Abstract

The problem of color constancy may be solved if we can recover the physical properties of illuminants and surfaces from photosensor responses. We consider this problem within the framework of Bayesian decision theory. First, we model the relation among illuminants, surfaces, and photosensor responses. Second, we construct prior distributions that describe the probability that particular illuminants and surfaces exist in the world. Given a set of photosensor responses, we can then use Bayes’s rule to compute the posterior distribution for the illuminants and the surfaces in the scene. There are two widely used methods for obtaining a single best estimate from a posterior distribution. These are maximum a posteriori (MAP) and minimum mean-squared-error (MMSE) estimation. We argue that neither is appropriate for perception problems. We describe a new estimator, which we call the maximum local mass (MLM) estimate, that integrates local probability density. The new method uses an optimality criterion that is appropriate for perception tasks: It finds the most probable approximately correct answer. For the case of low observation noise, we provide an efficient approximation. We develop the MLM estimator for the color-constancy problem in which flat matte surfaces are uniformly illuminated. In simulations we show that the MLM method performs better than the MAP estimator and better than a number of standard color-constancy algorithms. We note conditions under which even the optimal estimator produces poor estimates: when the spectral properties of the surfaces in the scene are biased.

© 1997 Optical Society of America

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1996 (2)

1995 (3)

1994 (4)

W. T. Freeman, “The generic viewpoint assumption in a framework for visual perception,” Nature (London) 368, 542–545 (1994).
[CrossRef]

K. H. Bauml, “Color appearance: effects of illuminant changes under different surface collections,” J. Opt. Soc. Am. A 11, 531–542 (1994).
[CrossRef]

D. H. Brainard, J. M. Speigle, “Achromatic loci measured under realistic viewing conditions,” Invest. Ophthalmol. Visual Sci. Suppl. 35, 1328 (1994).

B. Singer, M. D’Zmura, “Color contrast induction,” Vision Res. 34, 3111–3126 (1994).
[CrossRef] [PubMed]

1993 (5)

1992 (8)

1991 (4)

T. Marill, “Emulating the human interpretation of line-drawings as three-dimensional objects,” Int. J. Comput. Vision 6, 147–161 (1991).
[CrossRef]

P. Meer, D. Mintz, A. Rosenfeld, “Robust regression methods for computer vision: a review,” Int. J. Comput. Vision 6, 59–70 (1991).
[CrossRef]

J. J. Koenderink, A. J. van Doorn, “Affine structure from motion,” J. Opt. Soc. Am. A 8, 377–385 (1991).
[CrossRef] [PubMed]

L. E. Arend, A. Reeves, J. Schirillo, R. Goldstein, “Simultaneous color constancy: papers with diverse Munsell values,” J. Opt. Soc. Am. A 8, 661–672 (1991).
[CrossRef] [PubMed]

1990 (3)

T. Jaaskelainen, J. Parkkinen, S. Toyooka, “A vector-subspace model for color representation,” J. Opt. Soc. Am. A 7, 725–730 (1990).
[CrossRef]

A. P. Pentland, “Automatic extraction of deformable part models,” Int. J. Comput. Vision 4, 107–126 (1990).
[CrossRef]

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

1989 (2)

D. H. Brainard, B. A. Wandell, W. B. Cowan, “Black light: how sensors filter spectral variation of the illuminant,” IEEE Trans. Biomed. Eng. 36, 140–149 (1989).
[CrossRef] [PubMed]

Y. G. Leclerc, “Constructing simple stable descriptions for image partitioning,” Int. J. Comput. Vision 3, 73–102 (1989).
[CrossRef]

1988 (2)

A. L. Gilchrist, “Lightness contrast and failures of constancy: a common explanation,” Percept. Psychophys. 43, 415–424 (1988).
[CrossRef] [PubMed]

K. R. K. Nielsen, B. A. Wandell, “Discrete analysis of spatial sensitivity models,” J. Opt. Soc. Am. A 5, 743–755 (1988).
[CrossRef] [PubMed]

1987 (3)

A. Valberg, B. Lange-Malecki, “Mondrian complexity does not improve ‘color constancy’,” Invest. Ophthalmol. Visual Sci. Suppl. 28, 92 (1987).

