Tungsten illumination can’t have a colour temperature higher than tungsten’s melting point, 3695 K.

The reciprocal of correlated colour temperature is somewhat more perceptually uniform than correlated colour temperature itself. Cinematographers use units of mirek (micro reciprocal kelvin [MK-1]), that is, 106/t, where t is in units of kelvin [K]. Mirek units are more perceptually uniform than kelvin. For typical video or cinema acquisition, CCT typically ranges from 2000 K to 10,000 K; that is, from 500 to 100 mirek.

The mirek unit is sometimes called reciprocal megakelvin, and was historically called mired (“micro reciprocal degree”) .

Chromatic adaptation

Human vision adapts to the viewing environment. An image viewed in isolation – such as a 35 mm slide, or motion picture film projected in a dark room – creates its own white reference; a viewer will be quite tolerant of variation in white point. However, if the same image is viewed alongside an external white reference, or with a second image, differences in white point can be objectionable. Complete adaptation seems to be confined to colour temperatures from about 5000 K to 6500 K. Tungsten illumination, at about 3200 K, almost always appears somewhat yellow.

Perceptually uniform colour spaces

As I outlined in Perceptual uniformity, on page 30,

a system is perceptually uniform if a small perturbation to a component value is approximately equally perceptible across the range of that value.

Luminance is not perceptually uniform. On page 259, I described how luminance can be transformed to lightness, denoted L*, which is nearly perceptually uniform:

L*u*v* and L*a*b* are often written CIELUV and CIELAB; they are usually pronounced SEA-love and SEA-lab. The u* and v* quantities of colour science – and the u’ and v’ quantities, to be described – are unrelated to the U and V colour difference components of video.

Extending this concept to colour, XYZ and RGB tristimulus values, and xyY (chromaticity and luminance), are far from perceptually uniform. Finding a transformation of XYZ into a reasonably perceptually uniform space occupied the CIE for a decade, and in the end no single system could be agreed upon. In 1976, the CIE standardized two systems, L*u*v* and L*a*b*, which

I will now describe. In both systems, perceptual difference is approximated as Euclidean distance.

CIE L*u*v*

Computation of CIE L*u*v* starts with a projective transformation of [X, Y, Z] into intermediate u’ and v’ quantities:

Equivalently, u’ and v’ can be computed from x and y chromaticity:

To recover X and Z tristimulus values from u’ and v’, use these relations:

To recover x and y chromaticity from u’ and v’, use these relations:

The primes in the CIE 1976 u’ and v’ quantities denote the successor to the obsolete 1960 CIE u and v quantities. u=u’; v=2⁄3v’ – that is, the 1960 v quantity underestimated visual perceptibility, and was multiplied by a factor of 1.5 to form the 1976 system. (To compute 1960 v, replace the numerator 9y in Eq 25.5 by 6y.) The primes are not formally related to the primes in R’, G’, B’, and Y’, though all imply some degree of perceptual uniformity.

Since u’ and v’ are formed by a projective transformation, u’ and v’ coordinates are associated with

a chromaticity diagram similar to the CIE 1931 2° [x, y] chromaticity diagram on page 274. You can use the [u’, v’] diagram if you want to produce 2-D plots that are more suggestive of the perceptibility of colour differences than an [x, y] plot would be. However,

[u’, v’] are subsequently multiplied by L* (see Equation 25.8 below) to form [u*, v*]. That multiplication effectively enlarges the perceptual increment as luminance decreases. Perceptual differences in a [u’, v’] diagram are dependant upon luminance, but that fact is

∆E* is pronounced delta E-star.

not evident from the diagram: Be careful not to draw strong conclusions from the diagram.

To compute u* and v*, first compute L*. Then compute u’n and v’n from your reference white Xn, Yn, and Zn. (The subscript n suggests normalized.) The u’n and v’n coordinates for several common white points are given in Table 25.1, White references, on page 279. (The [xn,yn] coordinates for a colour temperature of infinity are about [0.237, 0.237]; the [u’n,v’n] coordinates are about [0.177, 0.397].) Finally, compute u* and v*:

Gamut refers to the range of colours available in an imaging system. For gamuts typical of image reproduction, u* and v* values each range approximately ±100.

Euclidean distance in L*u*v* – denoted ∆E* – uv

estimates the perceptibility of colour differences:

If ∆E* is unity or less, the colour difference is uv

assumed to be imperceptible. However, L*u*v* does not achieve perceptual uniformity, it is merely an approxi-

mation. ∆E* values between about 1 and 4 may or uv

may not be perceptible, depending upon the region of

colour space being examined. ∆E* values greater than uv

4 are likely to be perceptible; whether such differences are objectionable depends upon circumstances.

A polar-coordinate version of the [u*, v*] pair can be used to express chroma and hue:

In addition, there is a “psychometric saturation” term:

Chroma, hue, and saturation defined here are not directly related to saturation and hue in the HSB, HSI, HSL, HSV, and IHS systems used in computing and in digital image processing: Most of the published descriptions of these spaces, and most of the published formulæ, disregard the principles of colour science. In

Eq 25.12

Eq 25.13

Eq 25.14

particular, the quantities called lightness and value are wildly inconsistent with their definitions in colour science.

CIE L*u*v* exhibits reasonable perceptual uniformity. L*u*v* has been common in video because the mapping of XYZ, xyY, and RGB to the u’v’ coordinates is projective: Straight lines in any of these spaces map to straight lines in u’v’. Despite the convenience and utility of L*u*v*, colour scientists today generally agree that better perceptual performance is exhibited by L*a*b*, which I will now describe.

CIE L*a*b* (CIELAB)

The quantities a* and b* are computed as follows:

The coefficients are approximately 4.310 and 1.724. My definition is written in an unusual way, using L* instead of the traditional auxiliary function f. The definition of L* involves a linear segment having C1 continuity with a power function segment. That linear segment is incorporated (by way of L*) into a* and b*.

The reference L* range from black to white is zero to 100. For the BT.709 primaries typical of SD and HD, a* and b* are contained within the ranges [-87…+97] and [-108…+95] respectively, not including any undershoot, overshoot, or “illegal” or “invalid” CBCR values.

As in L*u*v*, one unit of Euclidean distance in L*a*b* –

denoted ∆E* – approximates the perceptibility of ab

colour differences:

If ∆E*ab is unity or less, the colour difference is taken to be imperceptible. However, L*a*b* does not achieve perceptual uniformity: It is merely an approximation.

A polar-coordinate version of the [a*, b*] pair can be used to express chroma and hue: