Abstract

A neural network can learn color constancy, defined here as the ability to estimate the chromaticity of a scene’s overall illumination. We describe a multilayer neural network that is able to recover the illumination chromaticity given only an image of the scene. The network is previously trained by being presented with a set of images of scenes and the chromaticities of the corresponding scene illuminants. Experiments with real images show that the network performs better than previous color constancy methods. In particular, the performance is better for images with a relatively small number of distinct colors. The method has application to machine vision problems such as object recognition, where illumination-independent color descriptors are required, and in digital photography, where uncontrolled scene illumination can create an unwanted color cast in a photograph.

© 2002 Optical Society of America

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2002 (1)

K. Barnard, B. Funt, “Camera characterization for color research,” Color Res. Appl. 27, 153–164 (2002).
[CrossRef]

2001 (2)

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

K. Barnard, F. Ciurea, B. Funt, “Sensor sharpening for computational color constancy,” J. Opt. Soc. Am. A 18, 2728–2743 (2001).
[CrossRef]

2000 (1)

V. Cardei, B. Funt, “Color correcting uncalibrated digital images,” J. Imaging Sci. Technol. 44, 288–294 (2000).

1997 (3)

1996 (1)

G. Finlayson, “Color in perspective,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 1034–1038 (1996).
[CrossRef]

1995 (1)

S. M. Courtney, L. F. Finkel, G. Buchsbaum, “A multistage neural network for color constancy and color induction,” IEEE Trans. Neural Netw. 6, 972–985 (1995).
[CrossRef] [PubMed]

1994 (3)

1992 (2)

D. H. Brainard, B. A. Wandell, “Asymmetric color matching: how color appearance depends on the illuminant,” J. Opt. Soc. Am. A 9, 1433–1448 (1992).
[CrossRef] [PubMed]

S. Geman, E. Bienenstock, R. Doursat, “Neural networks and the bias/variance dilemma,” Neural Comput. 4, 1–58 (1992).
[CrossRef]

1991 (2)

M. J. Swain, D. Ballard, “Color indexing,” Int. J. Comput. Vision 7, 11–32 (1991).
[CrossRef]

A. Moore, J. Allman, R. M. Goodman, “A real-time neural system for color constancy,” IEEE Trans. Neural Netw. 2, 237–247 (1991).
[CrossRef] [PubMed]

1990 (1)

D. A. Forsyth, “A novel algorithm for color constancy,” Int. J. Comput. Vision 5, 5–36 (1990).
[CrossRef]

1988 (2)

R. Gershon, A. D. Jepson, J. K. Tsotsos, “From [R, G, B] to surface reflectance: computing color constant descriptors in images,” Perception 17, 755–758 (1988).

A. C. Hurlbert, T. A. Poggio, “Synthesizing a color algorithm from examples,” Science 239, 482–485 (1988).
[CrossRef] [PubMed]

1987 (1)

B. A. Wandell, “The synthesis and analysis of color images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI9, 2–13 (1987).
[CrossRef]

1986 (3)

1985 (1)

S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
[CrossRef]

1980 (1)

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

1971 (1)

1964 (2)

Allman, J.

A. Moore, J. Allman, R. M. Goodman, “A real-time neural system for color constancy,” IEEE Trans. Neural Netw. 2, 237–247 (1991).
[CrossRef] [PubMed]

Anderson, M.

M. Anderson, R. Motta, S. Chandrasekar, M. Stokes, “Proposal for a standard default color space for the Internet–sRGB,” in Proceedings of the IS&T/SID Fourth Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, Springfield, Va., 1996), pp. 238–246.

Ballard, D.

M. J. Swain, D. Ballard, “Color indexing,” Int. J. Comput. Vision 7, 11–32 (1991).
[CrossRef]

Barnard, K.

K. Barnard, B. Funt, “Camera characterization for color research,” Color Res. Appl. 27, 153–164 (2002).
[CrossRef]

K. Barnard, F. Ciurea, B. Funt, “Sensor sharpening for computational color constancy,” J. Opt. Soc. Am. A 18, 2728–2743 (2001).
[CrossRef]

K. Barnard, G. Finlayson, B. Funt, “Color constancy for scenes with varying illumination,” Comput. Vision Image Understand. 65, 311–321 (1997).
[CrossRef]

G. Finlayson, B. Funt, K. Barnard, “Color constancy under varying illumination,” in Proceedings of the Fifth International Conference on Computer Vision, W. E. L. Grimson, ed. (IEEE Computer Society Press, Los Alamitos, Calif., 1995), pp. 720–725.

