Abstract

We investigated the influence of motion on color constancy using a chromatic stimulus presented in various conditions (static, motion, and rotation). Attention to the stimulus and background was also controlled in different gaze modes, constant fixation of the stimulus, and random viewing of the stimulus. Color constancy was examined in six young observers using a haploscopic view of a computer monitor. The target and background were illuminated in simulation by red, green, blue, and yellow, shifted from daylight (D65) by specific color differences along L − M or S − (L + M) axes on the equiluminance plane. The standard pattern (under D65) and test pattern (under the color illuminant) of a 5-deg square were presented side by side, consisting of 1.2-deg square targets with one of 12 colors at each center, surrounded by 230 background ellipses consisting of eight other colors. The central color targets in both patterns flipped between top and bottom locations at the rate of 3 deg/s in the motion condition. The results indicated an average reduction of color constancy over the 12 test colors by motion. The random viewing parameter indicated better color constancy by more attention to the background, although the difference was not significant. Color constancy of the four color illuminations was better to worse in green, red, yellow, and blue, respectively. The reduction of color constancy by motion could be explained by less contribution of the illumination estimation effect on color constancy. In the motion with constant fixation condition, the retina strongly adapted to the mean chromaticity of the background. However, motion resulted in less attention to the color of the background, causing a weaker effect of the illumination estimation. Conversely, in the static state with a random viewing condition, more attention to the background colors caused a stronger illumination estimation effect, and color constancy was improved overall.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (1)

K. Uchikawa, T. Morimoto, and T. Matsumoto, “Understanding individual differences in color appearance of ‘#TheDress’ based on the optimal color hypothesis,” J. Vis. 17(8), 10, 1–14 (2017).
[Crossref]

2016 (1)

2015 (1)

S. B. Gao, “Color constancy using double-opponency,” IEEE Trans. Pattern Anal. Mach. Intell. 37, 1973–1985 (2015).
[Crossref]

2014 (2)

A. Werner, “Spatial and temporal aspects of chromatic adaptation and their functional significance for colour constancy,” Vis. Res. 104, 80–89 (2014).
[Crossref]

B. Pearce and A. Hurlbert, “Chromatic illumination discrimination ability reveals that human color constancy is optimised for blue daylight illuminations,” Plos One 9, 1–10 (2014).
[Crossref]

2012 (2)

2011 (4)

M. Ebner, “On the effect of scene motion on color constancy,” Biol. Cybern. 105, 319–330 (2011).
[Crossref]

J. W. Suchow and A. A. George, “Motion silences awareness of visual change,” Current Biol. 21, 140–143 (2011).
[Crossref]

D. H. Foster, “Review: color constancy,” Vis. Res. 51, 674–700 (2011).
[Crossref]

R. Shapley and M. J. Hawken, “Color in the cortex: single- and double-opponent cells,” Vis. Res. 51, 701–717 (2011).
[Crossref]

2010 (1)

J. Golz, “Colour constancy: influence of viewing behaviour on grey settings,” Perception 39, 606–619 (2010).
[Crossref]

2009 (1)

M. Ebner, “Color constancy based on local space average color,” Mach. Vis. Appl. J. 20, 283–301 (2009).
[Crossref]

2008 (3)

E. N. Johnson, “The orientation selectivity of color-responsive neurons in Macaque V1,” J. Neurosci. 28, 8096–8106 (2008).
[Crossref]

M. Olkkonen, T. Hansen, and K. R. Gegenfurtner, “Color appearance of familiar objects: effects of object shape, texture, and illumination changes,” J. Vis. 8(5), 13, 1–16 (2008).
[Crossref]

J. Golz, “The role of chromatic scene statistics in color constancy: spatial integration,” J. Vis. 8(13), 6, 1–16 (2008).
[Crossref]

2007 (1)

A. Werner, “Color constancy improves, when an object moves: high-level motion influences color perception,” J. Vis. 7(14), 19, 1–14 (2007).
[Crossref]

