, S. Hordley, and P. Hubel, “Colour by correlation: a simple, unifying framework for colour constancy,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 1209–1221 (2001).
    [Crossref]
  10. M. Mohammadzadeh Darrodi, G. D. Finlayson, T. Good-man, and M. Mackiewicz, “A reference data set for camera spectral sensitivity estimation,” J. Opt. Soc. Am. A 32, 381–391 (2014).
  11. J. Jiang, D. Liu, J. Gu, and S. Susstrunk, “What is the space of spectral sensitivity functions for digital colour cameras,” in IEEE Workshop on the Applications of Computer Vision (IEEE, 2013), pp. 168–179.
  12. P. L. Vora, J. E. Fareel, J. D. Tietz, and D. Brainard, “Digital colour cameras—2 Spectral response,” in HP Technical Report (HP, 1997).
  13. P. M. Hubel, D. Sherman, and J. E. Farell, “A comparison of methods of sensor spectral sensitivity estimation,” in Proceedings of Colour Imaging Conference: Colour Science, Systems and Applications (IS & T, 1994), pp. 45–48.
  14. G. D. Finlayson, S. Hordley, and P. M. Hubel, “Recovering device sensitivities with quadratic programming,” in Proceedings of The Sixth Colour Imaging Conference: Colour Science, Systems, and Applications (Society for Imaging Science and Technology, 1998), pp. 90–95.
  15. R. Martin, Z. Arno, and K. Reinhard, “Practical spectral characterization of trichromatic cameras,” in Proceedings of the SIGGRAPH Asia Conference (ACM, 2011).
  16. P. Urban, M. Desch, K. Happel, and D. Spiehl, “Recovering camera sensitivities using target-based reflectances captured under multiple LED-illuminations,” in 16th Workshop on Colour Image Processing (2010), pp. 295–301.
  17. R. Ramanath, W. E. Snyder, Y. Yoo, and M. S. Drew, “Color image processing pipeline,” IEEE Signal Process. Mag. 22(1), 34–43 (2005).
  18. S. J. Kim, H. T. Lin, Z. Lu, S. Susstrunk, S. Lin, and M. S. Brown, “A new in-camera imaging model for colour computer vision and its application,” IEEE Trans. Pattern Anal. Mach. Intell. 34, 2289–2302 (2012).
    [Crossref]
  19. R. W. G. Hunt, The Reproduction of Colour, 6th ed. (Voyageur, 2004).
  20. J. Singnoo and G. D. Finlayson, “RGBE vs modified TIFF for encoding high dynamic range,” in 4th Conference on Colour in Graphics, Imaging, and Vision (UEA, 2010), pp. 431–436.
  21. J. Trussell and M. Vrhel, Fundamentals of Digital Imaging (Cambridge University, 2009).
  22. B. Smith, C. Spiekermann, and R. Sember, “Numerical methods for colorimetric calculations: Sampling density requirements,” Color Res. Appl. 17, 394–401 (1992).
    [Crossref]
  23. E. Moore, “On the reciprocal of the general algebraic matrix,” Bull. Am. Math. Soc. 26, 394–395 (1920).
  24. J. A. Worthey, “Spectrally smooth reflectances that match,” Color Res. Appl. 19, 395–396 (1994).
    [Crossref]
  25. J. P. S. Parkkinen, J. Hallikainen, and T. Jaaskelainen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318–322 (1989).
    [Crossref]
  26. Y. H. Hardeberg, H. Brettel, and F. J. Schmitt, “Spectral characterization of electronic cameras, electronic imaging: processing, printing, and publishing,” Proc. SPIE 3409, 100–109 (1998).
    [Crossref]
  27. R. L. Burden and D. Faires, Numerical Analysis, 8th ed. (Brooks/Cole, 2005).
  28. A. N. Tikhonov and V. Y. Arsenin, Solution of Ill-Posed Problems (Winston, 1977).
  29. B. Dyas, “Robust colour sensor response characterization,” in Proceedings of Eighth Colour Imaging Conference (Society for Imaging Science and Technology, 2000), pp. 144–148.
  30. P. C. Hansen and D. P. O’Leary, “The use of the L-curve in the regularisation of discrete ill-posed problems,” SIAM J. Sci. Comput. 14, 1487–1503 (1993).
    [Crossref]
  31. J. Gu, http://www.cis.rit.edu/people/faculty/jwgu .
  32. H. Zhao, K. Rei, T. T. Robby, and I. Katsushi, “Estimating basis functions for spectral sensitivity of digital cameras,” in Meeting on Image Recognition and Understanding (2009), pp. 7–13.
  33. J. J. Fuch, “Linear programming in spectral estimation. Application to array processing,” in IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 1996), pp. 3161–3164.
  34. M. Mohammadzadeh Darrodi, https://spectralestimation.wordpress.com/data .
  35. M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A Standard Default Color Space for the Internet—sRGB,” (Hewlett-Packard, Microsoft, 1996), http://www.w3.org/Graphics/Color/sRGB .
  36. J. Morovic, Color Gamut Mapping (Wiley, 2008).
  37. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulas (Wiley, 1969), Vol. 71, p. 628.
  38. J. Vazquez-Corral, D. Connah, and M. Bertalm, “Perceptual color characterization of cameras,” Sensors 14, 23205–23229 (2014).
    [Crossref]
  39. K. Barnard, L. Martin, B. Funt, and A. Coath, “A data set for colour research,” Color Res. Appl. 27, 147–151 (2002).
    [Crossref]
  40. P. Vora, L. Poorvi, J. E. Farell, J. Tietz, and D. H. Brainard, “Digital Color Cameras—1—Response Models,” HP Labs Technical Report.

