Abstract

We have analyzed the changes in the color of objects in natural scenes due to atmospheric scattering according to changes in the distance of observation. Hook-shaped curves were found in the chromaticity diagram when the object moved from zero distance to long distances, where the object chromaticity coordinates approached the color coordinates of the horizon. This trend is the result of the combined effect of attenuation in the direct light arriving to the observer from the object and the airlight added during its trajectory. Atmospheric scattering leads to a fall in the object’s visibility, which is measurable as a difference in color between the object and the background (taken here to be the horizon). Focusing on color difference instead of luminance difference could produce different visibility values depending on the color tolerance used. We assessed the cone-excitation ratio constancy for several objects at different distances. Affine relationships were obtained when an object’s cone excitations were represented both at zero distance and increasing distances. These results could help to explain color constancy in natural scenes for objects at different distances, a phenomenon that has been pointed out by different authors.

© 2011 Optical Society of America

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References

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2011 (1)

D. H. Foster, “Color constancy,” Vis. Res. 51, 674–700 (2011).
[CrossRef]

2007 (1)

J. Romero, D. Partal, J. L. Nieves, and J. Hernández-Andrés, “Sensor-response constancy under changes in natural and artificial illuminants,” Color Res. Appl. 32, 284–292 (2007).
[CrossRef]

2003 (2)

S. G. Narasimhan and S. K. Nayar, “Contrast restoration of weather degraded images,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 713–724 (2003).
[CrossRef]

M. S. Drew and G. D. Finlayson, “Multispectral processing without spectra,” J. Opt. Soc. Am. A 20, 1181–1193 (2003).
[CrossRef]

2002 (1)

2001 (1)

2000 (2)

R. C. Henry, S. Mahadey, S. Urquijo, and D. Chitwood, “Color perception through atmospheric haze,” J. Opt. Soc. Am. A 17, 831–835 (2000).
[CrossRef]

J. Hagedorn and M. D’Zmura, “Color appearance of surfaces viewed through fog,” Perception 29, 1169–1184 (2000).
[CrossRef]

1998 (3)

1997 (2)

1994 (2)

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

D. H. Foster and S. M. C. Nascimento, “Relational colour constancy from invariant cone-excitation ratios,” in Proc. R. Soc. B 257, 115–121 (1994).
[CrossRef] [PubMed]

1992 (1)

1991 (1)

1987 (1)

1981 (1)

H. Horvath, “Atmospheric visibility,” Atmos. Environ. 15, 1785–1796 (1981).
[CrossRef]

1971 (1)

H. Horvath, “On the applicability of the Koschmider visibility formula,” Atmos. Environ. 5, 177–184 (1971).
[CrossRef]

1949 (1)

Banerjee, P. P.

P. P. Banerjee and T. Poon, Principles of Applied Optics(McGraw-Hill, 1991).

Burton, G. J.

Chitwood, D.

D’Zmura, M.

J. Hagedorn and M. D’Zmura, “Color appearance of surfaces viewed through fog,” Perception 29, 1169–1184 (2000).
[CrossRef]

DeBonet, J.

DeMarco, P.

Drew, M. S.

Dror, I.

Ferreira, F. P.

Finlayson, G. D.

Foster, D. H.

D. H. Foster, “Color constancy,” Vis. Res. 51, 674–700 (2011).
[CrossRef]

S. M. C. Nascimento, F. P. Ferreira, and D. H. Foster, “Statistics of spatial cone-excitation ratios in natural scenes,” J. Opt. Soc. Am. A 19, 1484–1490 (2002).
[CrossRef]

D. H. Foster and S. M. C. Nascimento, “Relational colour constancy from invariant cone-excitation ratios,” in Proc. R. Soc. B 257, 115–121 (1994).
[CrossRef] [PubMed]

Gershon, R.

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

Hagedorn, J.

J. Hagedorn and M. D’Zmura, “Color appearance of surfaces viewed through fog,” Perception 29, 1169–1184 (2000).
[CrossRef]

Hecht, S.

Hendley, C. D.

Henry, R. C.

Hernández-Andrés, J.

J. Romero, D. Partal, J. L. Nieves, and J. Hernández-Andrés, “Sensor-response constancy under changes in natural and artificial illuminants,” Color Res. Appl. 32, 284–292 (2007).
[CrossRef]

Horvath, H.

H. Horvath, “Atmospheric visibility,” Atmos. Environ. 15, 1785–1796 (1981).
[CrossRef]

H. Horvath, “On the applicability of the Koschmider visibility formula,” Atmos. Environ. 5, 177–184 (1971).
[CrossRef]

Iqbal, M.

M. Iqbal, An Introduction to Solar Radiation (Academic, 1983).

Iwan, L. S.

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

King, T. A.

F. G. Smith, T. A. King, and D. Wilkins, Optics and Photonics (Wiley, 2007).

Kopeika, N. S.

Lenoble, J.

J. Lenoble, Atmospheric Radiative Transfer (A. Deepak Publishing, 1993).

Lynch, D. K.

Mahadey, S.

McCartney, E. J.

E. J. McCartney, Optics of the Atmosphere, Scattering by Molecules and Particles (Wiley-Interscience, 1976).

Minnaert, M.

M. Minnaert, The Nature of Light and Color in the Open Air (Dover, 1954).

Mollon, J. D.

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

Moorhead, I. R.

Narasimhan, S. G.

S. G. Narasimhan and S. K. Nayar, “Contrast restoration of weather degraded images,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 713–724 (2003).
[CrossRef]

S. G. Narasimhan and S. K. Nayar, “Vision and the atmosphere,” in ACM Siggraph Asia 2008 Courses (ACM, 2008), pp. 1–22.
[CrossRef]

S. G. Narasimhan and S. K. Nayar, “Chromatic framework for vision in bad weather,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2000, Vol. 1 (IEEE, 2000), pp. 598–605.
[CrossRef]

S. K. Nayar and S. G. Narasimhan, “Vision in bad weather,” in Proceedings of IEEE Seventh International Conference on Computer Vision (IEEE, 2002), pp. 820–827.

Nascimento, S. M. C.

S. M. C. Nascimento, F. P. Ferreira, and D. H. Foster, “Statistics of spatial cone-excitation ratios in natural scenes,” J. Opt. Soc. Am. A 19, 1484–1490 (2002).
[CrossRef]

D. H. Foster and S. M. C. Nascimento, “Relational colour constancy from invariant cone-excitation ratios,” in Proc. R. Soc. B 257, 115–121 (1994).
[CrossRef] [PubMed]

Nayar, S. K.

S. G. Narasimhan and S. K. Nayar, “Contrast restoration of weather degraded images,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 713–724 (2003).
[CrossRef]

S. G. Narasimhan and S. K. Nayar, “Vision and the atmosphere,” in ACM Siggraph Asia 2008 Courses (ACM, 2008), pp. 1–22.
[CrossRef]

S. G. Narasimhan and S. K. Nayar, “Chromatic framework for vision in bad weather,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2000, Vol. 1 (IEEE, 2000), pp. 598–605.
[CrossRef]

S. K. Nayar and S. G. Narasimhan, “Vision in bad weather,” in Proceedings of IEEE Seventh International Conference on Computer Vision (IEEE, 2002), pp. 820–827.

Nieves, J. L.

J. Romero, D. Partal, J. L. Nieves, and J. Hernández-Andrés, “Sensor-response constancy under changes in natural and artificial illuminants,” Color Res. Appl. 32, 284–292 (2007).
[CrossRef]

Oakley, J. P.

K. K. Tan and J. P. Oakley, “Physics based approach to color image enhancement in poor visibility conditions,” J. Opt. Soc. Am. A 18, 2460–2467 (2001).
[CrossRef]

J. P. Oakley and B. L. Satherley, “Improving image quality in poor visibility conditions using a physical model for contrast degradation,” IEEE Trans. Image Process. 7, 167–179 (1998).
[CrossRef]

Ohta, N.

