Abstract

Thin-plate spline interpolation is used to interpolate the chromaticity of the color of the incident scene illumination across a training set of images. Given the image of a scene under unknown illumination, the chromaticity of the scene illumination can be found from the interpolated function. The resulting illumination-estimation method can be used to provide color constancy under changing illumination conditions and automatic white balancing for digital cameras. A thin-plate spline interpolates over a nonuniformly sampled input space, which in this case is a training set of image thumbnails and associated illumination chromaticities. To reduce the size of the training set, incremental k medians are applied. Tests on real images demonstrate that the thin-plate spline method can estimate the color of the incident illumination quite accurately, and the proposed training set pruning significantly decreases the computation.

© 2011 Optical Society of America

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  1. G. D. Knott, Interpolating Cubic Splines (Birkhauser, 2000).
    [CrossRef]
  2. F. L. Bookstein, “Principal warps: thin-plate splines and decomposition of deformations,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 567–585 (1989).
    [CrossRef]
  3. V. Cardei, B. Funt, and K. Barnard, “Estimating the scene illumination chromaticity using a neural network,” J. Opt. Soc. Am. A 19, 2374–2386 (2002).
    [CrossRef]
  4. B. V. Funt and W. H. Xiong, “Estimating illumination chromaticity via Support Vector Regression,” J. Imaging Sci. Technol. 50, 341–348 (2006).
    [CrossRef]
  5. M. H. Davis, A. Khotanzad, D. Flamig, and S. Harms, “A physics-based coordinate transformation for 3-d image matching,” IEEE Trans. Med. Imaging 16, 317–328 (1997).
    [CrossRef] [PubMed]
  6. N. Arad and D. Reisfeld, “Image warping using few anchor points and radial functions,” Comput. Graph. Forum 14, 35–46(1995).
    [CrossRef]
  7. A. M. Bazen and S. H. Gerez, “Elastic minutiae matching by means of thin-plate spline models,” in Proceedings of 16th International Conference on Pattern Recognition (IEEE, 2002), pp. 985–988.
  8. W. Xiong and B. V. Funt, “Nonlinear RGB-to-XYZ mapping for device calibration,” in Proceedings of Imaging Science and Technology Thirteenth Color Imaging Conference (Society for Imaging Sciences and Technology, 2005), pp. 200–204.
  9. A. Zandifar, S. Lim, R. Duraiswami, N. Gumerov, and L. S. Davis, “Multi-level fast multipole method for thin plate spline evaluation,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2004), pp. 1683–1686.
  10. F. L. Bookstein, Morphometric Tools for Landmark Data Geometry and Biology (Cambridge University, 1991).
  11. J. Meinguet, “Multivariate interpolation at arbitrary points made simple,” Z. Angew Math. Phys. 30, 292–304 (1979).
    [CrossRef]
  12. R. Gershon, A. D. Jepson, and J. K. Tsotsos, “From [R,G,B] to surface reflectance: computing color constant descriptors in images,” in Proceedings of the 10th International Joint Conference on Artificial Intelligence (Morgan Kaufmann, 1987), pp. 755–758.
  13. F. Ciurea and B. Funt, “A large image database for color constancy research,” in Proceedings of IS&T/SID Eleventh Color Imaging Conference (Society for Imaging Science and Technology, 2003), pp. 160–163.
  14. G. D. Finlayson, S. D. Hordley, and P. M. Hubel, “Color by correlation: a simple, unifying framework for color constancy,” IEEE Trans. Pattern Anal. Mach. Intell. 23, 1209–1221 (2001).
    [CrossRef]
  15. S. D. Hordley and G. D. Finlayson, “Re-evaluating colour constancy algorithms,” in Proceedings of 17th International Conference on Pattern Recognition (IEEE, 2004), pp. 76–79.
    [CrossRef]
  16. K. Barnard, L. Martin, A. Coath, and B. Funt, “A comparison of computational color constancy algorithms. Part two: experiments on image data,” IEEE Trans. Image Process. 11, 985–996(2002).
    [CrossRef]
  17. P. V. Gehler, C. Rother, A. Blake, T. P. Minka, and T. Sharp, “Bayesian color constancy revisited,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–8.
  18. G. D. Finlayson, “Retinex viewed as a Gamut Mapping theory of color constancy,” in Proceedings of AIC International Color Association Color 97 (International Color Association, 1997), Vol.  2, pp. 527–530.
  19. B. Funt and L. Shi, “The rehabilitation of MaxRGB,” in Proceedings of the Eighteenth IS&T Color Imaging Conference (Society for Imaging Science and Technology, 2010), pp. 256–259.
  20. B. Buchsbaum, “A spatial processor model for object color perception,” J. Franklin Inst. 310, 1–26 (1980).
    [CrossRef]
  21. G. D. Finlayson and E. Trezzi, “Shades of Gray and colour constancy,” in Proceedings of IS&T/SID Twelfth Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, 2004), pp. 37–41.
  22. J. van de Weijer, T. Gevers, and A. Gijsenij, “Edge-based color constancy,” IEEE Trans. Image Process. 16, 2207–2214(2007).
    [CrossRef] [PubMed]
  23. W. Xiong, B. Funt, L. Shi, S. Kim, B. Kang, and S. D. Lee, “Automatic white balancing via Gray Surface Identification,” in Proceedings of the Fifteenth IS&T Color Imaging Conference (Society for Imaging Science and Technology, 2007), pp. 143–146.
  24. S. Hordley and G. Finlayson, “A reevaluation of color constancy algorithm performance,” J. Opt. Soc. Am. A 23, 1008–1020(2006).
    [CrossRef]
  25. G. Finlayson, S. Hordley, and I. Tastl, “Gamut constrained illumination estimation,” Int. J. Comput. Vis. 67, 93–109(2006).
    [CrossRef]
  26. A. Gijsenij, T. Gevers, and J. van deWeijer, “Generalized Gamut Mapping using image derivative structures for color constancy,” Int. J. Comput. Vis. 86, 127–139 (2008).
    [CrossRef]
  27. D. Coffin, “Dcraw,” http://en.wikipedia.org/wiki/Dcraw.
  28. S. Bianco, G. Ciocca, C. Cusano, and R. Schettini, “Improving color constancy using indoor–outdoor image classification,” IEEE Trans. Image Process. 17, 2381–2392 (2008).
    [CrossRef] [PubMed]