2014 (2)

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

M. Mohammadzadeh Darrodi, G. D. Finlayson, T. Good-man, and M. Mackiewicz, “A reference data set for camera spectral sensitivity estimation,” J. Opt. Soc. Am. A 32, 381–391 (2014).

2012 (1)

S. J. Kim, H. T. Lin, Z. Lu, S. Susstrunk, S. Lin, and M. S. Brown, “A new in-camera imaging model for colour computer vision and its application,” IEEE Trans. Pattern Anal. Mach. Intell. 34, 2289–2302 (2012).
[Crossref]

2007 (1)

N. Shimano, K. Terai, and M. Hironaga, “Recovery of spectral reflectances of objects being imaged by multi-spectral cameras,” J. Opt. Soc. Am. A. 24, 3211–3219 (2007).
[Crossref]

2005 (1)

R. Ramanath, W. E. Snyder, Y. Yoo, and M. S. Drew, “Color image processing pipeline,” IEEE Signal Process. Mag. 22(1), 34–43 (2005).

2002 (1)

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

2001 (1)

G. Finlayson, S. Hordley, and P. Hubel, “Colour by correlation: a simple, unifying framework for colour constancy,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 1209–1221 (2001).
[Crossref]

1998 (1)

Y. H. Hardeberg, H. Brettel, and F. J. Schmitt, “Spectral characterization of electronic cameras, electronic imaging: processing, printing, and publishing,” Proc. SPIE 3409, 100–109 (1998).
[Crossref]

1997 (1)

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

1994 (1)

J. A. Worthey, “Spectrally smooth reflectances that match,” Color Res. Appl. 19, 395–396 (1994).
[Crossref]

1993 (1)

P. C. Hansen and D. P. O’Leary, “The use of the L-curve in the regularisation of discrete ill-posed problems,” SIAM J. Sci. Comput. 14, 1487–1503 (1993).
[Crossref]

1992 (1)

B. Smith, C. Spiekermann, and R. Sember, “Numerical methods for colorimetric calculations: Sampling density requirements,” Color Res. Appl. 17, 394–401 (1992).
[Crossref]

1990 (1)

A. Forsyth, “A novel algorithm for colour constancy,” Int. J. Comput. Vis. 5, 5–35 (1990).
[Crossref]

1989 (1)

1920 (1)

E. Moore, “On the reciprocal of the general algebraic matrix,” Bull. Am. Math. Soc. 26, 394–395 (1920).

Anderson, M.

M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A Standard Default Color Space for the Internet—sRGB,” (Hewlett-Packard, Microsoft, 1996), http://www.w3.org/Graphics/Color/sRGB .

Arno, Z.

R. Martin, Z. Arno, and K. Reinhard, “Practical spectral characterization of trichromatic cameras,” in Proceedings of the SIGGRAPH Asia Conference (ACM, 2011).

Arsenin, V. Y.

A. N. Tikhonov and V. Y. Arsenin, Solution of Ill-Posed Problems (Winston, 1977).

Barnard, K.

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

Berns, R.

F. H. Imai and R. Berns, “Spectral estimation using trichromatic digital cameras,” in Proceedings of International Symposium on Multispectral Imaging and Colour Reproduction for Digital Archives (Society of Multispectral Imaging, 1999), pp. 42–49.

Bertalm, M.

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

Brainard, D.

P. L. Vora, J. E. Fareel, J. D. Tietz, and D. Brainard, “Digital colour cameras—2 Spectral response,” in HP Technical Report (HP, 1997).

Brainard, D. H.

P. Vora, L. Poorvi, J. E. Farell, J. Tietz, and D. H. Brainard, “Digital Color Cameras—1—Response Models,” HP Labs Technical Report.

Brettel, H.

Y. H. Hardeberg, H. Brettel, and F. J. Schmitt, “Spectral characterization of electronic cameras, electronic imaging: processing, printing, and publishing,” Proc. SPIE 3409, 100–109 (1998).
[Crossref]

Brown, M. S.

