# Lightness (color)

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Lightness (sometimes called value or tone) 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 along a lightness–darkness axis. A color's lightness also corresponds to its amplitude.

Various color models have an explicit term for this property. The Munsell color model uses the term value, while the HSL color model and Lab color space use the term lightness. The HSV model uses the term value a little differently: a color with a low value is nearly black, but one with a high value is the pure, fully saturated color.

In subtractive color (i.e. paints) value changes can be achieved by adding black or white to the color. However, this also reduces saturation. Chiaroscuro and Tenebrism both take advantage of dramatic contrasts of value to heighten drama in art. Artists may also employ shading, subtle manipulation of value.

## 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]

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]
$V^2=1.4742Y-0.004743Y^2$
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]
$Y=1.2219V-0.23111V^2+0.23951V^3-0.021009V^4+0.0008404V^5$
1943
Using Table II of the O.S.A. report, Moon and Spencer express the value in terms of the luminance:[8]
$V=5 (Y/19.77)^{0.426}=1.4 Y^{0.426}$
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]
$V=2.357 Y^{0.343}-1.52$
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]
$V=2.217 Y^{0.352}-1.324$
Realizing this is quite close to the cube root, they simplify it to:
$V=2.468 Y^{1/3}-1.636$
1958
Glasser et al. define the lightness as ten times the Munsell value (so that the lightness ranges from 0 to 100):[13]
$L^*=25.29 Y^{1/3} - 18.38$
1964
Wyszecki simplifies this to:[14]
$W^*=25Y^{1/3}-17$
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:
$L^* = 116 (Y/Y_n)^{1/3}-16$
where $Y_n$ is the Y tristimulus value of a "specified white object" and is subject to the restriction $Y/Y_n > 0.01$. 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 $L^*=116 f(Y/Y_n)-16$.

At first glance, you might approximate the lightness function by a cube root, an approximation that is found in much of the technical literature. However, the linear segment near black is significant. The best-fit pure power function has an exponent of about 0.42, far from 1/3.

An 18% grey card, having a reflectance of 0.18, has lightness very close to 50. It is called "mid grey" because its lightness is midway between black and white.

## References

1. Kuehni, Rolf G. (February 2002). The early development of the Munsell system. Color Research & Application 27 (1): 20–27.
2. Hunt, Robert W. G. (May 18 1957). Light Energy and Brightness Sensation. Nature 179 (4568).
3. Valberg, Arne (2006). Light Vision Color, John Wiley and Sons.
4. Priest, Irwin G. (September 1920). An examination of the Munsell color system. I: Spectral and total reflection and the Munsell scale of Value (3).
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. Journal of the Optical Society of America 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.
11. Jameson, Dorothea, Leo M., Hurvich (May 1964). Theory of brightness and color contrast in human vision. Vision Research 4 (1-2): 135–154.
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).
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 (11): 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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