Abstract

The luminance and color of surfaces in natural scenes are relatively independent under certain linear transformations, with the luminance of a surface providing little information about the color of that surface, and vice versa. However, differences in luminance between two locations in a natural scene remain strongly associated with differences in color. We used the statistics of the spatiochromatic structure of natural scenes as the priors for a Bayesian model that decides whether or not two points within an image fall on the same surface. This model provides a biologically plausible algorithm for surface segmentation that models observer segmentations well.

© 2003 Optical Society of America

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  27. R. Ohlander, K. E. Price, R. Reddy, “Picture segmentation by a recursive region splitting method,” Comput. Graph. Image Process. 8, 313–323 (1978).
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  29. E. P. Simoncelli, B. A. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1216 (2001).
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    [CrossRef] [PubMed]

2001 (7)

T. von der Twer, D. I. MacLeod, “Optimal nonlinear codes for the perception of natural colours,” Network 12, 395–407 (2001).
[CrossRef] [PubMed]

T. Wachtler, T. W. Lee, T. J. Sejnowski, “Chromatic structure of natural scenes,” J. Opt. Soc. Am. A 18, 65–77 (2001).
[CrossRef]

N. J. Dominy, P. W. Lucas, “Ecological importance of trichromatic vision to primates,” Nature 410, 363–366 (2001).
[CrossRef] [PubMed]

E. P. Simoncelli, B. A. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1216 (2001).
[CrossRef] [PubMed]

W. S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly, “Edge co-occurrence in natural images predicts contour grouping performance,” Vision Res. 41, 711–724 (2001).
[CrossRef] [PubMed]

M. Sigman, G. A. Cecchi, C. D. Gilbert, M. O. Magnasco, “On a common circle: natural scenes and Gestalt rules,” Proc. Natl. Acad. Sci. USA 98, 1935–1940 (2001).

E. N. Johnson, M. J. Hawken, R. Shapley, “The spatial transformation of color in the primary visual cortex of the macaque monkey,” Nat. Neurosci. 4, 409–416 (2001).
[CrossRef] [PubMed]

2000 (2)

K. R. Gegenfurtner, J. Rieger, “Sensory and cognitive contributions of color to the recognition of natural scenes,” Curr. Biol. 10, 805–808 (2000).
[CrossRef] [PubMed]

D. R. Tailor, L. H. Finkel, G. Buchsbaum, “Color-opponent receptive fields derived from independent component analysis of natural images,” Vision Res. 40, 2671–2676 (2000).
[CrossRef] [PubMed]

1998 (3)

1997 (4)

D. C. Kiper, S. B. Fenstemaker, K. R. Gegenfurtner, “Chromatic properties of neurons in macaque area V2,” Visual Neurosci. 14, 1061–1072 (1997).
[CrossRef]

A. Li, P. Lennie, “Mechanisms underlying segmentation of colored textures,” Vision Res. 37, 83–97 (1997).
[CrossRef] [PubMed]

M. A. Webster, J. D. Mollon, “Adaptation and the color statistics of natural images,” Vision Res. 37, 3283–3298 (1997).
[CrossRef]

A. J. Bell, T. J. Sejnowski, “The “independent components” of natural scenes are edge filters,” Vision Res. 37, 3327–3338 (1997).
[CrossRef]

1994 (2)

D. L. Ruderman, “The statistics of natural images,” Network 6, 345–358 (1994).

J. Liu, Y. Yang, “Multi-resolution color image segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 689–700 (1994).
[CrossRef]

1993 (2)

L. H. Wurm, G. E. Legge, L. M. Isenberg, A. Luebker, “Color improves object recognition in normal and low vision,” J. Exp. Psychol. Hum. Percept. Perform. 19, 899–911 (1993).
[CrossRef] [PubMed]

A. Stockman, D. I. MacLeod, N. E. Johnson, “Spectral sensitivities of the human cones,” J. Opt. Soc. Am. A 10, 2491–2521 (1993).
[CrossRef]

1992 (2)