2010 (1)

B. Funt and L. Shi, “The rehabilitation of MaxRGB,” in Proceedings of the Eighteenth IS&T Color Imaging Conference (Society for Imaging Science and Technology, 2010), pp. 256–259.

2008 (3)

A. Gijsenij, T. Gevers, and J. van deWeijer, “Generalized Gamut Mapping using image derivative structures for color constancy,” Int. J. Comput. Vis. 86, 127–139 (2008).
[CrossRef]

S. Bianco, G. Ciocca, C. Cusano, and R. Schettini, “Improving color constancy using indoor–outdoor image classification,” IEEE Trans. Image Process. 17, 2381–2392 (2008).
[CrossRef] [PubMed]

P. V. Gehler, C. Rother, A. Blake, T. P. Minka, and T. Sharp, “Bayesian color constancy revisited,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–8.

2007 (2)

J. van de Weijer, T. Gevers, and A. Gijsenij, “Edge-based color constancy,” IEEE Trans. Image Process. 16, 2207–2214(2007).
[CrossRef] [PubMed]

W. Xiong, B. Funt, L. Shi, S. Kim, B. Kang, and S. D. Lee, “Automatic white balancing via Gray Surface Identification,” in Proceedings of the Fifteenth IS&T Color Imaging Conference (Society for Imaging Science and Technology, 2007), pp. 143–146.

2006 (3)

S. Hordley and G. Finlayson, “A reevaluation of color constancy algorithm performance,” J. Opt. Soc. Am. A 23, 1008–1020(2006).
[CrossRef]

G. Finlayson, S. Hordley, and I. Tastl, “Gamut constrained illumination estimation,” Int. J. Comput. Vis. 67, 93–109(2006).
[CrossRef]

B. V. Funt and W. H. Xiong, “Estimating illumination chromaticity via Support Vector Regression,” J. Imaging Sci. Technol. 50, 341–348 (2006).
[CrossRef]

2005 (1)

W. Xiong and B. V. Funt, “Nonlinear RGB-to-XYZ mapping for device calibration,” in Proceedings of Imaging Science and Technology Thirteenth Color Imaging Conference (Society for Imaging Sciences and Technology, 2005), pp. 200–204.

2004 (3)

A. Zandifar, S. Lim, R. Duraiswami, N. Gumerov, and L. S. Davis, “Multi-level fast multipole method for thin plate spline evaluation,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2004), pp. 1683–1686.

S. D. Hordley and G. D. Finlayson, “Re-evaluating colour constancy algorithms,” in Proceedings of 17th International Conference on Pattern Recognition (IEEE, 2004), pp. 76–79.
[CrossRef]

G. D. Finlayson and E. Trezzi, “Shades of Gray and colour constancy,” in Proceedings of IS&T/SID Twelfth Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, 2004), pp. 37–41.

2003 (1)

F. Ciurea and B. Funt, “A large image database for color constancy research,” in Proceedings of IS&T/SID Eleventh Color Imaging Conference (Society for Imaging Science and Technology, 2003), pp. 160–163.

2002 (3)

V. Cardei, B. Funt, and K. Barnard, “Estimating the scene illumination chromaticity using a neural network,” J. Opt. Soc. Am. A 19, 2374–2386 (2002).
[CrossRef]

A. M. Bazen and S. H. Gerez, “Elastic minutiae matching by means of thin-plate spline models,” in Proceedings of 16th International Conference on Pattern Recognition (IEEE, 2002), pp. 985–988.

K. Barnard, L. Martin, A. Coath, and B. Funt, “A comparison of computational color constancy algorithms. Part two: experiments on image data,” IEEE Trans. Image Process. 11, 985–996(2002).
[CrossRef]

2001 (1)

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

2000 (1)

G. D. Knott, Interpolating Cubic Splines (Birkhauser, 2000).
[CrossRef]

1997 (2)

M. H. Davis, A. Khotanzad, D. Flamig, and S. Harms, “A physics-based coordinate transformation for 3-d image matching,” IEEE Trans. Med. Imaging 16, 317–328 (1997).
[CrossRef] [PubMed]

G. D. Finlayson, “Retinex viewed as a Gamut Mapping theory of color constancy,” in Proceedings of AIC International Color Association Color 97 (International Color Association, 1997), Vol.  2, pp. 527–530.

1995 (1)

N. Arad and D. Reisfeld, “Image warping using few anchor points and radial functions,” Comput. Graph. Forum 14, 35–46(1995).
[CrossRef]

1991 (1)

F. L. Bookstein, Morphometric Tools for Landmark Data Geometry and Biology (Cambridge University, 1991).

1989 (1)

F. L. Bookstein, “Principal warps: thin-plate splines and decomposition of deformations,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 567–585 (1989).
[CrossRef]

1987 (1)

R. Gershon, A. D. Jepson, and J. K. Tsotsos, “From [R,G,B] to surface reflectance: computing color constant descriptors in images,” in Proceedings of the 10th International Joint Conference on Artificial Intelligence (Morgan Kaufmann, 1987), pp. 755–758.

1980 (1)

B. Buchsbaum, “A spatial processor model for object color perception,” J. Franklin Inst. 310, 1–26 (1980).
[CrossRef]

1979 (1)

J. Meinguet, “Multivariate interpolation at arbitrary points made simple,” Z. Angew Math. Phys. 30, 292–304 (1979).
[CrossRef]

Arad, N.

N. Arad and D. Reisfeld, “Image warping using few anchor points and radial functions,” Comput. Graph. Forum 14, 35–46(1995).
[CrossRef]

Barnard, K.