N. Ohta and A. R. Robertson, Colorimetry. Fundamentals and Applications (Wiley, 2005).
[CrossRef]

Partal, D.

J. Romero, D. Partal, J. L. Nieves, and J. Hernández-Andrés, “Sensor-response constancy under changes in natural and artificial illuminants,” Color Res. Appl. 32, 284–292 (2007).
[CrossRef]

Pokorny, J.

Poon, T.

P. P. Banerjee and T. Poon, Principles of Applied Optics(McGraw-Hill, 1991).

Robertson, A. R.

N. Ohta and A. R. Robertson, Colorimetry. Fundamentals and Applications (Wiley, 2005).
[CrossRef]

Romero, J.

J. Romero, D. Partal, J. L. Nieves, and J. Hernández-Andrés, “Sensor-response constancy under changes in natural and artificial illuminants,” Color Res. Appl. 32, 284–292 (2007).
[CrossRef]

Sadot, D.

Satherley, B. L.

J. P. Oakley and B. L. Satherley, “Improving image quality in poor visibility conditions using a physical model for contrast degradation,” IEEE Trans. Image Process. 7, 167–179 (1998).
[CrossRef]

Smith, F. G.

F. G. Smith, T. A. King, and D. Wilkins, Optics and Photonics (Wiley, 2007).

Smith, V. C.

Spehar, B.

Stiles, W. S.

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

Tan, K. K.

Urquijo, S.

Vrhel, M. J.

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

Webster, M. A.

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

Wilkins, D.

F. G. Smith, T. A. King, and D. Wilkins, Optics and Photonics (Wiley, 2007).

Wyszecki, G.

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

Zaidi, Q.

Appl. Opt. (2)

Atmos. Environ. (2)

H. Horvath, “Atmospheric visibility,” Atmos. Environ. 15, 1785–1796 (1981).
[CrossRef]

H. Horvath, “On the applicability of the Koschmider visibility formula,” Atmos. Environ. 5, 177–184 (1971).
[CrossRef]

Color Res. Appl. (2)

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

J. Romero, D. Partal, J. L. Nieves, and J. Hernández-Andrés, “Sensor-response constancy under changes in natural and artificial illuminants,” Color Res. Appl. 32, 284–292 (2007).
[CrossRef]

IEEE Trans. Image Process. (1)

J. P. Oakley and B. L. Satherley, “Improving image quality in poor visibility conditions using a physical model for contrast degradation,” IEEE Trans. Image Process. 7, 167–179 (1998).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

S. G. Narasimhan and S. K. Nayar, “Contrast restoration of weather degraded images,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 713–724 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (8)

Perception (1)

J. Hagedorn and M. D’Zmura, “Color appearance of surfaces viewed through fog,” Perception 29, 1169–1184 (2000).
[CrossRef]

Proc. R. Soc. B (1)

D. H. Foster and S. M. C. Nascimento, “Relational colour constancy from invariant cone-excitation ratios,” in Proc. R. Soc. B 257, 115–121 (1994).
[CrossRef] [PubMed]

Vis. Res. (2)

D. H. Foster, “Color constancy,” Vis. Res. 51, 674–700 (2011).
[CrossRef]

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

Other (13)

E. J. McCartney, Optics of the Atmosphere, Scattering by Molecules and Particles (Wiley-Interscience, 1976).

M. Minnaert, The Nature of Light and Color in the Open Air (Dover, 1954).

S. G. Narasimhan and S. K. Nayar, “Vision and the atmosphere,” in ACM Siggraph Asia 2008 Courses (ACM, 2008), pp. 1–22.
[CrossRef]

S. G. Narasimhan and S. K. Nayar, “Chromatic framework for vision in bad weather,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2000, Vol. 1 (IEEE, 2000), pp. 598–605.
[CrossRef]

S. K. Nayar and S. G. Narasimhan, “Vision in bad weather,” in Proceedings of IEEE Seventh International Conference on Computer Vision (IEEE, 2002), pp. 820–827.