2006 (1)

I. J. Murray, A. Daugirdiene, H. Vaitkevicius, J. J. Kulikowski, and R. Stanikunas, “Almost complete colour constancy achieved with full-field adaptation,” Vis. Res. 46, 3067–3078 (2006).
[Crossref]

2004 (2)

P. B. Delahunt and D. H. Brainard, “Does human color constancy incorporate the statistical regularity of natural daylight?” J. Vis. 4(2), 1, 57–81 (2004).
[Crossref]

A. Hurlbert, “Color contrast: a contributory mechanism to color constancy,” Prog. Brain Res. 144, 147–160 (2004).
[Crossref]

2002 (1)

J. Golz and D. I. A. MacLeod, “Influence of scene statistics on colour constancy,” Nature 415, 637–640 (2002).
[Crossref]

2000 (1)

J. L. Nieves, A. García-Beltrán, and J. Romero, “Response of the human visual system to variable illuminant conditions: an analysis of opponent-colour mechanisms in colour constancy,” Ophthalmic Physiolog. Opt. 20, 44–58 (2000).
[Crossref]

1999 (3)

K.-H. Bäuml, “Simultaneous color constancy: how surface color perception varies with the illuminant,” Vis. Res. 39, 1531–1550 (1999).
[Crossref]

K.-H. Bäuml, “Color constancy: the role of image surfaces in illuminant adjustment,” J. Opt. Soc. Am. A 16, 1521–1530 (1999).
[Crossref]

J. M. Kraft and D. H. Brainard, “Mechanisms of color constancy under nearly natural viewing,” Proc. Natl. Acad. Sci. USA 96, 307–312 (1999).
[Crossref]

1997 (2)

1996 (1)

1995 (1)

E.-J. Chichilnisky and B. A. Wandell, “Photoreceptor sensitivity changes explain color appearance shifts induced by large uniform backgrounds in dichoptic matching,” Vis. Res. 35, 239–254 (1995).
[Crossref]

1994 (1)

1992 (1)

1991 (1)

1989 (1)

1986 (1)

1980 (1)

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

1975 (1)

V. C. Smith and J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500  nm,” Vis. Res. 15, 161–171 (1975).
[Crossref]

1964 (1)

Arend, L. E.

Barnard, K.

B. Funt, K. Barnard, and L. Martin, “Is machine colour constancy good enough?” in 5th European Conference on Computer Vision (ECCV’98), Freiburg, Germany (Springer, 1998), pp. 445–459.

Bäuml, K.-H.

K.-H. Bäuml, “Color constancy: the role of image surfaces in illuminant adjustment,” J. Opt. Soc. Am. A 16, 1521–1530 (1999).
[Crossref]

K.-H. Bäuml, “Simultaneous color constancy: how surface color perception varies with the illuminant,” Vis. Res. 39, 1531–1550 (1999).
[Crossref]

Boynton, R. M.

P. K. Kaiser and R. M. Boynton, Human Color Vision, 2nd ed. (Optical Society of America, 1996), p. 557.

Brainard, D. H.

P. B. Delahunt and D. H. Brainard, “Does human color constancy incorporate the statistical regularity of natural daylight?” J. Vis. 4(2), 1, 57–81 (2004).
[Crossref]

J. M. Kraft and D. H. Brainard, “Mechanisms of color constancy under nearly natural viewing,” Proc. Natl. Acad. Sci. USA 96, 307–312 (1999).
[Crossref]

D. H. Brainard, W. A. Brunt, and J. M. Speigle, “Color constancy in the nearly natural image: I. Asymmetric matches,” J. Opt. Soc. Am. A 14, 2091–2110 (1997).
[Crossref]

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

Brunt, W. A.

Buchsbaum, G.

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

Chichilnisky, E.-J.