S. J. Kim, H. T. Lin, Z. Lu, S. Susstrunk, S. Lin, and M. S. Brown, “A new in-camera imaging model for colour computer vision and its application,” IEEE Trans. Pattern Anal. Mach. Intell. 34, 2289–2302 (2012).
[Crossref]

Burden, R. L.

R. L. Burden and D. Faires, Numerical Analysis, 8th ed. (Brooks/Cole, 2005).

Chandrasekar, S.

M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A Standard Default Color Space for the Internet—sRGB,” (Hewlett-Packard, Microsoft, 1996), http://www.w3.org/Graphics/Color/sRGB .

Coath, A.

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

Connah, D.

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

Desch, M.

P. Urban, M. Desch, K. Happel, and D. Spiehl, “Recovering camera sensitivities using target-based reflectances captured under multiple LED-illuminations,” in 16th Workshop on Colour Image Processing (2010), pp. 295–301.

Drew, M. S.

R. Ramanath, W. E. Snyder, Y. Yoo, and M. S. Drew, “Color image processing pipeline,” IEEE Signal Process. Mag. 22(1), 34–43 (2005).

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

G. D. Finlayson and M. S. Drew, “White-point preserving colour correction,” in Proceedings of the Fifth Colour Imaging Conference: Colour Standards and Colour Measurements (IS & T, 1997), pp. 258–261.

Dyas, B.

B. Dyas, “Robust colour sensor response characterization,” in Proceedings of Eighth Colour Imaging Conference (Society for Imaging Science and Technology, 2000), pp. 144–148.

Faires, D.

R. L. Burden and D. Faires, Numerical Analysis, 8th ed. (Brooks/Cole, 2005).

Fareel, J. E.

P. L. Vora, J. E. Fareel, J. D. Tietz, and D. Brainard, “Digital colour cameras—2 Spectral response,” in HP Technical Report (HP, 1997).

Farell, J. E.

P. M. Hubel, D. Sherman, and J. E. Farell, “A comparison of methods of sensor spectral sensitivity estimation,” in Proceedings of Colour Imaging Conference: Colour Science, Systems and Applications (IS & T, 1994), pp. 45–48.

P. Vora, L. Poorvi, J. E. Farell, J. Tietz, and D. H. Brainard, “Digital Color Cameras—1—Response Models,” HP Labs Technical Report.

Finlayson, G.

G. Finlayson, S. Hordley, and P. Hubel, “Colour by correlation: a simple, unifying framework for colour constancy,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 1209–1221 (2001).
[Crossref]

Finlayson, G. D.

M. Mohammadzadeh Darrodi, G. D. Finlayson, T. Good-man, and M. Mackiewicz, “A reference data set for camera spectral sensitivity estimation,” J. Opt. Soc. Am. A 32, 381–391 (2014).

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

G. D. Finlayson and M. S. Drew, “White-point preserving colour correction,” in Proceedings of the Fifth Colour Imaging Conference: Colour Standards and Colour Measurements (IS & T, 1997), pp. 258–261.

G. D. Finlayson, P. M. Hubel, and S. Hordley, “Colour by correction,” in Proceedings of the Fifth Colour Imaging Conference: Colour Standards and Colour Measurements (IS & T, 1997), pp. 6–11.

G. D. Finlayson, S. Hordley, and P. M. Hubel, “Recovering device sensitivities with quadratic programming,” in Proceedings of The Sixth Colour Imaging Conference: Colour Science, Systems, and Applications (Society for Imaging Science and Technology, 1998), pp. 90–95.

J. Singnoo and G. D. Finlayson, “RGBE vs modified TIFF for encoding high dynamic range,” in 4th Conference on Colour in Graphics, Imaging, and Vision (UEA, 2010), pp. 431–436.

Forsyth, A.

A. Forsyth, “A novel algorithm for colour constancy,” Int. J. Comput. Vis. 5, 5–35 (1990).
[Crossref]

Fuch, J. J.

J. J. Fuch, “Linear programming in spectral estimation. Application to array processing,” in IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 1996), pp. 3161–3164.

Funt, B.

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

Good-man, T.

Grossberg, M. D.

J. Park, M. Lee, M. D. Grossberg, and S. K. Nayar, “Multispectral imaging using multiplexed illumination,” in International Conference on Computer Vision (IEEE, 2007).

Gu, J.

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

Hallikainen, J.

Han, S.

S. Han, I. Sato, T. Okabe, and Y. Sato, “Fast spectral reflectance recovery using dlp projector,” in Proceedings of the Asian Conference on Computer Vision (Springer, 2010).

Hansen, P. C.

P. C. Hansen and D. P. O’Leary, “The use of the L-curve in the regularisation of discrete ill-posed problems,” SIAM J. Sci. Comput. 14, 1487–1503 (1993).
[Crossref]

Happel, K.