V. Cardei, B. Funt, and K. Barnard, “Estimating the scene illumination chromaticity using a neural network,” J. Opt. Soc. Am. A 19, 2374–2386 (2002).
[CrossRef]

K. Barnard, L. Martin, A. Coath, and B. Funt, “A comparison of computational color constancy algorithms. Part two: experiments on image data,” IEEE Trans. Image Process. 11, 985–996(2002).
[CrossRef]

Bazen, A. M.

A. M. Bazen and S. H. Gerez, “Elastic minutiae matching by means of thin-plate spline models,” in Proceedings of 16th International Conference on Pattern Recognition (IEEE, 2002), pp. 985–988.

Bianco, S.

S. Bianco, G. Ciocca, C. Cusano, and R. Schettini, “Improving color constancy using indoor–outdoor image classification,” IEEE Trans. Image Process. 17, 2381–2392 (2008).
[CrossRef] [PubMed]

Blake, A.

P. V. Gehler, C. Rother, A. Blake, T. P. Minka, and T. Sharp, “Bayesian color constancy revisited,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–8.

Bookstein, F. L.

F. L. Bookstein, Morphometric Tools for Landmark Data Geometry and Biology (Cambridge University, 1991).

F. L. Bookstein, “Principal warps: thin-plate splines and decomposition of deformations,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 567–585 (1989).
[CrossRef]

Buchsbaum, B.

B. Buchsbaum, “A spatial processor model for object color perception,” J. Franklin Inst. 310, 1–26 (1980).
[CrossRef]

Cardei, V.

Ciocca, G.

S. Bianco, G. Ciocca, C. Cusano, and R. Schettini, “Improving color constancy using indoor–outdoor image classification,” IEEE Trans. Image Process. 17, 2381–2392 (2008).
[CrossRef] [PubMed]

Ciurea, F.

F. Ciurea and B. Funt, “A large image database for color constancy research,” in Proceedings of IS&T/SID Eleventh Color Imaging Conference (Society for Imaging Science and Technology, 2003), pp. 160–163.

Coath, A.

K. Barnard, L. Martin, A. Coath, and B. Funt, “A comparison of computational color constancy algorithms. Part two: experiments on image data,” IEEE Trans. Image Process. 11, 985–996(2002).
[CrossRef]

Coffin, D.

D. Coffin, “Dcraw,” http://en.wikipedia.org/wiki/Dcraw.

Cusano, C.

S. Bianco, G. Ciocca, C. Cusano, and R. Schettini, “Improving color constancy using indoor–outdoor image classification,” IEEE Trans. Image Process. 17, 2381–2392 (2008).
[CrossRef] [PubMed]

Davis, L. S.

A. Zandifar, S. Lim, R. Duraiswami, N. Gumerov, and L. S. Davis, “Multi-level fast multipole method for thin plate spline evaluation,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2004), pp. 1683–1686.

Davis, M. H.

M. H. Davis, A. Khotanzad, D. Flamig, and S. Harms, “A physics-based coordinate transformation for 3-d image matching,” IEEE Trans. Med. Imaging 16, 317–328 (1997).
[CrossRef] [PubMed]

Duraiswami, R.

A. Zandifar, S. Lim, R. Duraiswami, N. Gumerov, and L. S. Davis, “Multi-level fast multipole method for thin plate spline evaluation,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2004), pp. 1683–1686.

Finlayson, G.

S. Hordley and G. Finlayson, “A reevaluation of color constancy algorithm performance,” J. Opt. Soc. Am. A 23, 1008–1020(2006).
[CrossRef]

G. Finlayson, S. Hordley, and I. Tastl, “Gamut constrained illumination estimation,” Int. J. Comput. Vis. 67, 93–109(2006).
[CrossRef]

Finlayson, G. D.

G. D. Finlayson and E. Trezzi, “Shades of Gray and colour constancy,” in Proceedings of IS&T/SID Twelfth Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, 2004), pp. 37–41.

S. D. Hordley and G. D. Finlayson, “Re-evaluating colour constancy algorithms,” in Proceedings of 17th International Conference on Pattern Recognition (IEEE, 2004), pp. 76–79.
[CrossRef]

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

G. D. Finlayson, “Retinex viewed as a Gamut Mapping theory of color constancy,” in Proceedings of AIC International Color Association Color 97 (International Color Association, 1997), Vol.  2, pp. 527–530.