B. Funt, K. Barnard, L. Martin, “Is color constancy good enough?” in Proceedings of the Fifth European Conference on Computer Vision, H. Burkhardt, B. Neumann, eds. (Springer, Berlin, 1998), pp. 445–459.

K. Barnard, V. Cardei, B. Funt, “A comparison of computational color constancy algorithms; part one: methodology and experiments with synthesized data,” IEEE Trans. Image Process. (to be published).

V. Cardei, B. Funt, K. Barnard, “Modeling color constancy with neural networks,” in Proceedings of the International Conference on Vision, Recognition, and Action: Neural Models of Mind and Machine (Center for Adaptive Systems, Boston University, Boston, Mass., 1997).

B. Funt, V. Cardei, K. Barnard, “Learning Color Constancy,” in Proceedings of the IS&T/SID Fourth Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, Springfield, Va., 1996), pp. 58–60.

K. Barnard, “Practical colour constancy,” Ph.D. thesis (Simon Fraser University, Burnaby, B.C., Canada, 1999).

B. Funt, V. Cardei, K. Barnard, “Neural network color constancy and specularly reflecting surfaces,” in AIC Color 97 Proceedings of the 8th Congress of the International Colour Association (Color Science Association of Japan, Tokyo, 1997), Vol. II, pp. 523–526.

Bienenstock, E.

S. Geman, E. Bienenstock, R. Doursat, “Neural networks and the bias/variance dilemma,” Neural Comput. 4, 1–58 (1992).
[CrossRef]

Brainard, D. H.

Brill, M. H.

Brunt, W. A.

Buchsbaum, G.

S. M. Courtney, L. F. Finkel, G. Buchsbaum, “A multistage neural network for color constancy and color induction,” IEEE Trans. Neural Netw. 6, 972–985 (1995).
[CrossRef] [PubMed]

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

Cardei, V.

V. Cardei, B. Funt, “Color correcting uncalibrated digital images,” J. Imaging Sci. Technol. 44, 288–294 (2000).

B. Funt, V. Cardei, K. Barnard, “Neural network color constancy and specularly reflecting surfaces,” in AIC Color 97 Proceedings of the 8th Congress of the International Colour Association (Color Science Association of Japan, Tokyo, 1997), Vol. II, pp. 523–526.

B. Funt, V. Cardei, K. Barnard, “Learning Color Constancy,” in Proceedings of the IS&T/SID Fourth Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, Springfield, Va., 1996), pp. 58–60.

V. Cardei, B. Funt, K. Barnard, “Modeling color constancy with neural networks,” in Proceedings of the International Conference on Vision, Recognition, and Action: Neural Models of Mind and Machine (Center for Adaptive Systems, Boston University, Boston, Mass., 1997).

K. Barnard, V. Cardei, B. Funt, “A comparison of computational color constancy algorithms; part one: methodology and experiments with synthesized data,” IEEE Trans. Image Process. (to be published).

Chandrasekar, S.

M. Anderson, R. Motta, S. Chandrasekar, M. Stokes, “Proposal for a standard default color space for the Internet–sRGB,” in Proceedings of the IS&T/SID Fourth Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, Springfield, Va., 1996), pp. 238–246.

Ciurea, F.

Cohen, J.

J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychon. Sci. 1, 369–370 (1964).
[CrossRef]

Courtney, S. M.

S. M. Courtney, L. F. Finkel, G. Buchsbaum, “A multistage neural network for color constancy and color induction,” IEEE Trans. Neural Netw. 6, 972–985 (1995).
[CrossRef] [PubMed]

Doursat, R.

S. Geman, E. Bienenstock, R. Doursat, “Neural networks and the bias/variance dilemma,” Neural Comput. 4, 1–58 (1992).
[CrossRef]

Drew, M.

Eubank, R. L.

R. L. Eubank, Spline Smoothing and Nonparametric Regression (Marcel Dekker, New York, 1988).

Finkel, L. F.