P. Urban, M. Desch, K. Happel, and D. Spiehl, “Recovering camera sensitivities using target-based reflectances captured under multiple LED-illuminations,” in 16th Workshop on Colour Image Processing (2010), pp. 295–301.

Hardeberg, Y. H.

Y. H. Hardeberg, H. Brettel, and F. J. Schmitt, “Spectral characterization of electronic cameras, electronic imaging: processing, printing, and publishing,” Proc. SPIE 3409, 100–109 (1998).
[Crossref]

Hironaga, M.

N. Shimano, K. Terai, and M. Hironaga, “Recovery of spectral reflectances of objects being imaged by multi-spectral cameras,” J. Opt. Soc. Am. A. 24, 3211–3219 (2007).
[Crossref]

Hordley, S.

G. Finlayson, S. Hordley, and P. Hubel, “Colour by correlation: a simple, unifying framework for colour constancy,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 1209–1221 (2001).
[Crossref]

G. D. Finlayson, P. M. Hubel, and S. Hordley, “Colour by correction,” in Proceedings of the Fifth Colour Imaging Conference: Colour Standards and Colour Measurements (IS & T, 1997), pp. 6–11.

G. D. Finlayson, S. Hordley, and P. M. Hubel, “Recovering device sensitivities with quadratic programming,” in Proceedings of The Sixth Colour Imaging Conference: Colour Science, Systems, and Applications (Society for Imaging Science and Technology, 1998), pp. 90–95.

Hubel, P.

G. Finlayson, S. Hordley, and P. Hubel, “Colour by correlation: a simple, unifying framework for colour constancy,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 1209–1221 (2001).
[Crossref]

Hubel, P. M.

G. D. Finlayson, P. M. Hubel, and S. Hordley, “Colour by correction,” in Proceedings of the Fifth Colour Imaging Conference: Colour Standards and Colour Measurements (IS & T, 1997), pp. 6–11.

G. D. Finlayson, S. Hordley, and P. M. Hubel, “Recovering device sensitivities with quadratic programming,” in Proceedings of The Sixth Colour Imaging Conference: Colour Science, Systems, and Applications (Society for Imaging Science and Technology, 1998), pp. 90–95.

P. M. Hubel, D. Sherman, and J. E. Farell, “A comparison of methods of sensor spectral sensitivity estimation,” in Proceedings of Colour Imaging Conference: Colour Science, Systems and Applications (IS & T, 1994), pp. 45–48.

Hunt, R. W. G.

R. W. G. Hunt, The Reproduction of Colour, 6th ed. (Voyageur, 2004).

Imai, F. H.

F. H. Imai and R. Berns, “Spectral estimation using trichromatic digital cameras,” in Proceedings of International Symposium on Multispectral Imaging and Colour Reproduction for Digital Archives (Society of Multispectral Imaging, 1999), pp. 42–49.

Jaaskelainen, T.

Jiang, J.

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

Katsushi, I.

H. Zhao, K. Rei, T. T. Robby, and I. Katsushi, “Estimating basis functions for spectral sensitivity of digital cameras,” in Meeting on Image Recognition and Understanding (2009), pp. 7–13.

Kim, S. J.

S. J. Kim, H. T. Lin, Z. Lu, S. Susstrunk, S. Lin, and M. S. Brown, “A new in-camera imaging model for colour computer vision and its application,” IEEE Trans. Pattern Anal. Mach. Intell. 34, 2289–2302 (2012).
[Crossref]

Lee, M.

J. Park, M. Lee, M. D. Grossberg, and S. K. Nayar, “Multispectral imaging using multiplexed illumination,” in International Conference on Computer Vision (IEEE, 2007).

Lin, H. T.

S. J. Kim, H. T. Lin, Z. Lu, S. Susstrunk, S. Lin, and M. S. Brown, “A new in-camera imaging model for colour computer vision and its application,” IEEE Trans. Pattern Anal. Mach. Intell. 34, 2289–2302 (2012).
[Crossref]

Lin, S.

S. J. Kim, H. T. Lin, Z. Lu, S. Susstrunk, S. Lin, and M. S. Brown, “A new in-camera imaging model for colour computer vision and its application,” IEEE Trans. Pattern Anal. Mach. Intell. 34, 2289–2302 (2012).
[Crossref]

Liu, D.

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

Lu, Z.

S. J. Kim, H. T. Lin, Z. Lu, S. Susstrunk, S. Lin, and M. S. Brown, “A new in-camera imaging model for colour computer vision and its application,” IEEE Trans. Pattern Anal. Mach. Intell. 34, 2289–2302 (2012).
[Crossref]

Mackiewicz, M.

Martin, L.

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

Martin, R.

R. Martin, Z. Arno, and K. Reinhard, “Practical spectral characterization of trichromatic cameras,” in Proceedings of the SIGGRAPH Asia Conference (ACM, 2011).

Mohammadzadeh Darrodi, M.

Moore, E.

E. Moore, “On the reciprocal of the general algebraic matrix,” Bull. Am. Math. Soc. 26, 394–395 (1920).

Morovic, J.

J. Morovic, Color Gamut Mapping (Wiley, 2008).

Motta, R.

M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A Standard Default Color Space for the Internet—sRGB,” (Hewlett-Packard, Microsoft, 1996), http://www.w3.org/Graphics/Color/sRGB .

Nayar, S. K.

J. Park, M. Lee, M. D. Grossberg, and S. K. Nayar, “Multispectral imaging using multiplexed illumination,” in International Conference on Computer Vision (IEEE, 2007).

O’Leary, D. P.

P. C. Hansen and D. P. O’Leary, “The use of the L-curve in the regularisation of discrete ill-posed problems,” SIAM J. Sci. Comput. 14, 1487–1503 (1993).
[Crossref]

Okabe, T.

S. Han, I. Sato, T. Okabe, and Y. Sato, “Fast spectral reflectance recovery using dlp projector,” in Proceedings of the Asian Conference on Computer Vision (Springer, 2010).

Park, J.

J. Park, M. Lee, M. D. Grossberg, and S. K. Nayar, “Multispectral imaging using multiplexed illumination,” in International Conference on Computer Vision (IEEE, 2007).

Parkkinen, J. P. S.

Poorvi, L.

P. Vora, L. Poorvi, J. E. Farell, J. Tietz, and D. H. Brainard, “Digital Color Cameras—1—Response Models,” HP Labs Technical Report.

Ramanath, R.

R. Ramanath, W. E. Snyder, Y. Yoo, and M. S. Drew, “Color image processing pipeline,” IEEE Signal Process. Mag. 22(1), 34–43 (2005).

Rei, K.

H. Zhao, K. Rei, T. T. Robby, and I. Katsushi, “Estimating basis functions for spectral sensitivity of digital cameras,” in Meeting on Image Recognition and Understanding (2009), pp. 7–13.

Reinhard, K.

R. Martin, Z. Arno, and K. Reinhard, “Practical spectral characterization of trichromatic cameras,” in Proceedings of the SIGGRAPH Asia Conference (ACM, 2011).

Robby, T. T.

H. Zhao, K. Rei, T. T. Robby, and I. Katsushi, “Estimating basis functions for spectral sensitivity of digital cameras,” in Meeting on Image Recognition and Understanding (2009), pp. 7–13.

Sato, I.

S. Han, I. Sato, T. Okabe, and Y. Sato, “Fast spectral reflectance recovery using dlp projector,” in Proceedings of the Asian Conference on Computer Vision (Springer, 2010).

Sato, Y.

S. Han, I. Sato, T. Okabe, and Y. Sato, “Fast spectral reflectance recovery using dlp projector,” in Proceedings of the Asian Conference on Computer Vision (Springer, 2010).

Schmitt, F. J.

Y. H. Hardeberg, H. Brettel, and F. J. Schmitt, “Spectral characterization of electronic cameras, electronic imaging: processing, printing, and publishing,” Proc. SPIE 3409, 100–109 (1998).
[Crossref]

Sember, R.

B. Smith, C. Spiekermann, and R. Sember, “Numerical methods for colorimetric calculations: Sampling density requirements,” Color Res. Appl. 17, 394–401 (1992).
[Crossref]

Sherman, D.

P. M. Hubel, D. Sherman, and J. E. Farell, “A comparison of methods of sensor spectral sensitivity estimation,” in Proceedings of Colour Imaging Conference: Colour Science, Systems and Applications (IS & T, 1994), pp. 45–48.

Shimano, N.

N. Shimano, K. Terai, and M. Hironaga, “Recovery of spectral reflectances of objects being imaged by multi-spectral cameras,” J. Opt. Soc. Am. A. 24, 3211–3219 (2007).
[Crossref]

Singnoo, J.

J. Singnoo and G. D. Finlayson, “RGBE vs modified TIFF for encoding high dynamic range,” in 4th Conference on Colour in Graphics, Imaging, and Vision (UEA, 2010), pp. 431–436.

Smith, B.

B. Smith, C. Spiekermann, and R. Sember, “Numerical methods for colorimetric calculations: Sampling density requirements,” Color Res. Appl. 17, 394–401 (1992).
[Crossref]

Snyder, W. E.

R. Ramanath, W. E. Snyder, Y. Yoo, and M. S. Drew, “Color image processing pipeline,” IEEE Signal Process. Mag. 22(1), 34–43 (2005).

Spiehl, D.

P. Urban, M. Desch, K. Happel, and D. Spiehl, “Recovering camera sensitivities using target-based reflectances captured under multiple LED-illuminations,” in 16th Workshop on Colour Image Processing (2010), pp. 295–301.

Spiekermann, C.

