Table 26.3 NTSC primaries (obsolete) were used in 480i SD systems from 1953 until about 1970, when the primaries now documented in SMPTE RP 145 were adopted.

Table 26.4 EBU Tech. 3213 primaries apply to 576i SD systems.

Table 26.5 SMPTE RP 145 primaries apply to 480i SD systems.

Leggacy SD primaries

In 1953, the NTSC established primaries for emergent colour television. Those primaries were standardized by the FCC; they are now obsolete. RP 145 (“SMPTE-C”) primaries have historically been used for SD in North America and Japan. EBU primaries have historically been used for SD in Europe. I detail these systems in Chapter 3, Summary of obsolete RGB standards, of Composite NTSC and PAL: Legacy Video Systems. The chromaticities of these sets of primaries are indicated below:

Interpreting RP 145 RGB values as BT.709 leads to colour errors of up to 20 ∆E, with an average error of about 14 ∆E. There are differences in primary chromaticities between the EBU standards and BT.709. Interpreting EBU RGB values as BT.709 leads to colour errors of up to 5 ∆E on the primaries, with an average error of about 2 ∆E.

Despite these differences between SD practice and BT.709, the BT.709 primaries are effectively being retrofitted into SD, albeit slowly.

IEC 61966-2-1, Multimedia systems and equipment – Colour measurement and management – Part 2-1: Colour management – Default RGB colour space – sRGB.

SMPTE ST 2048-1, 2048× 1080 and 4096× 2160 Digital Cinematography Production Image Formats FS/709.

The notation FS/709 is supposed to indicate that the standard applies either to imagery coded to FS-Gamut or to imagery coded to BT.709.

Table 26.6 SMPTE “Free Scale” default primaries exceed the gamut of motion picture film as conventionally aquired, processed, and projected. Image data is scene-referred.

sRGB system

The sRGB standard is widely used in computing; the BT.709 primaries have been incorporated into sRGB. Beware that although the primary chromaticities are identical, the sRGB transfer function is somewhat different from the transfer functions standardized for studio video.

In the 1980s and 1990s, RGB image data in computing was commonly exchanged without information about primary chromaticities, white reference, or transfer function (to be described in Gamma, on

page 315). If you have RGB image data without information about these parameters, you cannot accurately reproduce the image. The sRGB standard saw widespread deployment starting in about 2000, and today if you have an untagged RGB image it is safe to interpret the data according to sRGB.

SMPTE Free Scale (FS) primaries

In 2011, SMPTE standardized a scheme termed Free Scale Gamut (FS-Gamut) that accommodates widegamut image data for 2 K and 4 K digital cinema production. (See Free Scale Gamut, Free Scale Log, on page 312.) A set of default primaries is defined. The primaries are nonphysical, so as to exceed the gamut of original camera negative film as normally processed and printed. The white point is D65. The scheme is intended to encode scene-referred image data, typically using

a quasilog coding specified in the same standard. The chromaticities of the default FS primaries and white are specified in Table 26.6:

AMPAS Specification S-2008-001,

Academy Color Encoding Specification (ACES).

AMPAS ACES primaries

The Science and Technology Council (STC) of the Academy of Motion Picture Arts and Sciences (AMPAS) agreed upon a set of primaries for digital cinema acquisition and processing. ACES green and blue are nonphysical, so as to exceed the gamut of original

Some people will be surprised by the negative value of the ACES blue y coordinate: Adding ACES blue decreases luminance!

Table 26.7 AMPAS ACES primaries exceed the gamut of motion picture film as conventionally aquired, processed, and projected. ACES data is scene-referred.

camera negative film as normally processed and printed. The standard has a white point approximating D60. The system is intended to encode scene-referred image data. The chromaticities of the ACES primaries and white are specified in Table 26.7:

SMPTE ST 428-1, D-Cinema Distribution Master – Image Characteristics.

Table 26.8 SMPTE/DCI P3 primaries approximately encompass the gamut of film, and are used for digital cinema. P3 data is display-referred.

SMPTE/DCI P3 primaries

Participants in the Digital Cinema Initiative (DCI) in the year 2000 achieved agreement upon primaries for a reference projector whose primaries approximately encompass the gamut of motion picture film as conventionally illuminated. Image data is display-referred. DCI’s agreement has been promulgated as a SMPTE standard. The standard has a white point approximating current film practice; the tolerance on the white point specification encompasses D61. The chromaticities of the DCI primaries and white are specified in Table 26.8:

In establishing image data encoding standards for digital cinema, the DCI sought to make a ”future-proof” standard that would accommodate wider colour gamut without the need to represent negative data values or data values above unity and without the necessity to maintain metadata. The standards adopted call for image data to be encoded in XYZ tristimulus values representing colours to be displayed. XYZ encoding amounts to using primaries having chromaticities [1, 0], [0, 1], and [0, 0], with a white reference of [1⁄3, 1⁄3].