S. M. Courtney, L. F. Finkel, G. Buchsbaum, “A multistage neural network for color constancy and color induction,” IEEE Trans. Neural Netw. 6, 972–985 (1995).
[CrossRef] [PubMed]

Finlayson, G.

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

K. Barnard, G. Finlayson, B. Funt, “Color constancy for scenes with varying illumination,” Comput. Vision Image Understand. 65, 311–321 (1997).
[CrossRef]

G. Finlayson, “Color in perspective,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 1034–1038 (1996).
[CrossRef]

G. Finlayson, M. Drew, B. Funt, “Color constancy: generalized diagonal transforms suffice,” J. Opt. Soc. Am. A 11, 3011–3020 (1994).
[CrossRef]

G. Finlayson, M. Drew, B. Funt, “Spectral sharpening: sensor transformations for improved color constancy,” J. Opt. Soc. Am. A 11, 1553–1563 (1994).
[CrossRef]

G. Finlayson, B. Funt, K. Barnard, “Color constancy under varying illumination,” in Proceedings of the Fifth International Conference on Computer Vision, W. E. L. Grimson, ed. (IEEE Computer Society Press, Los Alamitos, Calif., 1995), pp. 720–725.

G. Finlayson, P. Hubel, S. Hordley, “Color by correlation,” in Proceedings of the IS&T/SID Fifth Color Imaging Conference: Color Science, Systems and Applications, (Society for Imaging Science and Technology, Springfield, Va., 1997), pp. 6–11.

Forsyth, D. A.

D. A. Forsyth, “A novel algorithm for color constancy,” Int. J. Comput. Vision 5, 5–36 (1990).
[CrossRef]

Freeman, W. T.

Funt, B.

K. Barnard, B. Funt, “Camera characterization for color research,” Color Res. Appl. 27, 153–164 (2002).
[CrossRef]

K. Barnard, F. Ciurea, B. Funt, “Sensor sharpening for computational color constancy,” J. Opt. Soc. Am. A 18, 2728–2743 (2001).
[CrossRef]

V. Cardei, B. Funt, “Color correcting uncalibrated digital images,” J. Imaging Sci. Technol. 44, 288–294 (2000).

K. Barnard, G. Finlayson, B. Funt, “Color constancy for scenes with varying illumination,” Comput. Vision Image Understand. 65, 311–321 (1997).
[CrossRef]

G. Finlayson, M. Drew, B. Funt, “Color constancy: generalized diagonal transforms suffice,” J. Opt. Soc. Am. A 11, 3011–3020 (1994).
[CrossRef]

G. Finlayson, M. Drew, B. Funt, “Spectral sharpening: sensor transformations for improved color constancy,” J. Opt. Soc. Am. A 11, 1553–1563 (1994).
[CrossRef]

B. Funt, V. Cardei, K. Barnard, “Learning Color Constancy,” in Proceedings of the IS&T/SID Fourth Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, Springfield, Va., 1996), pp. 58–60.

K. Barnard, V. Cardei, B. Funt, “A comparison of computational color constancy algorithms; part one: methodology and experiments with synthesized data,” IEEE Trans. Image Process. (to be published).

V. Cardei, B. Funt, K. Barnard, “Modeling color constancy with neural networks,” in Proceedings of the International Conference on Vision, Recognition, and Action: Neural Models of Mind and Machine (Center for Adaptive Systems, Boston University, Boston, Mass., 1997).

G. Finlayson, B. Funt, K. Barnard, “Color constancy under varying illumination,” in Proceedings of the Fifth International Conference on Computer Vision, W. E. L. Grimson, ed. (IEEE Computer Society Press, Los Alamitos, Calif., 1995), pp. 720–725.

B. Funt, K. Barnard, L. Martin, “Is color constancy good enough?” in Proceedings of the Fifth European Conference on Computer Vision, H. Burkhardt, B. Neumann, eds. (Springer, Berlin, 1998), pp. 445–459.

B. Funt, V. Cardei, K. Barnard, “Neural network color constancy and specularly reflecting surfaces,” in AIC Color 97 Proceedings of the 8th Congress of the International Colour Association (Color Science Association of Japan, Tokyo, 1997), Vol. II, pp. 523–526.

Geman, S.

S. Geman, E. Bienenstock, R. Doursat, “Neural networks and the bias/variance dilemma,” Neural Comput. 4, 1–58 (1992).
[CrossRef]

Gershon, R.

