Lightness: Difference between revisions

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.

Value is a measure of where a particular color lies along the lightness–darkness axis. A color's value is its amplitude. Various color models have an explicit term which places the color on a scale from utter black to pure white. The HSV color model and Munsell color model have an explicit value, while the HSL color model uses a related parameter called lightness instead.

In the HSV and Munsell color models, a color with a low value is nearly black, while one with a high value is the pure color.

The image shows three hues in the Munsell color model. Each color differs in value from top to bottom in equal perception steps. The right column undergoes a dramatic change in perceived 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.

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]

${\displaystyle V=10{\sqrt {Y}}}$

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]

${\displaystyle V^{2}=1.4742Y-0.004743Y^{2}}$

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]

${\displaystyle Y=1.2219V-0.23111V^{2}+0.23951V^{3}-0.021009V^{4}+0.0008404V^{5}}$

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

${\displaystyle V=5(Y/19.77)^{0.426}=1.4Y^{0.426}}$

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]

${\displaystyle V=2.357Y^{0.343}-1.52}$

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]

${\displaystyle V=2.217Y^{0.352}-1.324}$

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

${\displaystyle V=2.468Y^{1/3}-1.636}$

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

${\displaystyle L^{*}=25.29Y^{1/3}-18.38}$

1964: Wyszecki simplifies this to:^[14]

${\displaystyle W^{*}=25Y^{1/3}-17}$

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

1976: CIELAB uses the following formula:

${\displaystyle L^{*}=116(Y/Y_{n})^{1/3}-16}$

where ${\displaystyle Y_{n}}$ is the Y tristimulus value of a "specified white object" and is subject to the restriction ${\displaystyle Y/Y_{n}>0.01}$. Pauli removes this restriction by computing a linear extrapolation which maps Y/Y_n=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 ${\displaystyle Y/Y_{n}=(6/29)^{3}\approx 0.008856}$, then the slope of ${\displaystyle (29/3)^{3}\approx 903.3}$ is computed. This gives the two-part function:^[15]

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

The lightness is then ${\displaystyle L^{*}=116f(Y/Y_{n})-16}$.

• Elements of Design at Inkscape.org