Despite DCI’s adoption of XYZ coding, all digital cinema material mastered today is mastered to the DCI P3 gamut of the reference projector that I described above. I expect this situation to continue for the next 5

To understand the mathematical details of colour transforms, described in this section, you should be familiar with linear (matrix) algebra. If you are unfamiliar with linear algebra, see Strang, Gilbert

(1998), Introduction to Linear Algebra, Second Edition (Boston: Wellesley-Cambridge).

or 10 years. Issues of gamut mapping will eventually have to be addressed if new, wide-gamut material is to be sensibly displayed on legacy projectors. DCI standards are completely silent on issues of gamut mapping.

CMFs and SPDs

You might guess that you could implement a display whose primaries had spectral power distributions with the same shape as the CIE spectral analysis curves – the colour-matching functions for XYZ. You could make such a display, but when driven by XYZ tristimulus values, it would not properly reproduce colour. There are display primaries that reproduce colour accurately

when driven by XYZ tristimuli, but the SPDs of those

_ _

primaries do not have the same shape as the x(λ), y(λ),

_

and z(λ) CMFs. To see why requires understanding

a very subtle and important point about colour capture and reproduction.

To find a set of display primaries that reproduces colour according to XYZ tristimulus values would

The x(λ), y(λ), and z(λ) CMFs are positive across the entire spectrum. Producing [0, 1, 0] would require positive contribution from some wavelengths in the required primary SPDs, and that we could arrange; however, there is no wavelength that contributes to Y that does not also contribute positively to X or Z.

The solution to this dilemma is to force the X and Z contributions to zero by making the corresponding SPDs have negative power at certain wavelengths. Although this is not a problem for mathematics, or even for signal processing, an SPD with a negative lobe is not physically realizable in a transducer for light, because light power cannot go negative. So we cannot build

a real display that responds directly to XYZ. But as you will see, the concept of negative SPDs – and nonphysical SPDs or nonrealizable primaries – is very useful in theory and in practice.

SPDs that correspond to the x(λ), y(λ), and z(λ) colourmatching functions. One way is to arbitrarily choose three display primaries whose power is concentrated at

Table 26.9 Example primaries are used to explain the necessity of signal processing in accurate colour reproduction.

three discrete wavelengths. Consider three display

SPDs, each of which has some amount of power at

_ _

600 _nm, 550 nm, and 470 nm. Sample the x(λ), y(λ), and z(λ) functions of the matrix given earlier in Calculation of tristimulus values by matrix multiplication, on page 273, at those three wavelengths. This yields the tristimulus values shown in Table 26.9:

Eq 26.1 This matrix is based upon R, G, and B components with unusual spectral distributions. For typical R, G, and B, see Eq 26.8.

These coefficients can be expressed as a matrix, where the column vectors give the XYZ tristimulus values corresponding to pure red, green, and blue at the display, that is, [1, 0, 0], [0, 1, 0], and [0, 0, 1]. It is conventional to apply a scale factor in such a matrix to cause the middle row to sum to unity, since we wish to achieve only relative matches, not absolute:

R600nm

Eq 26.2 G550nm

B470nm

Michael Brill and Bob Hunt agree that R, G, and B tristimulus values have no units. See Hunt, Robert W.G. (1997),“The heights of the CIE colour-matching functions,” in

Color Research and Application,

22 (5): 335–335 (Oct.).

XYZ tristimulus values is necessarily supersaturated, more saturated than any realizable SPD could be.

To determine a set of physical SPDs that will reproduce colour when driven from XYZ, consider the problem in the other direction: Given a set of physically realizable display primaries, what CMFs are suitable to directly reproduce colour using mixtures of these primaries? In this case the matrix that relates RGB components to CIE XYZ tristimulus values is all-posi- tive, but the CMFs required for analysis of the scene have negative portions: The analysis filters are nonrealizable.

Figure 26.6 shows a set of primary SPDs conformant to SMPTE 240M, similar to BT.709. Many different SPDs can produce an exact match to these chromaticities; the set shown is from a Sony Trinitron display. Figure 26.5 shows the corresponding colour-matching functions. As expected, the CMFs have negative lobes and are therefore not directly realizable; nonetheless, these are the idealized CMFs, or idealized taking characterstics – of the BT.709 primaries.

We conclude that we can use physically realizable analysis CMFs, as in the first example, where XYZ components are displayed directly. But this requires nonphysical display primary SPDs. Or we can use physical display primary SPDs, but this requires nonphysical analysis CMFs. As a consequence of the way colour vision works, there is no set of nonnegative display primary SPDs that corresponds to an all-positive set of analysis functions.

The escape from this conundrum is to impose a 3× 3 matrix multiplication in the processing of the camera signals, instead of using the camera signals to directly drive the display. Consider these display primaries: monochromatic red at 600 nm, monochromatic green at 550 nm, and monochromatic blue at 470 nm. The 3× 3 matrix of Equation 26.2 can be used to process XYZ values into components suitable to drive that display. Such signal processing is not just desirable; it is a necessity for achieving accurate colour reproduction!