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

R. Gershon, A. D. Jepson, J. K. Tsotsos, “From [R, G, B] to surface reflectance: computing color constant descriptors in images,” Perception 17, 755–758 (1988).

Goodman, R. M.

A. Moore, J. Allman, R. M. Goodman, “A real-time neural system for color constancy,” IEEE Trans. Neural Netw. 2, 237–247 (1991).
[CrossRef] [PubMed]

Hertz, J.

J. Hertz, A. Krogh, R. G. Palmer, Introduction to the Theory of Neural Computation (Addison-Wesley, Reading, Mass., 1991).

Hinton, G.

D. Plaut, S. Nowlan, G. Hinton, “Experiments on learning by back propagation,” (Carnegie-Mellon University, Pittsburgh, Pa., 1986).

Hinton, G. E.

D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed Processing: Explorations in the Microstructure of Cognition. Vol. I: Foundations, D. E. Rumelhart, J. L. McClelland, and the PDP Research Group, eds. (MIT Press, Cambridge, Mass., 1986), pp. 318–362.

Hordley, S.

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

G. Finlayson, P. Hubel, S. Hordley, “Color by correlation,” in Proceedings of the IS&T/SID Fifth Color Imaging Conference: Color Science, Systems and Applications, (Society for Imaging Science and Technology, Springfield, Va., 1997), pp. 6–11.

Hubel, P.

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

G. Finlayson, P. Hubel, S. Hordley, “Color by correlation,” in Proceedings of the IS&T/SID Fifth Color Imaging Conference: Color Science, Systems and Applications, (Society for Imaging Science and Technology, Springfield, Va., 1997), pp. 6–11.

Hurlbert, A. C.

A. C. Hurlbert, T. A. Poggio, “Synthesizing a color algorithm from examples,” Science 239, 482–485 (1988).
[CrossRef] [PubMed]

A. C. Hurlbert, “Neural network approaches to color vision,” in Neural Networks for Perception: Vol. 1: Human and Machine Perception, H. Wechsler, ed. (Academic, San Diego, Calif., state, 1991), pp. 266–284.

Iwan, L. S.

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

Jepson, A. D.

R. Gershon, A. D. Jepson, J. K. Tsotsos, “From [R, G, B] to surface reflectance: computing color constant descriptors in images,” Perception 17, 755–758 (1988).

Judd, D. B.

Krogh, A.

J. Hertz, A. Krogh, R. G. Palmer, Introduction to the Theory of Neural Computation (Addison-Wesley, Reading, Mass., 1991).

Land, E. H.

Lee, H.

MacAdam, D. L.

Maloney, L.

Martin, L.

B. Funt, K. Barnard, L. Martin, “Is color constancy good enough?” in Proceedings of the Fifth European Conference on Computer Vision, H. Burkhardt, B. Neumann, eds. (Springer, Berlin, 1998), pp. 445–459.

McCann, J. J.

Miyamoto, Y.

S. Usui, S. Nakauchi, Y. Miyamoto, “A neural network model for color constancy based on the minimally redundant color representation,” in Proceedings of the International Joint Conference on Neural Networks (International Neural Network Society, Mt. Royal, N.J., 1992), Vol. 2, pp. 696–701.

Moody, J.

J. Moody, “Prediction risk and architecture selection for neural networks,” in From Statistics to Neural Networks: Theory and Pattern Recognition Applications, V. Cherkassky, J. H. Friedman, H. Wechsler, eds., NATO ASI Series F (Springer-Verlag, Berlin, 1994), pp. 147–165.

Moore, A.

A. Moore, J. Allman, R. M. Goodman, “A real-time neural system for color constancy,” IEEE Trans. Neural Netw. 2, 237–247 (1991).
[CrossRef] [PubMed]

Motta, R.

M. Anderson, R. Motta, S. Chandrasekar, M. Stokes, “Proposal for a standard default color space for the Internet–sRGB,” in Proceedings of the IS&T/SID Fourth Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, Springfield, Va., 1996), pp. 238–246.

Nakauchi, S.

S. Usui, S. Nakauchi, Y. Miyamoto, “A neural network model for color constancy based on the minimally redundant color representation,” in Proceedings of the International Joint Conference on Neural Networks (International Neural Network Society, Mt. Royal, N.J., 1992), Vol. 2, pp. 696–701.

Nowlan, S.

D. Plaut, S. Nowlan, G. Hinton, “Experiments on learning by back propagation,” (Carnegie-Mellon University, Pittsburgh, Pa., 1986).

Palmer, R. G.

J. Hertz, A. Krogh, R. G. Palmer, Introduction to the Theory of Neural Computation (Addison-Wesley, Reading, Mass., 1991).

Plaut, D.

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D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed Processing: Explorations in the Microstructure of Cognition. Vol. I: Foundations, D. E. Rumelhart, J. L. McClelland, and the PDP Research Group, eds. (MIT Press, Cambridge, Mass., 1986), pp. 318–362.

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D. Plaut, S. Nowlan, G. Hinton, “Experiments on learning by back propagation,” (Carnegie-Mellon University, Pittsburgh, Pa., 1986).

G. Wyszecki, W. Stiles, Color Science: Concepts and Methods, Quantitative data and Formulae, 2nd ed. (Wiley, New York, 1982).

M. Anderson, R. Motta, S. Chandrasekar, M. Stokes, “Proposal for a standard default color space for the Internet–sRGB,” in Proceedings of the IS&T/SID Fourth Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, Springfield, Va., 1996), pp. 238–246.

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W. M. Richard, Automatic Detection of Effective Scene Illuminant Chromaticity from Specular Highlights in Digital Images, M.Sc. thesis (Rochester Institute of Technology, Rochester, N.Y., 1995).

S. Usui, S. Nakauchi, Y. Miyamoto, “A neural network model for color constancy based on the minimally redundant color representation,” in Proceedings of the International Joint Conference on Neural Networks (International Neural Network Society, Mt. Royal, N.J., 1992), Vol. 2, pp. 696–701.

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Figures (9)

Fig. 1
Fig. 1

Binarized histograms of a scene taken under fluorescent illuminant, as represented in the rg-chromaticity input space of the neural network.

Fig. 2
Fig. 2

Binarized histogram of the same scene as the one depicted in Fig. 1, taken under tungsten illuminant, as represented in the rg-chromaticity input space of the neural network.

Fig. 3
Fig. 3

Perceptron architecture. Gray input neurons denote inactive nodes as determined by the data in the training set.

Fig. 4
Fig. 4

Average error during the ten training epochs for three different learning-rate (η) configurations.

Fig. 5
Fig. 5

Chromaticities of the 98 illuminants in our database, reflected from a surface of ideal 100% reflectance.

Fig. 6
Fig. 6

Chromaticities of the 260 surfaces in our database, illuminated with equal-energy white light.

Fig. 7
Fig. 7

Comparative results on synthesized scenes. The graph shows the average error as a function of the number of distinct colors in the scene.

Fig. 8
Fig. 8

Error as a function of the number of colors used. Colors were randomly selected from a single image. All values are relative to the base case of using only four distinct colors. Error drops noticeably as the number of colors increases.

Fig. 9
Fig. 9

Color correction of real images: Top left, original image; top right, target image; middle left, neural network estimate; middle right, gamut-mapping algorithm; bottom left, WP algorithm; bottom right, GW algorithm.

Tables (7)

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Table 1 Active and Inactive Nodes versus the Total Number of Nodes in the Input Layer (NI )

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Table 2 Neural Network Architectures a

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Table 3 Tests on Real Images a

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Table 4 Results with Network C with Use of Specularity Modeling a

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Table 5 Results with Network B with Use of Specularity Modeling a

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Table 6 Estimation Errors of Color Constancy algorithms (I) a

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Table 7 Estimation Errors of Color Constancy Algorithms (II) a

Equations (10)

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

RGB=kR000kG000kB RGB.
r=R/(R+G+B),
g=G/(R+G+B).
b=1-r-g.
y=11+exp(-A),
R=iEikSijρiR,G=iEikSijρiG,
B=iEikSijρiB.
Li=HiC.
rμ=Rav/(Rav+Gav+Bav),gμ=Gav/(Rav+Gav+Bav).
rGW=rwhrμrillgGW=gwh gμ/gill  rGW=1/3rμ/rill,gGW=1/3gμ/gill.

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