K. R. Gegenfurtner, D. C. Kiper, “Contrast detection in luminance and chromatic noise,” J. Opt. Soc. Am. A 9, 1880–1888 (1992).
[CrossRef] [PubMed]

A. L. Nagy, R. R. Sanchez, “Chromaticity and luminance as coding dimensions in visual search,” Hum. Factors 34, 601–614 (1992).
[PubMed]

1991 (1)

M. A. Webster, J. D. Mollon, “Changes in colour appearance following post-receptoral adaptation,” Nature 349, 235–238 (1991).
[CrossRef] [PubMed]

1990 (2)

P. Flanagan, P. Cavanagh, O. E. Favreau, “Independent orientation-selective mechanisms for the cardinal directions of colour space,” Vision Res. 30, 769–778 (1990).
[CrossRef] [PubMed]

P. Lennie, J. Krauskopf, G. Sclar, “Chromatic mechanisms in striate cortex of macaque,” J. Neurosci. 10, 649–669 (1990).
[PubMed]

1986 (2)

L. T. Maloney, “Evaluation of linear models of surface spectral reflectance with small numbers of parameters,” J. Opt. Soc. Am. A 3, 1673–1683 (1986).
[CrossRef] [PubMed]

M. Celenk, S. H. Smith, “Gross segmentation of color images of natural scenes for computer vision systems,” Appl. Artif. Intell. III, 333–344 (1986).

1983 (1)

G. Buchsbaum, A. Gottschalk, “Trichromacy, opponent colours coding and optimum colour information transmission in the retina,” Proc. R. Soc. London Sec. B 220, 89–113 (1983).
[CrossRef]

1982 (1)

J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of color space,” Vision Res. 22, 1123–1131 (1982).
[CrossRef] [PubMed]

1980 (1)

Y. I. Ohta, T. Kanade, T. Sakai, “Color information for region segmentation,” Comput. Graph. Image Process. 13, 222–241 (1980).
[CrossRef]

1978 (1)

R. Ohlander, K. E. Price, R. Reddy, “Picture segmentation by a recursive region splitting method,” Comput. Graph. Image Process. 8, 313–323 (1978).
[CrossRef]

1960 (1)

S. S. Stevens, “Psychophysics of sensory function,” Am. Sci. 48, 226–252 (1960).

Bell, A. J.

A. J. Bell, T. J. Sejnowski, “The “independent components” of natural scenes are edge filters,” Vision Res. 37, 3327–3338 (1997).
[CrossRef]

Brelstaff, G.

Buchsbaum, G.

D. R. Tailor, L. H. Finkel, G. Buchsbaum, “Color-opponent receptive fields derived from independent component analysis of natural images,” Vision Res. 40, 2671–2676 (2000).
[CrossRef] [PubMed]

G. Buchsbaum, A. Gottschalk, “Trichromacy, opponent colours coding and optimum colour information transmission in the retina,” Proc. R. Soc. London Sec. B 220, 89–113 (1983).
[CrossRef]

Cavanagh, P.

P. Flanagan, P. Cavanagh, O. E. Favreau, “Independent orientation-selective mechanisms for the cardinal directions of colour space,” Vision Res. 30, 769–778 (1990).
[CrossRef] [PubMed]

Cecchi, G. A.

M. Sigman, G. A. Cecchi, C. D. Gilbert, M. O. Magnasco, “On a common circle: natural scenes and Gestalt rules,” Proc. Natl. Acad. Sci. USA 98, 1935–1940 (2001).

Celenk, M.

M. Celenk, S. H. Smith, “Gross segmentation of color images of natural scenes for computer vision systems,” Appl. Artif. Intell. III, 333–344 (1986).

Charles-Dominique, P.

B. C. Regan, C. Julliot, B. Simmen, F. Vienot, P. Charles-Dominique, J. D. Mollon, “Frugivory and colour vision in Alouatta seniculus, a trichromatic platyrrhine monkey,” Vision Res. 38, 3321–3327 (1998).
[CrossRef]

Chiao, C. C.

Cronin, T. W.

Dominy, N. J.

N. J. Dominy, P. W. Lucas, “Ecological importance of trichromatic vision to primates,” Nature 410, 363–366 (2001).
[CrossRef] [PubMed]

Favreau, O. E.

P. Flanagan, P. Cavanagh, O. E. Favreau, “Independent orientation-selective mechanisms for the cardinal directions of colour space,” Vision Res. 30, 769–778 (1990).
[CrossRef] [PubMed]

Fenstemaker, S. B.

D. C. Kiper, S. B. Fenstemaker, K. R. Gegenfurtner, “Chromatic properties of neurons in macaque area V2,” Visual Neurosci. 14, 1061–1072 (1997).
[CrossRef]

Finkel, L. H.

D. R. Tailor, L. H. Finkel, G. Buchsbaum, “Color-opponent receptive fields derived from independent component analysis of natural images,” Vision Res. 40, 2671–2676 (2000).
[CrossRef] [PubMed]

Flanagan, P.

P. Flanagan, P. Cavanagh, O. E. Favreau, “Independent orientation-selective mechanisms for the cardinal directions of colour space,” Vision Res. 30, 769–778 (1990).
[CrossRef] [PubMed]

Gallogly, D. P.

W. S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly, “Edge co-occurrence in natural images predicts contour grouping performance,” Vision Res. 41, 711–724 (2001).
[CrossRef] [PubMed]

Gegenfurtner, K. R.

K. R. Gegenfurtner, J. Rieger, “Sensory and cognitive contributions of color to the recognition of natural scenes,” Curr. Biol. 10, 805–808 (2000).
[CrossRef] [PubMed]

D. C. Kiper, S. B. Fenstemaker, K. R. Gegenfurtner, “Chromatic properties of neurons in macaque area V2,” Visual Neurosci. 14, 1061–1072 (1997).
[CrossRef]

K. R. Gegenfurtner, D. C. Kiper, “Contrast detection in luminance and chromatic noise,” J. Opt. Soc. Am. A 9, 1880–1888 (1992).
[CrossRef] [PubMed]

Geisler, W. S.

W. S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly, “Edge co-occurrence in natural images predicts contour grouping performance,” Vision Res. 41, 711–724 (2001).
[CrossRef] [PubMed]

Gilbert, C. D.

M. Sigman, G. A. Cecchi, C. D. Gilbert, M. O. Magnasco, “On a common circle: natural scenes and Gestalt rules,” Proc. Natl. Acad. Sci. USA 98, 1935–1940 (2001).

Gottschalk, A.

G. Buchsbaum, A. Gottschalk, “Trichromacy, opponent colours coding and optimum colour information transmission in the retina,” Proc. R. Soc. London Sec. B 220, 89–113 (1983).
[CrossRef]

Hawken, M. J.

E. N. Johnson, M. J. Hawken, R. Shapley, “The spatial transformation of color in the primary visual cortex of the macaque monkey,” Nat. Neurosci. 4, 409–416 (2001).
[CrossRef] [PubMed]

Heeley, D. W.

J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of color space,” Vision Res. 22, 1123–1131 (1982).
[CrossRef] [PubMed]

Isenberg, L. M.

L. H. Wurm, G. E. Legge, L. M. Isenberg, A. Luebker, “Color improves object recognition in normal and low vision,” J. Exp. Psychol. Hum. Percept. Perform. 19, 899–911 (1993).
[CrossRef] [PubMed]

Johnson, E. N.

E. N. Johnson, M. J. Hawken, R. Shapley, “The spatial transformation of color in the primary visual cortex of the macaque monkey,” Nat. Neurosci. 4, 409–416 (2001).
[CrossRef] [PubMed]

Johnson, N. E.

Julliot, C.

B. C. Regan, C. Julliot, B. Simmen, F. Vienot, P. Charles-Dominique, J. D. Mollon, “Frugivory and colour vision in Alouatta seniculus, a trichromatic platyrrhine monkey,” Vision Res. 38, 3321–3327 (1998).
[CrossRef]

Kanade, T.

Y. I. Ohta, T. Kanade, T. Sakai, “Color information for region segmentation,” Comput. Graph. Image Process. 13, 222–241 (1980).
[CrossRef]

Kiper, D. C.