Flamig, D.

M. H. Davis, A. Khotanzad, D. Flamig, and S. Harms, “A physics-based coordinate transformation for 3-d image matching,” IEEE Trans. Med. Imaging 16, 317–328 (1997).
[CrossRef] [PubMed]

Funt, B.

B. Funt and L. Shi, “The rehabilitation of MaxRGB,” in Proceedings of the Eighteenth IS&T Color Imaging Conference (Society for Imaging Science and Technology, 2010), pp. 256–259.

W. Xiong, B. Funt, L. Shi, S. Kim, B. Kang, and S. D. Lee, “Automatic white balancing via Gray Surface Identification,” in Proceedings of the Fifteenth IS&T Color Imaging Conference (Society for Imaging Science and Technology, 2007), pp. 143–146.

F. Ciurea and B. Funt, “A large image database for color constancy research,” in Proceedings of IS&T/SID Eleventh Color Imaging Conference (Society for Imaging Science and Technology, 2003), pp. 160–163.

K. Barnard, L. Martin, A. Coath, and B. Funt, “A comparison of computational color constancy algorithms. Part two: experiments on image data,” IEEE Trans. Image Process. 11, 985–996(2002).
[CrossRef]

V. Cardei, B. Funt, and K. Barnard, “Estimating the scene illumination chromaticity using a neural network,” J. Opt. Soc. Am. A 19, 2374–2386 (2002).
[CrossRef]

Funt, B. V.

B. V. Funt and W. H. Xiong, “Estimating illumination chromaticity via Support Vector Regression,” J. Imaging Sci. Technol. 50, 341–348 (2006).
[CrossRef]

W. Xiong and B. V. Funt, “Nonlinear RGB-to-XYZ mapping for device calibration,” in Proceedings of Imaging Science and Technology Thirteenth Color Imaging Conference (Society for Imaging Sciences and Technology, 2005), pp. 200–204.

Gehler, P. V.

P. V. Gehler, C. Rother, A. Blake, T. P. Minka, and T. Sharp, “Bayesian color constancy revisited,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–8.

Gerez, S. H.

A. M. Bazen and S. H. Gerez, “Elastic minutiae matching by means of thin-plate spline models,” in Proceedings of 16th International Conference on Pattern Recognition (IEEE, 2002), pp. 985–988.

Gershon, R.

R. Gershon, A. D. Jepson, and J. K. Tsotsos, “From [R,G,B] to surface reflectance: computing color constant descriptors in images,” in Proceedings of the 10th International Joint Conference on Artificial Intelligence (Morgan Kaufmann, 1987), pp. 755–758.

Gevers, T.

A. Gijsenij, T. Gevers, and J. van deWeijer, “Generalized Gamut Mapping using image derivative structures for color constancy,” Int. J. Comput. Vis. 86, 127–139 (2008).
[CrossRef]

J. van de Weijer, T. Gevers, and A. Gijsenij, “Edge-based color constancy,” IEEE Trans. Image Process. 16, 2207–2214(2007).
[CrossRef] [PubMed]

Gijsenij, A.

A. Gijsenij, T. Gevers, and J. van deWeijer, “Generalized Gamut Mapping using image derivative structures for color constancy,” Int. J. Comput. Vis. 86, 127–139 (2008).
[CrossRef]

J. van de Weijer, T. Gevers, and A. Gijsenij, “Edge-based color constancy,” IEEE Trans. Image Process. 16, 2207–2214(2007).
[CrossRef] [PubMed]

Gumerov, N.

A. Zandifar, S. Lim, R. Duraiswami, N. Gumerov, and L. S. Davis, “Multi-level fast multipole method for thin plate spline evaluation,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2004), pp. 1683–1686.

Harms, S.

M. H. Davis, A. Khotanzad, D. Flamig, and S. Harms, “A physics-based coordinate transformation for 3-d image matching,” IEEE Trans. Med. Imaging 16, 317–328 (1997).
[CrossRef] [PubMed]

Hordley, S.

S. Hordley and G. Finlayson, “A reevaluation of color constancy algorithm performance,” J. Opt. Soc. Am. A 23, 1008–1020(2006).
[CrossRef]

G. Finlayson, S. Hordley, and I. Tastl, “Gamut constrained illumination estimation,” Int. J. Comput. Vis. 67, 93–109(2006).
[CrossRef]

Hordley, S. D.

S. D. Hordley and G. D. Finlayson, “Re-evaluating colour constancy algorithms,” in Proceedings of 17th International Conference on Pattern Recognition (IEEE, 2004), pp. 76–79.
[CrossRef]

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

Hubel, P. M.

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

Jepson, A. D.

R. Gershon, A. D. Jepson, and J. K. Tsotsos, “From [R,G,B] to surface reflectance: computing color constant descriptors in images,” in Proceedings of the 10th International Joint Conference on Artificial Intelligence (Morgan Kaufmann, 1987), pp. 755–758.

Kang, B.

W. Xiong, B. Funt, L. Shi, S. Kim, B. Kang, and S. D. Lee, “Automatic white balancing via Gray Surface Identification,” in Proceedings of the Fifteenth IS&T Color Imaging Conference (Society for Imaging Science and Technology, 2007), pp. 143–146.

Khotanzad, A.

M. H. Davis, A. Khotanzad, D. Flamig, and S. Harms, “A physics-based coordinate transformation for 3-d image matching,” IEEE Trans. Med. Imaging 16, 317–328 (1997).
[CrossRef] [PubMed]

Kim, S.

W. Xiong, B. Funt, L. Shi, S. Kim, B. Kang, and S. D. Lee, “Automatic white balancing via Gray Surface Identification,” in Proceedings of the Fifteenth IS&T Color Imaging Conference (Society for Imaging Science and Technology, 2007), pp. 143–146.

Knott, G. D.

G. D. Knott, Interpolating Cubic Splines (Birkhauser, 2000).
[CrossRef]

Lee, S. D.

W. Xiong, B. Funt, L. Shi, S. Kim, B. Kang, and S. D. Lee, “Automatic white balancing via Gray Surface Identification,” in Proceedings of the Fifteenth IS&T Color Imaging Conference (Society for Imaging Science and Technology, 2007), pp. 143–146.

Lim, S.

A. Zandifar, S. Lim, R. Duraiswami, N. Gumerov, and L. S. Davis, “Multi-level fast multipole method for thin plate spline evaluation,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2004), pp. 1683–1686.

Martin, L.

K. Barnard, L. Martin, A. Coath, and B. Funt, “A comparison of computational color constancy algorithms. Part two: experiments on image data,” IEEE Trans. Image Process. 11, 985–996(2002).
[CrossRef]

Meinguet, J.

J. Meinguet, “Multivariate interpolation at arbitrary points made simple,” Z. Angew Math. Phys. 30, 292–304 (1979).
[CrossRef]

Minka, T. P.

P. V. Gehler, C. Rother, A. Blake, T. P. Minka, and T. Sharp, “Bayesian color constancy revisited,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–8.

Reisfeld, D.

N. Arad and D. Reisfeld, “Image warping using few anchor points and radial functions,” Comput. Graph. Forum 14, 35–46(1995).
[CrossRef]

Rother, C.

P. V. Gehler, C. Rother, A. Blake, T. P. Minka, and T. Sharp, “Bayesian color constancy revisited,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–8.

Schettini, R.

S. Bianco, G. Ciocca, C. Cusano, and R. Schettini, “Improving color constancy using indoor–outdoor image classification,” IEEE Trans. Image Process. 17, 2381–2392 (2008).
[CrossRef] [PubMed]

Sharp, T.

P. V. Gehler, C. Rother, A. Blake, T. P. Minka, and T. Sharp, “Bayesian color constancy revisited,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–8.

Shi, L.

B. Funt and L. Shi, “The rehabilitation of MaxRGB,” in Proceedings of the Eighteenth IS&T Color Imaging Conference (Society for Imaging Science and Technology, 2010), pp. 256–259.

