Lightness (color)

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Lightness is a property of a color, or a dimension of a color space, that is defined in a way to reflect the subjective brightness perception of a color for humans. The Munsell value is an example of a lightness scale.

[edit] Relationship between lightness, value, and luminance

The Munsell value has long been used as a perceptually uniform lightness scale. A question of interest is the relationship between the Munsell value scale and the relative luminance. Aware of the Weber–Fechner law, Munsell remarked "Should we use a logarithmic curve or curve of squares?"[1] Neither option turned out to be quite correct; scientists eventually converged on a roughly cube-root curve, consistent with the Stevens power law for brightness perception, reflecting the fact that lightness is proportional to the number of nerve impulses per nerve fiber per unit time.[2] The remainder of this section is a chronology of lightness approximations, leading to CIELAB.

Note: Munsell's V runs from 0 to 10, while Y typically runs from 0 to 100 (often interpreted as a percent). Typically, the relative luminance is normalized so that the "reference white" (say, magnesium oxide) has a tristimulus value of Y=100. Since the reflectance of magnesium oxide (MgO) relative to the perfect reflecting diffuser is 97.5%, V=10 corresponds to Y=100/97.5%≈102.6 if MgO is used as the reference.[3]

Observe that the lightness is 50% for a luminance of around 18% relative to the reference white.
Observe that the lightness is 50% for a luminance of around 18% relative to the reference white.

1920: Priest et al provide a basic estimate of the Munsell value (with Y running from 0 to 1 in this case):[4]

V=10 \sqrt{Y}

1933: Munsell, Sloan, and Godlove launch a study on the Munsell neutral value scale, considering several proposals relating the relative luminance to the Munsell value, and suggest:[5][6]

V2 = 1.4742Y − 0.004743Y2

1943: Newhall, Nickerson, and Judd prepare a report for the Optical Society of America. They suggest a quintic parabola (relating the reflectance in terms of the value):[7]

Y = 1.2219V − 0.23111V2 + 0.23951V3 − 0.021009V4 + 0.0008404V5

1943: Using Table II of the O.S.A. report, Moon and Spencer express the value in terms of the luminance:[8]

V = 5(Y / 19.77)0.426 = 1.4Y0.426

1944: Saunderson and Milner introduce a subtractive constant in the previous expression, for a better fit to the Munsell value.[9] Later, Jameson and Hurvich claim that this corrects for simultaneous contrast effects.[10][11]

V = 2.357Y0.343 − 1.52

1955: Ladd and Pinney of Eastman Kodak are interested in the Munsell value as a perceptually uniform lightness scale for use in television. After considering one logarithmic and five power-law functions (per Stevens' power law), they relate value to reflectance by raising the reflectance to the power of 0.352:[12]

V = 2.217Y0.352 − 1.324

Realizing this is quite close to the cube root, they simplify it to

V = 2.468Y1 / 3 − 1.636

1958: Glasser et al define the lightness as ten times the Munsell value (so that the lightness ranges from 0 to 100):[13]

L * = 25.29Y1 / 3 − 18.38

1964: Wyszecki simplifies this to:[14]

W * = 25Y1 / 3 − 17

This formula approximates the Munsell value function for 1% < Y < 98% (it is not applicable for Y<1%) and is used for the CIE 1964 color space.

1976: CIELAB uses the following formula:

L * = 116(Y / Yn)1 / 3 − 16

where Yn is the Y tristimulus value of a "specified white object" and is subject to the restriction Y / Yn > 0.01. Pauli removes this restriction by computing a linear extrapolation which maps Y/Yn=0 to L*=0 and is tangent to the formula above at the point at which the linear extension takes effect. First, the transition point is determined to be Y/Y_n=(6/29)^3 \approx 0.008856, then the slope of (29/3)^3 \approx 903.3 is computed. This gives the two-part function:[15]

f(u)= \left\{\begin{array}{ll}\frac{841}{108}u + \frac{4}{29}, & u \le (6/29)^3 \\ \\ u^{1/3}, & u > (6/29)^3\end{array}\right.

The lightness is then L * = 116f(Y / Yn) − 16

[edit] References

  1. ^ Kuehni, Rolf G. (February 2002). "The early development of the Munsell system". Color Research & Application 27 (1): 20–27. doi:10.1002/col.10002. 
  2. ^ Hunt, Robert W. G. (May 18 1957). "Light Energy and Brightness Sensation". Nature 179 (4568): 1026. doi:10.1038/1791026a0. 
  3. ^ Valberg, Arne (2006). Light Vision Color. John Wiley and Sons, 200. ISBN 0470849029. 
  4. ^ Priest, Irwin G.; Gibson, K.S. & McNicholas, H.J. (1920), An examination of the Munsell color system. I: Spectral and total reflection and the Munsell scale of Value, Technical paper 167, United States Bureau of Standards, p. 27 
  5. ^ Munsell, A.E.O.; Sloan, L.L.; Godlove, I.H. (November 1933). "Neutral value scales. I. Munsell neutral value scale". JOSA 23 (11): 394–411.  Note: This paper contains a historical survey stretching to 1760.
  6. ^ Munsell, A.E.O.; Sloan, L.L.; Godlove, I.H. (December 1933). "Neutral value scales. II. A comparison of results and equations describing value scales". JOSA 23 (12): 419–425. 
  7. ^ Newhall, Sidney M.; Nickerson, Dorothy; Judd, Deane B (May 1943). "Final report of the O.S.A. subcommittee on the spacing of the Munsell colors" 33 (7): 385–418. 
  8. ^ Moon, Parry; Spencer, Domina Eberle (May 1943). "Metric based on the composite color stimulus". JOSA 33 (5): 270–277. 
  9. ^ Saunderson, Jason L.; Milner, B.I. (March 1944). "Further study of ω space". JOSA 34 (3): 167–173. 
  10. ^ Hurvich, Leo M.; Jameson, Dorothea (November 1957). "An Opponent-Process Theory of Color Vision". Psychological Review 64 (6): 384–404. doi:10.1037/h0041403. PMID 13505974. 
  11. ^ Dorothea, Jameson; Leo M., Hurvich (May 1964). "Theory of brightness and color contrast in human vision". Vision Research 4 (1-2): 135–154. doi:10.1016/0042-6989(64)90037-9. PMID 5888593. 
  12. ^ Ladd, J.H.; Pinney, J.E. (September 1955). "Empirical relationships with the Munsell Value scale". Proceedings of the Institute of Radio Engineers 43 (9): 1137. doi:10.1109/JRPROC.1955.277892. ISSN 0096-8390. 
  13. ^ Glasser, L.G.; A.H. McKinney, C.D. Reilly, and P.D. Schnelle (October 1958). "Cube-root color coordinate system". JOSA 48 (10): 736–740. 
  14. ^ Wyszecki, Günther (November 1963). "Proposal for a New Color-Difference Formula". JOSA 53: 1318–1319.  Note: The asterisks are not used in the paper.
  15. ^ Pauli, Hartmut K.A. (1976). "Proposed extension of the CIE recommendation on "Uniform color spaces, color spaces, and color-difference equations, and metric color terms"". JOSA 66 (8): 866–867. 
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