B. A. Wandell, “The synthesis and analysis of color images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 2–13 (1987).
[CrossRef]

R. N. Shepard, “Toward a universal law of generalization for psychological science,” Science 237, 1317–1323 (1987).
[CrossRef] [PubMed]

1986 (9)

1985 (1)

T. Poggio, V. Torre, C. Koch, “Computational vision and regularization theory,” Nature (London) 317, 314–319 (1985).
[CrossRef]

1984 (1)

S. Geman, D. Geman, “Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 721–741 (1984).
[CrossRef]

1983 (1)

E. H. Land, “Recent advances in retinex theory and some implications for cortical computations: color vision and the natural image,” Proc. Natl. Acad. Sci. USA 80, 5163–5169 (1983).
[CrossRef]

1981 (1)

B. K. P. Horn, B. G. Schunk, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
[CrossRef]

1980 (3)

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

A. L. Gilchrist, “When does perceived lightness depend on perceived spatial arrangements?” Percept. Psychophys. 28, 527–538 (1980).
[CrossRef] [PubMed]

M. R. Pointer, “The gamut of real surface colours,” Color Res. Appl. 5, 145–155 (1980).
[CrossRef]

1977 (1)

J. J. McCann, J. A. Hall, E. H. Land, “Color Mondrian experiments: the study of average spectral distributions,” J. Opt. Soc. Am. 67, 1380 (1977).

1976 (1)

J. J. McCann, S. P. McKee, T. H. Taylor, “Quantitative studies in retinex theory: a comparison between theoretical predictions and observer responses to the ‘Color Mondrian’ experiments,” Vision Res. 16, 445–458 (1976).
[CrossRef]

1971 (1)

1964 (2)

D. B. Judd, D. L. MacAdam, G. W. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031–1040 (1964).
[CrossRef]

G. E. P. Box, G. C. Tiao, “A Bayesian approach to the importance of assumptions applied to the comparison of variances,” Biometrika 51, 153–167 (1964).

1943 (1)

1935 (1)

1928 (1)

S. Rosch, “Die Kennzeichnung der Farben,” Phys. Z. 29, 83–91 (1928), as discussed in Ref. 72.

1920 (1)

E. Schrodinger, “Theorie der pigmente von grosster leuchtkraft,” Ann. Phys. (Leipzig) 62, 603–622 (1920), as discussed in Ref. 72.
[CrossRef]

Adelson, E. H.

P. Sinha, E. H. Adelson, “Recovering reflectance and illumination in a world of painted polyhedra,” in Proceedings of the 4th International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1993), pp. 156–163.

Anandan, P.

M. J. Black, P. Anandan, “A framework for the robust estimation of optical flow,” in Proceedings of the 4th International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1993), pp. 231–236.

Arend, L. E.

Bauml, K. H.

Berger, T. O.

T. O. Berger, Statistical Decision Theory and Bayesian Analysis (Springer-Verlag, New York, 1985).

Black, M. J.

M. J. Black, P. Anandan, “A framework for the robust estimation of optical flow,” in Proceedings of the 4th International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1993), pp. 231–236.

Blake, A.

A. Blake, A. Zisserman, Visual Reconstruction (MIT Press, Cambridge, Mass., 1987).

Bleistein, N.

N. Bleistein, R. A. Handelsman, Asymptotic Expansions of Integrals (Dover, New York, 1986).

Box, G. E. P.

G. E. P. Box, G. C. Tiao, “A Bayesian approach to the importance of assumptions applied to the comparison of variances,” Biometrika 51, 153–167 (1964).

G. E. P. Box, G. C. Tiao, Bayesian Inference in Statistical Analysis (Wiley, New York, 1973).

Brainard, D. H.

J. M. Speigle, D. H. Brainard, “Luminosity thresholds: effects of test chromaticity and ambient illumination,” J. Opt. Soc. Am. A 13, 436–451 (1996).
[CrossRef]

D. H. Brainard, J. M. Speigle, “Achromatic loci measured under realistic viewing conditions,” Invest. Ophthalmol. Visual Sci. Suppl. 35, 1328 (1994).

D. H. Brainard, B. A. Wandell, E.-J. Chichilnisky, “Color constancy: from physics to appearance,” Curr. Dir. Psychol. Sci. 2, 165–170 (1993).

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]

D. H. Brainard, B. A. Wandell, W. B. Cowan, “Black light: how sensors filter spectral variation of the illuminant,” IEEE Trans. Biomed. Eng. 36, 140–149 (1989).
[CrossRef] [PubMed]

D. H. Brainard, B. A. Wandell, “Analysis of the retinex theory of color vision,” J. Opt. Soc. Am. A 3, 1651–1661 (1986).
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Artif. Intell. (1)

B. K. P. Horn, B. G. Schunk, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
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Biometrika (1)

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Curr. Dir. Psychol. Sci. (1)

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IEEE Trans. Biomed. Eng. (1)

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Invest. Ophthalmol. Visual Sci. Suppl. (2)

D. H. Brainard, J. M. Speigle, “Achromatic loci measured under realistic viewing conditions,” Invest. Ophthalmol. Visual Sci. Suppl. 35, 1328 (1994).

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J. Franklin Inst. (1)

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J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (22)

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