D. C. Kiper, S. B. Fenstemaker, K. R. Gegenfurtner, “Chromatic properties of neurons in macaque area V2,” Visual Neurosci. 14, 1061–1072 (1997).
[CrossRef]

K. R. Gegenfurtner, D. C. Kiper, “Contrast detection in luminance and chromatic noise,” J. Opt. Soc. Am. A 9, 1880–1888 (1992).
[CrossRef] [PubMed]

Krauskopf, J.

P. Lennie, J. Krauskopf, G. Sclar, “Chromatic mechanisms in striate cortex of macaque,” J. Neurosci. 10, 649–669 (1990).
[PubMed]

J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of color space,” Vision Res. 22, 1123–1131 (1982).
[CrossRef] [PubMed]

Lee, T. W.

Legge, G. E.

L. H. Wurm, G. E. Legge, L. M. Isenberg, A. Luebker, “Color improves object recognition in normal and low vision,” J. Exp. Psychol. Hum. Percept. Perform. 19, 899–911 (1993).
[CrossRef] [PubMed]

Lennie, P.

A. Li, P. Lennie, “Mechanisms underlying segmentation of colored textures,” Vision Res. 37, 83–97 (1997).
[CrossRef] [PubMed]

P. Lennie, J. Krauskopf, G. Sclar, “Chromatic mechanisms in striate cortex of macaque,” J. Neurosci. 10, 649–669 (1990).
[PubMed]

Li, A.

A. Li, P. Lennie, “Mechanisms underlying segmentation of colored textures,” Vision Res. 37, 83–97 (1997).
[CrossRef] [PubMed]

Liu, J.

J. Liu, Y. Yang, “Multi-resolution color image segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 689–700 (1994).
[CrossRef]

Lucas, P. W.

N. J. Dominy, P. W. Lucas, “Ecological importance of trichromatic vision to primates,” Nature 410, 363–366 (2001).
[CrossRef] [PubMed]

Luebker, A.

L. H. Wurm, G. E. Legge, L. M. Isenberg, A. Luebker, “Color improves object recognition in normal and low vision,” J. Exp. Psychol. Hum. Percept. Perform. 19, 899–911 (1993).
[CrossRef] [PubMed]

MacLeod, D. I.

T. von der Twer, D. I. MacLeod, “Optimal nonlinear codes for the perception of natural colours,” Network 12, 395–407 (2001).
[CrossRef] [PubMed]

A. Stockman, D. I. MacLeod, N. E. Johnson, “Spectral sensitivities of the human cones,” J. Opt. Soc. Am. A 10, 2491–2521 (1993).
[CrossRef]

Magnasco, M. O.

M. Sigman, G. A. Cecchi, C. D. Gilbert, M. O. Magnasco, “On a common circle: natural scenes and Gestalt rules,” Proc. Natl. Acad. Sci. USA 98, 1935–1940 (2001).

Maloney, L. T.

Mollon, J. D.

B. C. Regan, C. Julliot, B. Simmen, F. Vienot, P. Charles-Dominique, J. D. Mollon, “Frugivory and colour vision in Alouatta seniculus, a trichromatic platyrrhine monkey,” Vision Res. 38, 3321–3327 (1998).
[CrossRef]

M. A. Webster, J. D. Mollon, “Adaptation and the color statistics of natural images,” Vision Res. 37, 3283–3298 (1997).
[CrossRef]

M. A. Webster, J. D. Mollon, “Changes in colour appearance following post-receptoral adaptation,” Nature 349, 235–238 (1991).
[CrossRef] [PubMed]

Moorhead, I.

Nagy, A. L.

A. L. Nagy, R. R. Sanchez, “Chromaticity and luminance as coding dimensions in visual search,” Hum. Factors 34, 601–614 (1992).
[PubMed]

Ohlander, R.

R. Ohlander, K. E. Price, R. Reddy, “Picture segmentation by a recursive region splitting method,” Comput. Graph. Image Process. 8, 313–323 (1978).
[CrossRef]

Ohta, Y. I.