E.-J. Chichilnisky and B. A. Wandell, “Photoreceptor sensitivity changes explain color appearance shifts induced by large uniform backgrounds in dichoptic matching,” Vis. Res. 35, 239–254 (1995).
[Crossref]

Daugirdiene, A.

J. J. Kulikowski, A. Daugirdiene, A. Panorgias, R. Stanikunas, H. Vaitkevicius, and I. J. Murray, “Systematic violations of von Kries rule reveal its limitations for explaining color and lightness constancy,” J. Opt. Soc. Am. A 29, A275–A289 (2012).
[Crossref]

I. J. Murray, A. Daugirdiene, H. Vaitkevicius, J. J. Kulikowski, and R. Stanikunas, “Almost complete colour constancy achieved with full-field adaptation,” Vis. Res. 46, 3067–3078 (2006).
[Crossref]

Delahunt, P. B.

P. B. Delahunt and D. H. Brainard, “Does human color constancy incorporate the statistical regularity of natural daylight?” J. Vis. 4(2), 1, 57–81 (2004).
[Crossref]

Ebner, M.

M. Ebner, “On the effect of scene motion on color constancy,” Biol. Cybern. 105, 319–330 (2011).
[Crossref]

M. Ebner, “Color constancy based on local space average color,” Mach. Vis. Appl. J. 20, 283–301 (2009).
[Crossref]

M. Ebner, Color Constancy (Wiley, 2007), pp. 30–31.

Foster, D. H.

D. H. Foster, “Review: color constancy,” Vis. Res. 51, 674–700 (2011).
[Crossref]

Fukuda, K.

Funt, B.

B. Funt, K. Barnard, and L. Martin, “Is machine colour constancy good enough?” in 5th European Conference on Computer Vision (ECCV’98), Freiburg, Germany (Springer, 1998), pp. 445–459.

Gao, S. B.

S. B. Gao, “Color constancy using double-opponency,” IEEE Trans. Pattern Anal. Mach. Intell. 37, 1973–1985 (2015).
[Crossref]

García-Beltrán, A.

J. L. Nieves, A. García-Beltrán, and J. Romero, “Response of the human visual system to variable illuminant conditions: an analysis of opponent-colour mechanisms in colour constancy,” Ophthalmic Physiolog. Opt. 20, 44–58 (2000).
[Crossref]

Gegenfurtner, K. R.

M. Olkkonen, T. Hansen, and K. R. Gegenfurtner, “Color appearance of familiar objects: effects of object shape, texture, and illumination changes,” J. Vis. 8(5), 13, 1–16 (2008).
[Crossref]

George, A. A.

J. W. Suchow and A. A. George, “Motion silences awareness of visual change,” Current Biol. 21, 140–143 (2011).
[Crossref]

Goldstein, R.

Golz, J.

J. Golz, “Colour constancy: influence of viewing behaviour on grey settings,” Perception 39, 606–619 (2010).
[Crossref]

J. Golz, “The role of chromatic scene statistics in color constancy: spatial integration,” J. Vis. 8(13), 6, 1–16 (2008).
[Crossref]

J. Golz and D. I. A. MacLeod, “Influence of scene statistics on colour constancy,” Nature 415, 637–640 (2002).
[Crossref]

Hallikainen, J.

Hansen, T.

M. Olkkonen, T. Hansen, and K. R. Gegenfurtner, “Color appearance of familiar objects: effects of object shape, texture, and illumination changes,” J. Vis. 8(5), 13, 1–16 (2008).
[Crossref]

Hawken, M. J.

R. Shapley and M. J. Hawken, “Color in the cortex: single- and double-opponent cells,” Vis. Res. 51, 701–717 (2011).
[Crossref]

Hurlbert, A.

B. Pearce and A. Hurlbert, “Chromatic illumination discrimination ability reveals that human color constancy is optimised for blue daylight illuminations,” Plos One 9, 1–10 (2014).
[Crossref]

A. Hurlbert, “Color contrast: a contributory mechanism to color constancy,” Prog. Brain Res. 144, 147–160 (2004).
[Crossref]

Jaaskelainen, T.