N. Ohta and A. R. Robertson, Colorimetry. Fundamentals and Applications (Wiley, 2005).
[CrossRef]

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

ColorChecker DC. Chart from Gretag Macbeth Ltd. (“GMB”), 2004.

F. G. Smith, T. A. King, and D. Wilkins, Optics and Photonics (Wiley, 2007).

P. P. Banerjee and T. Poon, Principles of Applied Optics(McGraw-Hill, 1991).

Centro Andaluz del Medio Ambiente, Universidad de Granada, Granada, Spain, http://atmosfera.ugr.es.

M. Iqbal, An Introduction to Solar Radiation (Academic, 1983).

J. Lenoble, Atmospheric Radiative Transfer (A. Deepak Publishing, 1993).

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Figures (7)

Fig. 1
Fig. 1

Schematic representation of different light contributions.

Fig. 2
Fig. 2

Chromaticity coordinate evolution in CIE 1931 diagram for sample 4L of ColorChecker DC on four days.

Fig. 3
Fig. 3

Chromaticity coordinate evolution for several samples of ColorChecker DC, 20 April 2010, overcast day. (a) CIELAB ( a * b * components) and (b) CIE 1931 ( x y components) color systems.

Fig. 4
Fig. 4

Color gamut reduction as the distance increases in CIE 1931 color system ( x y components), 16 March 2010, clear day.

Fig. 5
Fig. 5

(a) Color gamut reduction as the distance increases in CIE 1931 color system ( x y components), 19 March 2010, overcast day; (b) enlarged version of the figure.

Fig. 6
Fig. 6

Difference in lightness ( Δ L * ), chromaticity ( Δ E a * b * ), and color ( Δ E L * a * b * ) between an object and the background (horizon), calculated in terms of the CIELAB system, are shown in order to demonstrate the influence of the color of an object on its visibility against the horizon. (a) Color differences as a function of the distance for sample 5F of ColorChecker DC against the horizon, 20 April 2010, overcast day; (b) enlarged version of the figure.

Fig. 7
Fig. 7

Cone-excitation ratio constancy for 20 samples (1F, 2C, 2G, 2I, 2R, 4I, 4K, 5F, 5M, 5R, 6G, 6F, 6H, 7M, 9M, 10F, 10H, 11H, 11I, 11N) of ColorChecker DC, 16 April 2010, overcast day. (a) L sensor ratio constancy at zero distance, (b) M sensor ratio constancy at different distances.

Tables (5)

Tables Icon

Table 1 Measure Days, Sky Conditions, and u Coefficient

Tables Icon

Table 2 Chromaticity Coordinate Evolution for the 6G Sample of ColorChecker DC in CIE 1931 x y and CIE 1976 L * a * b * for Different Distances, 9 March 2010, Clear Day, u = 1.9

Tables Icon

Table 3 Chromaticity Coordinate Evolution for the 6G Sample of ColorChecker DC in CIE 1931 x y and CIE 1976 L * a * b * for Different Distances, 18 March 2010, Overcast, u = 1.4

Tables Icon

Table 4 Color Differences and Weber’s Fraction Thresholds for Different Samples of ColorChecker DC against the Horizon, 15 March (Clear), 16 April (Overcast), and 20 April (Overcast)

Tables Icon

Table 5 Data Analysis Results for Different Distances Simulated for 20 Samples (1F, 2C, 2G, 2I, 2R, 4I, 4K, 5F, 5M, 5R, 6G, 6F, 6H, 7M, 9M, 10F, 10H, 11H, 11I, 11N) of ColorChecker DC

Equations (4)

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

L ( λ ) = L 0 ( λ ) exp ( β ( λ ) d ) + L ( λ ) ( 1 exp ( β ( λ ) d ) ) ,
L ( λ ) = L ( λ ) ρ ( λ ) exp ( β ( λ ) d ) + L ( λ ) ( 1 exp ( β ( λ ) d ) ) ,
L ( λ ) = E d ( λ ) ρ ( λ ) π exp ( β ( λ ) d ) + L ( λ ) ( 1 exp ( β ( λ ) d ) ) ,
β sc ( λ ) 1 λ u .

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