Y. I. Ohta, T. Kanade, T. Sakai, “Color information for region segmentation,” Comput. Graph. Image Process. 13, 222–241 (1980).
[CrossRef]

Olshausen, B. A.

E. P. Simoncelli, B. A. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1216 (2001).
[CrossRef] [PubMed]

Parraga, C. A.

Perry, J. S.

W. S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly, “Edge co-occurrence in natural images predicts contour grouping performance,” Vision Res. 41, 711–724 (2001).
[CrossRef] [PubMed]

Price, K. E.

R. Ohlander, K. E. Price, R. Reddy, “Picture segmentation by a recursive region splitting method,” Comput. Graph. Image Process. 8, 313–323 (1978).
[CrossRef]

Reddy, R.

R. Ohlander, K. E. Price, R. Reddy, “Picture segmentation by a recursive region splitting method,” Comput. Graph. Image Process. 8, 313–323 (1978).
[CrossRef]

Regan, B. C.

B. C. Regan, C. Julliot, B. Simmen, F. Vienot, P. Charles-Dominique, J. D. Mollon, “Frugivory and colour vision in Alouatta seniculus, a trichromatic platyrrhine monkey,” Vision Res. 38, 3321–3327 (1998).
[CrossRef]

Rieger, J.

K. R. Gegenfurtner, J. Rieger, “Sensory and cognitive contributions of color to the recognition of natural scenes,” Curr. Biol. 10, 805–808 (2000).
[CrossRef] [PubMed]

Ruderman, D. L.

D. L. Ruderman, “The statistics of natural images,” Network 6, 345–358 (1994).

Ruderman, D. R.

Sakai, T.

Y. I. Ohta, T. Kanade, T. Sakai, “Color information for region segmentation,” Comput. Graph. Image Process. 13, 222–241 (1980).
[CrossRef]

Sanchez, R. R.

A. L. Nagy, R. R. Sanchez, “Chromaticity and luminance as coding dimensions in visual search,” Hum. Factors 34, 601–614 (1992).
[PubMed]

Sclar, G.

P. Lennie, J. Krauskopf, G. Sclar, “Chromatic mechanisms in striate cortex of macaque,” J. Neurosci. 10, 649–669 (1990).
[PubMed]

Sejnowski, T. J.

T. Wachtler, T. W. Lee, T. J. Sejnowski, “Chromatic structure of natural scenes,” J. Opt. Soc. Am. A 18, 65–77 (2001).
[CrossRef]

A. J. Bell, T. J. Sejnowski, “The “independent components” of natural scenes are edge filters,” Vision Res. 37, 3327–3338 (1997).
[CrossRef]

Shapley, R.

E. N. Johnson, M. J. Hawken, R. Shapley, “The spatial transformation of color in the primary visual cortex of the macaque monkey,” Nat. Neurosci. 4, 409–416 (2001).
[CrossRef] [PubMed]

Sigman, M.

M. Sigman, G. A. Cecchi, C. D. Gilbert, M. O. Magnasco, “On a common circle: natural scenes and Gestalt rules,” Proc. Natl. Acad. Sci. USA 98, 1935–1940 (2001).

Simmen, B.

B. C. Regan, C. Julliot, B. Simmen, F. Vienot, P. Charles-Dominique, J. D. Mollon, “Frugivory and colour vision in Alouatta seniculus, a trichromatic platyrrhine monkey,” Vision Res. 38, 3321–3327 (1998).
[CrossRef]

Simoncelli, E. P.

E. P. Simoncelli, B. A. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1216 (2001).
[CrossRef] [PubMed]

Smith, S. H.

M. Celenk, S. H. Smith, “Gross segmentation of color images of natural scenes for computer vision systems,” Appl. Artif. Intell. III, 333–344 (1986).

Stevens, S. S.

S. S. Stevens, “Psychophysics of sensory function,” Am. Sci. 48, 226–252 (1960).

Stockman, A.

Super, B. J.

W. S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly, “Edge co-occurrence in natural images predicts contour grouping performance,” Vision Res. 41, 711–724 (2001).
[CrossRef] [PubMed]

Tailor, D. R.