B. Smith, C. Spiekermann, and R. Sember, “Numerical methods for colorimetric calculations: Sampling density requirements,” Color Res. Appl. 17, 394–401 (1992).
[Crossref]

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulas (Wiley, 1969), Vol. 71, p. 628.

Stokes, M.

M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A Standard Default Color Space for the Internet—sRGB,” (Hewlett-Packard, Microsoft, 1996), http://www.w3.org/Graphics/Color/sRGB .

Susstrunk, S.

S. J. Kim, H. T. Lin, Z. Lu, S. Susstrunk, S. Lin, and M. S. Brown, “A new in-camera imaging model for colour computer vision and its application,” IEEE Trans. Pattern Anal. Mach. Intell. 34, 2289–2302 (2012).
[Crossref]

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

Terai, K.

N. Shimano, K. Terai, and M. Hironaga, “Recovery of spectral reflectances of objects being imaged by multi-spectral cameras,” J. Opt. Soc. Am. A. 24, 3211–3219 (2007).
[Crossref]

Tietz, J.

P. Vora, L. Poorvi, J. E. Farell, J. Tietz, and D. H. Brainard, “Digital Color Cameras—1—Response Models,” HP Labs Technical Report.

Tietz, J. D.

P. L. Vora, J. E. Fareel, J. D. Tietz, and D. Brainard, “Digital colour cameras—2 Spectral response,” in HP Technical Report (HP, 1997).

Tikhonov, A. N.

A. N. Tikhonov and V. Y. Arsenin, Solution of Ill-Posed Problems (Winston, 1977).

Trussell, J.

J. Trussell and M. Vrhel, Fundamentals of Digital Imaging (Cambridge University, 2009).

Urban, P.

P. Urban, M. Desch, K. Happel, and D. Spiehl, “Recovering camera sensitivities using target-based reflectances captured under multiple LED-illuminations,” in 16th Workshop on Colour Image Processing (2010), pp. 295–301.

Vazquez-Corral, J.

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

Vora, P.

P. Vora, L. Poorvi, J. E. Farell, J. Tietz, and D. H. Brainard, “Digital Color Cameras—1—Response Models,” HP Labs Technical Report.

Vora, P. L.

P. L. Vora, J. E. Fareel, J. D. Tietz, and D. Brainard, “Digital colour cameras—2 Spectral response,” in HP Technical Report (HP, 1997).

Vrhel, M.

J. Trussell and M. Vrhel, Fundamentals of Digital Imaging (Cambridge University, 2009).

Worthey, J. A.

J. A. Worthey, “Spectrally smooth reflectances that match,” Color Res. Appl. 19, 395–396 (1994).
[Crossref]

Wyszecki, G.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulas (Wiley, 1969), Vol. 71, p. 628.

Yoo, Y.

R. Ramanath, W. E. Snyder, Y. Yoo, and M. S. Drew, “Color image processing pipeline,” IEEE Signal Process. Mag. 22(1), 34–43 (2005).

Zhao, H.

H. Zhao, K. Rei, T. T. Robby, and I. Katsushi, “Estimating basis functions for spectral sensitivity of digital cameras,” in Meeting on Image Recognition and Understanding (2009), pp. 7–13.

Bull. Am. Math. Soc. (1)

E. Moore, “On the reciprocal of the general algebraic matrix,” Bull. Am. Math. Soc. 26, 394–395 (1920).

Color Res. Appl. (3)

J. A. Worthey, “Spectrally smooth reflectances that match,” Color Res. Appl. 19, 395–396 (1994).
[Crossref]

B. Smith, C. Spiekermann, and R. Sember, “Numerical methods for colorimetric calculations: Sampling density requirements,” Color Res. Appl. 17, 394–401 (1992).
[Crossref]

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

IEEE Signal Process. Mag. (1)

R. Ramanath, W. E. Snyder, Y. Yoo, and M. S. Drew, “Color image processing pipeline,” IEEE Signal Process. Mag. 22(1), 34–43 (2005).

IEEE Trans. Pattern Anal. Mach. Intell. (2)

S. J. Kim, H. T. Lin, Z. Lu, S. Susstrunk, S. Lin, and M. S. Brown, “A new in-camera imaging model for colour computer vision and its application,” IEEE Trans. Pattern Anal. Mach. Intell. 34, 2289–2302 (2012).
[Crossref]

G. Finlayson, S. Hordley, and P. Hubel, “Colour by correlation: a simple, unifying framework for colour constancy,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 1209–1221 (2001).
[Crossref]

Int. J. Comput. Vis. (1)

A. Forsyth, “A novel algorithm for colour constancy,” Int. J. Comput. Vis. 5, 5–35 (1990).
[Crossref]

J. Electron. Imaging (1)

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

J. Opt. Soc. Am. A (2)

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

N. Shimano, K. Terai, and M. Hironaga, “Recovery of spectral reflectances of objects being imaged by multi-spectral cameras,” J. Opt. Soc. Am. A. 24, 3211–3219 (2007).
[Crossref]