Johnson, E. N.

E. N. Johnson, “The orientation selectivity of color-responsive neurons in Macaque V1,” J. Neurosci. 28, 8096–8106 (2008).
[Crossref]

Judd, D. B.

Kaiser, P. K.

P. K. Kaiser and R. M. Boynton, Human Color Vision, 2nd ed. (Optical Society of America, 1996), p. 557.

Kawamoto, K.

Kitazawa, Y.

Kraft, J. M.

J. M. Kraft and D. H. Brainard, “Mechanisms of color constancy under nearly natural viewing,” Proc. Natl. Acad. Sci. USA 96, 307–312 (1999).
[Crossref]

Kulikowski, J. J.

J. J. Kulikowski, A. Daugirdiene, A. Panorgias, R. Stanikunas, H. Vaitkevicius, and I. J. Murray, “Systematic violations of von Kries rule reveal its limitations for explaining color and lightness constancy,” J. Opt. Soc. Am. A 29, A275–A289 (2012).
[Crossref]

I. J. Murray, A. Daugirdiene, H. Vaitkevicius, J. J. Kulikowski, and R. Stanikunas, “Almost complete colour constancy achieved with full-field adaptation,” Vis. Res. 46, 3067–3078 (2006).
[Crossref]

Kuriki, I.

Land, E. H.

E. H. Land, “Smitty Stevens’ test of retinex theory,” in Sensation and Measurement, H. R. Moskowitz, B. Scharf, and J. C. Stevens, eds. (Springer, 1974), pp. 363–368.

Ma, R.

MacAdam, D. L.

MacLeod, D. I. A.

Martin, L.

B. Funt, K. Barnard, and L. Martin, “Is machine colour constancy good enough?” in 5th European Conference on Computer Vision (ECCV’98), Freiburg, Germany (Springer, 1998), pp. 445–459.

Matsumoto, T.

K. Uchikawa, T. Morimoto, and T. Matsumoto, “Understanding individual differences in color appearance of ‘#TheDress’ based on the optimal color hypothesis,” J. Vis. 17(8), 10, 1–14 (2017).
[Crossref]

Morimoto, T.

K. Uchikawa, T. Morimoto, and T. Matsumoto, “Understanding individual differences in color appearance of ‘#TheDress’ based on the optimal color hypothesis,” J. Vis. 17(8), 10, 1–14 (2017).
[Crossref]

Murray, I. J.

J. J. Kulikowski, A. Daugirdiene, A. Panorgias, R. Stanikunas, H. Vaitkevicius, and I. J. Murray, “Systematic violations of von Kries rule reveal its limitations for explaining color and lightness constancy,” J. Opt. Soc. Am. A 29, A275–A289 (2012).
[Crossref]

I. J. Murray, A. Daugirdiene, H. Vaitkevicius, J. J. Kulikowski, and R. Stanikunas, “Almost complete colour constancy achieved with full-field adaptation,” Vis. Res. 46, 3067–3078 (2006).
[Crossref]

Nakano, Y.

Nieves, J. L.

J. L. Nieves, A. García-Beltrán, and J. Romero, “Response of the human visual system to variable illuminant conditions: an analysis of opponent-colour mechanisms in colour constancy,” Ophthalmic Physiolog. Opt. 20, 44–58 (2000).
[Crossref]

Olkkonen, M.

M. Olkkonen, T. Hansen, and K. R. Gegenfurtner, “Color appearance of familiar objects: effects of object shape, texture, and illumination changes,” J. Vis. 8(5), 13, 1–16 (2008).
[Crossref]

Panorgias, A.

Parkkinen, J. P. S.

Pearce, B.

B. Pearce and A. Hurlbert, “Chromatic illumination discrimination ability reveals that human color constancy is optimised for blue daylight illuminations,” Plos One 9, 1–10 (2014).
[Crossref]

Pokorny, J.