D. R. Tailor, L. H. Finkel, G. Buchsbaum, “Color-opponent receptive fields derived from independent component analysis of natural images,” Vision Res. 40, 2671–2676 (2000).
[CrossRef] [PubMed]

Troscianko, T.

Vienot, F.

B. C. Regan, C. Julliot, B. Simmen, F. Vienot, P. Charles-Dominique, J. D. Mollon, “Frugivory and colour vision in Alouatta seniculus, a trichromatic platyrrhine monkey,” Vision Res. 38, 3321–3327 (1998).
[CrossRef]

von der Twer, T.

T. von der Twer, D. I. MacLeod, “Optimal nonlinear codes for the perception of natural colours,” Network 12, 395–407 (2001).
[CrossRef] [PubMed]

Wachtler, T.

Webster, M. A.

M. A. Webster, J. D. Mollon, “Adaptation and the color statistics of natural images,” Vision Res. 37, 3283–3298 (1997).
[CrossRef]

M. A. Webster, J. D. Mollon, “Changes in colour appearance following post-receptoral adaptation,” Nature 349, 235–238 (1991).
[CrossRef] [PubMed]

Williams, D. R.

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Figures (5)

Fig. 1
Fig. 1

A, Scatterplot of l versus rg. B, small patch from a natural image (for an example of a full image, see Fig. 5A). Two pixels, separated by a radius of 18 min, are shown. C, Scatterplot of δl versus δrg. D, Joint pdf of differences along red–green and blue–yellow axes for pixels separated by 18 min. E, Joint pdf of differences along red–green and blue–yellow axes for pixels separated by 18 min assuming independence.

Fig. 2
Fig. 2

A, Solid curves: pdf for differences in luminance and chromaticity between two pixels separated by 3 min of visual angle. Dashed curves: modeled pdf for differences in luminance and chromaticity between two pixels falling on the same surface. Pdf’s for luminance differences are shown in black, pdf’s for red–green chromatic differences are shown in red, and pdf’s for blue–yellow chromatic differences are shown in blue. B, Sampled and modeled pdfs for differences in luminance and color between two pixels separated by 18 min. C, Sampled pdf for differences in luminance and color between two pixels on different surfaces. D, Kurtosis of pdf’s for differences in luminance and color between pixels as a function of pixel separation. For comparison, the standard normal distribution has a kurtosis of 0. E, Estimates of p(same|r) as a function of pixel separation for a simple model based on the assumption that adjacent pixels always belonged to the same surface (solid curves) and an exponential fit (dashed curves).

Fig. 3
Fig. 3

Probability, computed from the model, that two pixels separated by 18 min belong to the same surface, as a function of the difference in red–green and blue–yellow chromaticity between the two pixels.

Fig. 4
Fig. 4

A, Four of the scenes that were used, with a randomly chosen 12×12 excised patch outlined. B, Image patches. C, Mean estimates from a single observer of the likelihood of each pixel belonging to the same surface as the central pixel. D, Estimates from our Bayesian model. E, Comparison of estimates of p(same) made by two observers (IF, black symbols; SK, gray symbols) with estimates made by the model. Error bars subtend plus and minus one standard error.

Fig. 5
Fig. 5

A, Comparison of estimates of p(same) made by observers with estimates of p(same) made by the model averaged across all 36 sample patches of natural scenes. B, Comparison of estimates of p(same) made by observers with estimates of p(same) made by the model averaged across all 18 novel sample patches of man-made environments (IF, black symbols; SK, gray symbols). Error bars subtend plus and minus one standard error.

Equations (7)

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l=13 (L+M+S),rg=12 (L-M),
by=16 (L+M-2S).
p(δl, δrg, δby|same)p(δl, δrg, δby|r=3),
p(δl, δrg, δby|r)
=p(same|r)p(δl, δrg, δby|same)+{1-p(same|r)}p(δl, δrg, δby|diff).
p(same|δl, δrg, δby, r)
=p(same|r)p(δl, δrg, δby|same)/p(δl, δrg, δby|r).

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