Proc. SPIE (1)

Y. H. Hardeberg, H. Brettel, and F. J. Schmitt, “Spectral characterization of electronic cameras, electronic imaging: processing, printing, and publishing,” Proc. SPIE 3409, 100–109 (1998).
[Crossref]

Sensors (1)

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

SIAM J. Sci. Comput. (1)

P. C. Hansen and D. P. O’Leary, “The use of the L-curve in the regularisation of discrete ill-posed problems,” SIAM J. Sci. Comput. 14, 1487–1503 (1993).
[Crossref]

Other (25)

J. Gu, http://www.cis.rit.edu/people/faculty/jwgu .

H. Zhao, K. Rei, T. T. Robby, and I. Katsushi, “Estimating basis functions for spectral sensitivity of digital cameras,” in Meeting on Image Recognition and Understanding (2009), pp. 7–13.

J. J. Fuch, “Linear programming in spectral estimation. Application to array processing,” in IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 1996), pp. 3161–3164.

M. Mohammadzadeh Darrodi, https://spectralestimation.wordpress.com/data .

M. Stokes, M. Anderson, S. Chandrasekar, and R. Motta, “A Standard Default Color Space for the Internet—sRGB,” (Hewlett-Packard, Microsoft, 1996), http://www.w3.org/Graphics/Color/sRGB .

J. Morovic, Color Gamut Mapping (Wiley, 2008).

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulas (Wiley, 1969), Vol. 71, p. 628.

P. Vora, L. Poorvi, J. E. Farell, J. Tietz, and D. H. Brainard, “Digital Color Cameras—1—Response Models,” HP Labs Technical Report.

R. L. Burden and D. Faires, Numerical Analysis, 8th ed. (Brooks/Cole, 2005).

A. N. Tikhonov and V. Y. Arsenin, Solution of Ill-Posed Problems (Winston, 1977).

B. Dyas, “Robust colour sensor response characterization,” in Proceedings of Eighth Colour Imaging Conference (Society for Imaging Science and Technology, 2000), pp. 144–148.

R. W. G. Hunt, The Reproduction of Colour, 6th ed. (Voyageur, 2004).

J. Singnoo and G. D. Finlayson, “RGBE vs modified TIFF for encoding high dynamic range,” in 4th Conference on Colour in Graphics, Imaging, and Vision (UEA, 2010), pp. 431–436.

J. Trussell and M. Vrhel, Fundamentals of Digital Imaging (Cambridge University, 2009).

F. H. Imai and R. Berns, “Spectral estimation using trichromatic digital cameras,” in Proceedings of International Symposium on Multispectral Imaging and Colour Reproduction for Digital Archives (Society of Multispectral Imaging, 1999), pp. 42–49.

S. Han, I. Sato, T. Okabe, and Y. Sato, “Fast spectral reflectance recovery using dlp projector,” in Proceedings of the Asian Conference on Computer Vision (Springer, 2010).

G. D. Finlayson, P. M. Hubel, and S. Hordley, “Colour by correction,” in Proceedings of the Fifth Colour Imaging Conference: Colour Standards and Colour Measurements (IS & T, 1997), pp. 6–11.

J. Park, M. Lee, M. D. Grossberg, and S. K. Nayar, “Multispectral imaging using multiplexed illumination,” in International Conference on Computer Vision (IEEE, 2007).

G. D. Finlayson and M. S. Drew, “White-point preserving colour correction,” in Proceedings of the Fifth Colour Imaging Conference: Colour Standards and Colour Measurements (IS & T, 1997), pp. 258–261.

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

P. L. Vora, J. E. Fareel, J. D. Tietz, and D. Brainard, “Digital colour cameras—2 Spectral response,” in HP Technical Report (HP, 1997).

P. M. Hubel, D. Sherman, and J. E. Farell, “A comparison of methods of sensor spectral sensitivity estimation,” in Proceedings of Colour Imaging Conference: Colour Science, Systems and Applications (IS & T, 1994), pp. 45–48.

G. D. Finlayson, S. Hordley, and P. M. Hubel, “Recovering device sensitivities with quadratic programming,” in Proceedings of The Sixth Colour Imaging Conference: Colour Science, Systems, and Applications (Society for Imaging Science and Technology, 1998), pp. 90–95.

R. Martin, Z. Arno, and K. Reinhard, “Practical spectral characterization of trichromatic cameras,” in Proceedings of the SIGGRAPH Asia Conference (ACM, 2011).

P. Urban, M. Desch, K. Happel, and D. Spiehl, “Recovering camera sensitivities using target-based reflectances captured under multiple LED-illuminations,” in 16th Workshop on Colour Image Processing (2010), pp. 295–301.