V. C. Smith and J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500  nm,” Vis. Res. 15, 161–171 (1975).
[Crossref]

Reeves, A.

Romero, J.

J. L. Nieves, A. García-Beltrán, and J. Romero, “Response of the human visual system to variable illuminant conditions: an analysis of opponent-colour mechanisms in colour constancy,” Ophthalmic Physiolog. Opt. 20, 44–58 (2000).
[Crossref]

Schefrin, B. E.

Schirillo, J.

Shapley, R.

R. Shapley and M. J. Hawken, “Color in the cortex: single- and double-opponent cells,” Vis. Res. 51, 701–717 (2011).
[Crossref]

Shinomori, K.

Smith, V. C.

V. C. Smith and J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500  nm,” Vis. Res. 15, 161–171 (1975).
[Crossref]

Speigle, J. M.

Stanikunas, R.

J. J. Kulikowski, A. Daugirdiene, A. Panorgias, R. Stanikunas, H. Vaitkevicius, and I. J. Murray, “Systematic violations of von Kries rule reveal its limitations for explaining color and lightness constancy,” J. Opt. Soc. Am. A 29, A275–A289 (2012).
[Crossref]

I. J. Murray, A. Daugirdiene, H. Vaitkevicius, J. J. Kulikowski, and R. Stanikunas, “Almost complete colour constancy achieved with full-field adaptation,” Vis. Res. 46, 3067–3078 (2006).
[Crossref]

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, 1982).

Suchow, J. W.

J. W. Suchow and A. A. George, “Motion silences awareness of visual change,” Current Biol. 21, 140–143 (2011).
[Crossref]

Uchikawa, K.

Vaitkevicius, H.

J. J. Kulikowski, A. Daugirdiene, A. Panorgias, R. Stanikunas, H. Vaitkevicius, and I. J. Murray, “Systematic violations of von Kries rule reveal its limitations for explaining color and lightness constancy,” J. Opt. Soc. Am. A 29, A275–A289 (2012).
[Crossref]

I. J. Murray, A. Daugirdiene, H. Vaitkevicius, J. J. Kulikowski, and R. Stanikunas, “Almost complete colour constancy achieved with full-field adaptation,” Vis. Res. 46, 3067–3078 (2006).
[Crossref]

von Kries, J.

J. von Kries, “Chromatic adaptation,” in Sources of Color Science, D. L. MacAdam, ed. (MIT, 1970), pp. 145–148.

Wandell, B. A.

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Figures (21)