W. Xiong, B. Funt, L. Shi, S. Kim, B. Kang, and S. D. Lee, “Automatic white balancing via Gray Surface Identification,” in Proceedings of the Fifteenth IS&T Color Imaging Conference (Society for Imaging Science and Technology, 2007), pp. 143–146.

Tastl, I.

G. Finlayson, S. Hordley, and I. Tastl, “Gamut constrained illumination estimation,” Int. J. Comput. Vis. 67, 93–109(2006).
[CrossRef]

Trezzi, E.

G. D. Finlayson and E. Trezzi, “Shades of Gray and colour constancy,” in Proceedings of IS&T/SID Twelfth Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, 2004), pp. 37–41.

Tsotsos, J. K.

R. Gershon, A. D. Jepson, and J. K. Tsotsos, “From [R,G,B] to surface reflectance: computing color constant descriptors in images,” in Proceedings of the 10th International Joint Conference on Artificial Intelligence (Morgan Kaufmann, 1987), pp. 755–758.

van de Weijer, J.

J. van de Weijer, T. Gevers, and A. Gijsenij, “Edge-based color constancy,” IEEE Trans. Image Process. 16, 2207–2214(2007).
[CrossRef] [PubMed]

van deWeijer, J.

A. Gijsenij, T. Gevers, and J. van deWeijer, “Generalized Gamut Mapping using image derivative structures for color constancy,” Int. J. Comput. Vis. 86, 127–139 (2008).
[CrossRef]

Xiong, W.

W. Xiong, B. Funt, L. Shi, S. Kim, B. Kang, and S. D. Lee, “Automatic white balancing via Gray Surface Identification,” in Proceedings of the Fifteenth IS&T Color Imaging Conference (Society for Imaging Science and Technology, 2007), pp. 143–146.

W. Xiong and B. V. Funt, “Nonlinear RGB-to-XYZ mapping for device calibration,” in Proceedings of Imaging Science and Technology Thirteenth Color Imaging Conference (Society for Imaging Sciences and Technology, 2005), pp. 200–204.

Xiong, W. H.

B. V. Funt and W. H. Xiong, “Estimating illumination chromaticity via Support Vector Regression,” J. Imaging Sci. Technol. 50, 341–348 (2006).
[CrossRef]

Zandifar, A.

A. Zandifar, S. Lim, R. Duraiswami, N. Gumerov, and L. S. Davis, “Multi-level fast multipole method for thin plate spline evaluation,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2004), pp. 1683–1686.

Comput. Graph. Forum (1)

N. Arad and D. Reisfeld, “Image warping using few anchor points and radial functions,” Comput. Graph. Forum 14, 35–46(1995).
[CrossRef]

IEEE Trans. Image Process. (3)

K. Barnard, L. Martin, A. Coath, and B. Funt, “A comparison of computational color constancy algorithms. Part two: experiments on image data,” IEEE Trans. Image Process. 11, 985–996(2002).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

k-median (with k = 220 ) clustering of the 11,346 training real-world images [13]. The x axis and y axis stand for the first and second principal component vectors. Each red circle represents a cluster detected. Circle size is proportional to the standard derivation of the cluster. This shows graphically that the 220 colors cover the underlying data set quite well.

Fig. 2
Fig. 2

(a) Histogram of the measured illumination chromaticities from the full set of 11,346 images showing a distinct peak around gray (0.33, 0.33); (b) corresponding histogram for the reduced data set of 7661 images showing a more uniform distribution of illumination chromaticities. The x axis is the chromaticity r, the y axis is the chromaticity g, and the z axis is the count of the number of the same illuminations.

Fig. 3
Fig. 3

Plot of the median angular error (y) from Table 9 (excluding the last row) as a function of the size of the set of representative training images (x axis).

