Eq 27.1

γE ≈ 0.5;γD ≈ 2.4; γE γD ≈ 1.2

What I call OECF, in accordance with the nomenclature of

ISO 14524, is often called optoelectronic transfer function, OETF, in historical video literature.

BT.1361 was established by ITU-R but never deployed. It is now moribund, superseded by xvYCC.

ITU-R Rec. BT.709, Basic parameter values for the HDTV standard for the studio and for international programme exchange.

function whose exponent is about 1.2, as indicated in Equation 27.1 in the margin. This undercompensation achieves end-to-end reproduction that is subjectively correct (though not mathematically linear).

Opto-electronic conversion functions (OECFs)

Several different transfer functions have been standardized and are in use. In the sections to follow, I will detail these standards:

•BT.709 is an international standard that specifies the basic parameters of HD. Although intended for HD, it is representative of current SD technology, and it is being retrofitted into SD studio standards.

•The xvYCC “standard” extends Y’CBCR and Y’PBPR coding to accommodate a wide colour gamut. As

I write, xvYCC is not deployed.

•sRGB refers to the standard transfer function of PCs.

•The transfer function of the original 1953 NTSC specification, often written 1⁄2.2, has been effectively superseded by BT.1886.

•The transfer function of European standards for 576i is often given as 1⁄2.8. Professional encoding has never expected a decoding gamma as high as 2.8. In any event, that value has been effectively superseded by BT.1886.

It is unclear from historical documents whether the classic NTSC 2.2 “gamma” and the classic EBU 2.8

“gamma” were intended to define the camera or the display! In entertainment imaging, the content creator has licence to manipulate image data at acquisition and at postproduction to yield the intended picture appearance, potentially completely independently of any standard OECF at a camera. The standard EOCF predominates: The EOCF establishes how image data is to be displayed in a manner faithful to the content creation process. The standard camera OECFs merely serve as engineering guidelines.

BT.709 OECF

Figure 27.3 illustrates the transfer function defined by the international BT.709 standard for high-definition television (HD). It is based upon a pure power function with an exponent of 0.45. Theoretically, a pure power function suffices for gamma correction; however, the

Figure 27.3 BT.709 OECF is standardized as the reference mapping from scene tristimulus to video code in SD and HD.

The symbol T suggests tristimulus value; the same equation applies to R, G or B. The symbol V suggests voltage, or video, or [code/pixel] value. I write this unprimed.

slope of a pure power function (whose exponent is less than unity) is infinite at zero. In a practical system such as a video camera, in order to minimize noise in dark regions of the picture it is necessary to limit the slope (gain) of the function near black. BT.709 specifies

a slope of 4.5 below a tristimulus value of +0.018. The pure power function segment of the curve is scaled and offset to maintain function and tangent continuity at the breakpoint.

Reference BT.709 encoding is as follows. The tristimulus (linear light) component is denoted T, and the resulting gamma-corrected video signal – one of R’, G’, or B’ components – is denoted with a prime symbol, V709. R, G, and B are processed through identical functions to obtain R’, G’, and B’:

The reference BT.709 encoding equation includes an exponent of 0.45. I call this the “advertised” exponent. Some people describe BT.709 as having “gamma of 0.45”; broadcast video camera gamma controls are calibrated in terms comparable to this value. However, the effect of the scale factor and offset terms make the overall power function very similar to a square root

(γ E≈0.5); the effective power function exponent – and the value appropriate for picture rendering calculations – is 0.5.

SMPTE 240M, 1125-Line High-

Definition Production Systems –

Signal Parameters.

BT.709 encoding assumes that encoded R’G’B’ signals will be converted to tristimulus values at a display with an EOCF close to a pure 2.4-power function:

The product of the effective 0.5 exponent typically used at the camera and the 2.4 exponent at the display produces an end-to-end power of about 1.2, suitable for material acquired in a bright environment for display in a typical television viewing situation, as I explained in Picture rendering, on page 115. In 2011, ITU-R adopted BT.1886, which specifies a 2.4-power function EOCF for HD; see Reference display and viewing conditions, on page 427. Unfortunately, reference white luminance and viewing conditions aren’t standardized.

To recover RGB values proportional to scene tristimulus values, assuming that the camera was operated with

“factory” BT.709 settings, invert Equation 27.2:

Equation 27.4 is very similar to a square root. It does not incorporate correction for picture rendering: Recovered values are proportional to the scene tristimulus values, not to the intended display tristimulus values. BT.709 is misleading in its inclusion of this equation without discussing – or even mentioning – the issue of picture rendering.

For details of quantization to 8- or 10-bit components, see Studio-swing (footroom and headroom), on page 42.

SMPTE 240M OECF

SMPTE Standard 240M for 1125/60, 1035i30 HD was adopted two years before BT.709; virtually all HD equipment deployed in the decade 1988 to 1998 used the its parameters. For details, refer to the first edition of this book. The OECF specified in SMPTE 240M is intended to be used with a display EOCF comparable to that standardized (much later) in BT.1886.

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

γD≈2.4 0.45 · 2.4 ≈1.1

See Picture rendering, on page 115.

Stokes, Michael, Matthew Anderson, Srinivasan Chandrasekar, and Ricardo Motta

(1996), A Standard Default Color Space for the Internet – sRGB http://www.w3.org/Graphics/Color/ sRGB.

sRGB transfer function

The notation sRGB refers to a specification for colour image coding for personal computing, desktop graphics, and image exchange on the Internet.

The sRGB specificaton provides that a display will convert encoded R’G’B’ signals using an EOCF that is a pure 2.2-power function.

The sRGB specification anticipates a higher ambient light level for viewing than typical broadcast studio practice associated with BT.709 encoding. Imagery originated with BT.709 encoding, displayed on a display with a 2.2-power, results in an end-to-end power of 1.1, considerably lower than the 1.2 end-to-end power produced by BT.709 encoding, but appropriate for the high display luminance, light surround, and poor contrast ratio typical of sRGB display environments.

The sRGB specification includes a function that ostensibly defines an OECF:

The standard is not explicit about the use of this function. Evidently it maps linear-light values to sRGB codes, and it includes a linear segment near black that you would expect in an OECF. The function resembles the BT.709 OECF. However, no account is taken of picture rendering. I conclude – and section 5.1 of the standard implies – that the function is intended to describe the mapping from the tristimulus values presented on the display to sRGB codes; in other words, sRGB coding is display referred. The encoding specified by sRGB is inappropriate when picture rendering is to be applied at the time of image capture – for example, when capturing a scene with a digital camera. For the latter purpose, BT.709 coding is appropriate.

Although Equation 27.5 contains the exponent 1⁄2.4, which suggests “gamma of 0.42,” the scale factor and the offset cause the overall function to approximate

a pure 0.45-power function (γE≈0.45). It is misleading to describe sRGB as having “gamma of 0.42.”

It is standard to code sRGB components in 8-bit form from 0 to 255, with no footroom and no headroom.