Fig. 1.
Fig. 1. Example of test stimulus for red illumination condition. The standard pattern under D65 illumination (left) and the test pattern under colored illumination (right) were presented haploscopically in each trial. The left and right locations of patterns were changed from session to session.
Fig. 2.
Fig. 2. CIE 1976 u v chromaticity coordinates of the 12 central colored patches under D65 illumination. The label denotes the code in the Munsell color system. The value and chroma were 5 and 6.
Fig. 3.
Fig. 3. u v chromaticity coordinates of 12 test colors under the D65, red, green, blue, and yellow illuminants denoted by black, red, green, blue, and yellow circles, respectively. Slanted vertical and horizontal black lines denote S − (L + M) and L − M axes, respectively. The large triangle denotes the gamut of the monitor.
Fig. 4.
Fig. 4. Stimulus configuration under red (top left), green (bottom left), blue (top right), and yellow (bottom right) test illuminant conditions in haploscopic view. The central target is a 20% flat-reflectance surface.
Fig. 5.
Fig. 5. Constancy indices of color normal observers on 12 color patches under the red illuminant with eye-free (random viewing) conditions and eye-fix (fixation) conditions. Light color, dark color, and patterned bars represent the data of target-static, target-motion, and target-rotation conditions, respectively. The value for each color patch was averaged over six observers. Error bars represent the ± 2 SEM .
Fig. 6.
Fig. 6. Constancy indices under the green illumination. All other details are the same as in Fig. 5.
Fig. 7.
Fig. 7. Constancy indices under the blue illumination. All other details are the same as in Fig. 5.
Fig. 8.
Fig. 8. Constancy indices under the yellow illumination. All other details are the same as in Fig. 5.
Fig. 9.
Fig. 9. Mean constancy indices of six observers and 12 color surfaces with eye-free (random viewing) and eye-fix (fixation) conditions under red, green, blue, and yellow illuminants. Light, dark, and patterned bars represent target-static, target-motion, and target-rotation conditions, respectively. Error bars denote ± 2 SEM .
Fig. 10.
Fig. 10. Comparison between L-cone matched results by observers (ordinate) and those predicted by the von Kries model (abscissa) of 12 color patches under red, green, blue, and yellow illuminants in eye-free (top four panels) and eye-fix (bottom four panels) conditions. Diagonal dotted black lines indicate perfect von Kries-type adaptation. The red square, green circles, and blue triangles are matched results of target-static, target-motion, and target-rotation conditions, respectively. The red, green, and blue lines denote the best fits of target-static, target-motion, and target-rotation conditions, respectively. Each data point was averaged over six observers and six sessions. Black lines denote the prediction under D65 (see text for details).
Fig. 11.
Fig. 11. Comparison between the M-cone matched results (ordinate) and those predicted by the von Kries model (abscissa). All other details are the same as in Fig. 10.
Fig. 12.
Fig. 12. Comparison between the S-cone matched results (ordinate) and those predicted by the von Kries model (abscissa). All other details are the same as in Fig. 10.
Fig. 13.
Fig. 13. Comparison between the matched L-2M response by observers (ordinate) and the predicted L-2M response by the von Kries model (abscissa) under red, green, blue, and yellow illuminants in eye-free (top four panels) and eye-fix (bottom four panels) conditions. Diagonal dotted black lines indicate perfect von Kries-type adaptation. The red squares, green circles, and blue triangles are the matched result of static, motion, and rotation conditions, respectively. The red, green, and blue lines denote the best fits of static, motion, and rotation conditions, respectively. Black lines denote the prediction under D65, and gray lines denote the prediction by perfect illumination estimation effect (see text for details). Each data point was averaged over six observers and six sessions.
Fig. 14.
Fig. 14. Comparison between the matched blue-yellow S u n ( L + M ) response (ordinate) and the predicted blue-yellow by the von Kries model (abscissa). All other details are the same as in Fig. 13, except gray lines were not shown.
Fig. 15.
Fig. 15. Distance of matched points to the predicted points by von Kries model and reflectance model with four illuminants. Dark color and patterned bars denote the distance between matched points to the von Kries model and the reflectance model predictions, respectively. The red, green, blue, and yellow bars denote red, green, blue, and yellow illuminants, respectively. Error bars represent ± 1 SD .
Fig. 16.
Fig. 16. Perceived appearance under haploscopic view in static and motion conditions.
Fig. 17.
Fig. 17. Visual stimulus for experiment as measured at the aspect of retinal receptors under motion condition with pursuit eye movement (top row) and the result of convolution with Gaussian spatial filter (middle row). Local space averaged colors, a i ( x , y ) computed by Ebner’s mathematical model for static-state condition (bottom row, left) and that for motion condition (bottom row right) (see text for details).
Fig. 18.
Fig. 18. Color constancy descriptor, O i , cc ( x , y ) , computed for motion and static-state conditions.
Fig. 19.
Fig. 19. Angular error calculated by Ebner’s model. Light gray and black bars denote static-state and motion conditions, respectively.
Fig. 20.
Fig. 20. Double-opponency model for color constancy. First, the stimulus information is converted from LMS-cone to ganglion layer and LGN as red-green (L − M), blue-yellow (L + M − S), and luminance (L + M) channels, and then propagated to DO cells in V1 with convolution by difference-of-Gaussian functions.
Fig. 21.
Fig. 21. Angular error for double-opponency model. Light gray and black bars represent static-state and motion conditions, respectively.