Tables (9)

Tables Icon

Table 1 Performance Comparison of MaxRGB [18] and MaxRGB with Preprocessing of the Images ( MaxRBG + ) by Bicubic Resizing to 64 × 64 [19], GrayWorld (GW)[20], 3D Support Vector Regression (SVR) [4], Shades of Gray (SoG) [21], Edge-Based [22], Gray Surface Identification (GSI) [23], Color by Correlation (CbyC) [24], Gamut Mapping [25], N-Jet [26], and TPS a

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Table 2 Comparison of Several Different Algorithms in Table 1 via the Wilcoxon Signed-Rank Test with Rejection of the Null Hypothesis at the 5% Significance Level a

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Table 3 Performance Comparison of MaxRGB [18] and MaxRGB with Preprocessing (Labeled MaxRGB + ) of the Images by Bicubic Resizing to 64 × 64 [19], GrayWorld [20], Shades of Gray [21], Edge-Based [22], Color by Correlation [24], Gamut Mapping [25], N-Jet [26], Bayes-GT (with Threefold Cross-Validation) [17], and TPS a

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Table 4 Comparison of Several Different Algorithms in Table 3 via the Wilcoxon Signed-Rank Test with Rejection of the Null Hypothesis at the 5% Significance Level a

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Table 5 Performance Comparison of MaxRGB [18], MaxRGB with Preprocessing (Labeled MaxRGB + ) of the Images by Bicubic Resizing to 64 × 64 [19], GrayWorld [20], Shades of Gray [21], Edge-Based [22], and TPS a

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Table 6 Comparison of Several Different Algorithms in Table 5 via the Wilcoxon Signed-Rank Test with Rejection of the Null Hypothesis at the 5% Significance Level a

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Table 7 Performance Comparison of MaxRGB [18] and MaxRGB with Preprocessing of the Images by Bicubic Resizing to 64 × 64 [19], GrayWorld [20], 3D Support Vector Regression [4], Shades of Gray [21], Edge-Based [22], Gray Surface Identification [23], Color by Correlation [24], N-Jet [26], and TPS a

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Table 8 Comparison of the Performance Based on the Wilcoxon Signed-Rank Test with Rejection of the Null Hypothesis at the 5% Significance Level a

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Table 9 Median Angular Error of TPS Illumination Estimates Taken over 4080 Images along with Training and Test Times as a Function of the Size of the Reduced Training Set a

Equations (12)

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

{ r i = f r ( I i ) g i = f g ( I i ) .
f r ( I s ) = i = 1 N w i U ( I s I i ) + a 0 + j = 1 D a j I s , j ,
J ( f ) = 2 ( f x 1 x 1 2 + 2 f x 1 x 2 2 + f x 2 x 2 2 ) d x 1 x 2 .
J ( f r ) = θ 1 + θ 2 + + θ D = D [ D ! θ 1 ! θ 2 ! θ D ! R D ( D f r x 1 θ 1 x 2 θ 2 x D θ D ) 2 d x 1 d x 2 d x D ] ,
i = 1 N w i = i = 1 N I i , 1 w i = i = 1 N I 2 , 1 w i = = i = 1 N I i , D w i = 0 ,
U w + Q a = c Q T w = 0 ,
U = [ 0 U 1 , 2 U 1 , N U 2 , 1 0 U 2 , N U N , 1 U N , 2 0 ] Q = [ 1 I 1 , 1 I 1 , 2 I 1 , D 1 I 2 , 1 I 2 , 2 I 2 , D 1 I N , 1 I N , 2 I N , D ] ,
w = ( w 1 , w 2 , , w N ) T and a = ( a 0 , a 1 , , a D ) T , c = ( r 1 , r 2 , , r N ) T or c = ( g 1 , g 2 , , g N ) T , U i , j = U ( I i I j ) .
[ U Q Q T 0 ¯ ] × [ w a ] = [ c 0 ] or    L × W = C .
E L 2 - dist = [ ( r a r e ) 2 + ( g a g e ) 2 ] 1 / 2 ,
RMS = 1 M i = 1 M E L 2 - dist 2
E Ang = cos 1 [ ( r a , g a , b a ) · ( r e , g e , b e ) r a 2 + g a 2 + g a 2 · r e 2 + g e 2 + g e 2 ] · 2 π 360 .

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