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Figures (7)

Fig. 1.
Fig. 1. Image of the Macbeth SG color chart. Left: raw (color corrected). Right: rendered camera output.
Fig. 2.
Fig. 2. Top: spectral response function of Nikon camera measured at NPL [10]. Bottom: jaggy (high norm) spectral response function estimated using Eq. (7) on 140 reflectance patches of Xrite SG chart.
Fig. 3.
Fig. 3. Measured Nikon (top) and Sigma (bottom) camera sensitivities from NPL calibration facility [10,34].
Fig. 4.
Fig. 4. Illustration of the intersection of four half-planes with blue diagonal stripes.
Fig. 5.
Fig. 5. Solid lines, the Nikon D5100 (top) and Sigma spectral sensor sensitivities and estimated Nikon spectral sensor sensitivities (bottom). Dashed lines are the sensors recovered by Rank-based spectral estimation.
Fig. 6.
Fig. 6. Solid lines, the Nikon D5100 (top) and Sigma spectral sensitivities and estimated Nikon spectral sensor sensitivities (bottom). Dashed lines are the sensors recovered by Rank-based spectral estimation using rendered image.
Fig. 7.
Fig. 7. Plot of Vora (left) and averaged spectral error (right) calculated for Nikon raw image when raised to power values indicated on the x-axis.

Tables (6)

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Table 1. Percentage Spectral Error of Each Channel, the Average Across All Channels, and the Vora Values Are Shown for Raw Images from Nikon (First Five Columns) and Sigma (Last Five Columns) Cameras

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Table 2. CIE Lab Δ E Errors between the Predicted and Estimated Camera Responses to the 1995 Sample Reflectances [39] under the D65 Light [38] from Nikon (First Three Columns) and Sigma (Last Three Columns) Cameras

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Table 3. Percentage Spectral Error of Each Channel, the Average Across All Channels, and the Vora Values Are Shown for Rendered Images from Nikon (First Five Columns) and Sigma (Last Five Columns) Cameras

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Table 4. CIE Lab Δ E Errors between the Predicted and Estimated Color-Corrected Camera Responses to the 1995 Sample Reflectances [39] under the D65 Light [38] from Nikon (First Three Columns) and Sigma (Last Three Columns) Cameras

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Table 5. Percentage Spectral Error of Each Channel, the Average Across All Channels, and the Vora Values Are Shown for Rendered Images Linearized by Gamma Correction from Nikon (First Five Columns) and Sigma (Last Five Columns) Cameras

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Table 6. Percentage Spectral Error of Each Channel, the Average Across All Channels, and the Vora Values Are Shown for Rendered Images Linearized by Interpolation from Nikon (First Five Columns) and Sigma (Last Five Columns) Cameras

Equations (30)

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

p i j = ω E ( λ ) S j ( λ ) Q i ( λ ) d λ , i = { R , G , B } ,
p i j = l = 1 N E ( λ l ) S j ( λ l ) Q i ( λ l ) Δ λ , i = { R , G , B } ,
p i j = l = 1 N E l S l j Q l i , i = { R , G , B } .
c _ j = diag ( E _ ) S _ j ,
p i j = c _ j · q _ i = [ c _ j ] t q _ i .
P _ = C q _ .
min q _ C q _ P _ 2 .
q _ = C + P _ ,
c _ = ( C C t ) 1 P _ .
min q _ C q _ P _ 2 + γ T q _ 2 ,
T = [ 1 1 0 0 0 1 2 1 0 0 0 1 2 1 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 1 1 ] .
q _ = ( C t C + γ T t T ) 1 C t P _ .
Q ( λ ) = k = 1 m α k B k ( λ ) ,
min α _ C B α _ P _ 2 .
α _ = [ C B ] + P _ .
min q _ C q _ P _ 2 subject to the constraints q _ = B α _ q l 0 q l q l + 1 , l = 1 , , z 1 q l > q l + 1 , l = z , , m .
p a > p b .
f ( p a ) > f ( p b ) .
c _ a · q _ > c _ b · q _ ( c _ a c _ b ) · q _ > 0 ,
d _ j · q _ > 0 .
q _ j H ( d _ j ) .
Q = Q M .
p i = f i ( c _ t Q _ i ) ,
p a i > p b i f i ( c _ a t Q _ i ) > f i ( c _ b t Q _ i ) ( c _ a t c _ b t ) Q _ i > 0 .
min q _ C q _ P _ 2 subject to the constraints d _ j > 0    j = 1 , 2 , N q 1 = 0 q N = 0 q _ = B α _ i q i = 1 ,
p i = f i ( Γ ( c _ t Q _ i ) ) .
SE = 100 × q _ q ^ _ q _ .
RE = p _ p ^ _ i p _ .
RE = p _ M p ^ _ i p _ ,
Vora = 100 ( 1 ( trace ( Q Q + Q ^ Q ^ + ) 3 ) ) .

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