Tables (4)

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Table 1. Illumination Condition (CIE1931 x y Chromaticity Coordinates, Color Difference, Δ E u v * , and Difference of L- or S-Cone Excitation)

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Table 2. Multiple Comparisons Using Bonferroni’s Correction (Significance Level: 0.05)

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Table 3. Slope Coefficient k and Coefficient of Determination R 2 for Fitted Lines in Figs. 10, 11, and 12

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Table 4. Slope Coefficient k and Coefficient of Determination R 2 for Fitted Lines in Figs. 13 and 14

Equations (22)

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C I = 1 b a ,
D von Kries = 1 N i = 1 N ( L i , Match L i , v K ) 2 + ( M i , Match M i , v K ) 2 + ( S i , Match S i , v K ) 2 ,
D reflectance = 1 N i = 1 N ( L i , Match L i , Ref. ) 2 + ( M i , Match M i , Ref. ) 2 + ( S i , Match S i , Ref. ) 2 ,
O i , retina ( x , y ) = log R i ( x , y ) + log L i ( x , y ) ,
a i ( x , y ) = k O i , retina ( x , y ) g ( x x , y y ) d x d y .
g ( x , y ) = 1 2 π δ 2 e x 2 + y 2 2 δ 2 ( δ = 30 ) .
O i , cc ( x , y ) = O i , retina ( x , y ) a i ( x , y ) = log R i ( x , y ) + 1 .
R ( x , y ) = ( O cc ( x , y ) ) 3 .
e = cos 1 R c R D | R c | | R D | ,
[ o l m o y s o L + ] = [ 1 1 0 1 1 1 1 1 0 ] [ l m s ] , [ o m l o s y o L ] = [ o l m o y s o L + ] .
RF ( x , y , δ ) = 1 2 π δ 2 e x 2 + y 2 2 δ 2 ,
SO l + m ( x , y ; δ ) = O l m ( x , y ) RF ( x , y ; δ ) ,
DO l m ( x , y ) = SO l + m ( x , y ; δ ) + k 1 · SO m + l ( x , y ; γ δ ) ,
DO s y ( x , y ) = SO s + y ( x , y ; δ ) + k 2 · SO y + s ( x , y ; γ δ ) ,
DO L ( x , y ) = SO L + ( x , y ; δ ) + k 3 · SO L ( x , y ; γ δ ) ,
R = [ DO l m DO s y DO L ] .
( L post-adapted M post-adapted S post-adapted ) = ( k L , T 0 0 0 k M , T 0 0 0 k S , T ) ( L T M T S T ) = ( k L , D 65 0 0 0 k M , D 65 0 0 0 k S , D 65 ) ( L D 65 M D 65 S D 65 ) ,
{ k L , T = 1 L W , T k M , T = 1 M W , T k S , T = 1 S W , T , { k L , D 65 = 1 L W , D 65 k M , D 65 = 1 M W , D 65 k S , D 65 = 1 S W , D 65 ,
( L T M T S T ) = ( k L , D 65 k L , T 0 0 0 k M , D 65 k M , T 0 0 0 k S , D 65 k S , T ) ( L D 65 M D 65 S D 65 ) ,
{ k L , D 65 k L , T = L W , T L W , D 65 k M , D 65 k M , T = M W , T M W , D 65 k S , D 65 k S , T = S W , T S W , D 65 .
{ X = k λ R ( λ ) S R ( λ ) x ¯ ( λ ) d λ Y = k λ R ( λ ) S R ( λ ) y ¯ ( λ ) d λ Z = k λ R ( λ ) S R ( λ ) z ¯ ( λ ) d λ ,
k = 100 λ S R ( λ ) y ¯ ( λ ) d λ ,

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