Some people suggest that NTSC should be gamma-corrected with power of 1⁄2.2, and PAL with 1⁄2.8. I disagree with both interpretations; see page 325.

negative and print films. Projected imagery is typically intended for viewing in a dark surround; arrangements are made to have an end-to-end power function exponent considerably greater than unity – typically about 1.5 – so that the contrast range of the scene is expanded upon display. In cinema film, the correction is achieved through a combination of the transfer function (“gamma” of about 0.6) built into camera negative film and the transfer function (“gamma” of about 2.5) built into print film.

I have described video systems as if they use a pure 0.5-power law encoding function. Practical considerations necessitate modification of the pure power function by the insertion of a linear segment near black, as I will explain in Gamma, on page 315. The exponent in the BT.709 standard is written (“advertised”) as 0.45; however, the insertion of the linear segment, and the offsetting and scaling of the pure power function segment of the curve, cause an exponent of about 0.51 to best describe the overall curve. (To describe gamma as 0.45 in this situation is misleading.)

Rendering in desktop computing

In the desktop computer environment, the ambient condition is considerably brighter, and the surround is brighter than is typical of television viewing. An end-to- end exponent lower than the 1.2 of video is called for; a value around 1.1 is generally suitable. However, desktop computers are used in a variety of different viewing conditions. It is not practical to originate every image in several forms, optimized for several potential

In the sRGB standard, the exponent is written (“advertised”) as 1⁄2.4 (about 0.42). However, the insertion of the linear segment, and the offsetting and scaling of the pure power function segment of the curve, cause an exponent of about 0.45 to best describe the overall curve. See sRGB transfer function, on page 324.

viewing conditions! A specific encoding function needs to be chosen. Achieving optimum reproduction in diverse viewing conditions requires selecting a suitable correction at display time. Technically, this is easy to achieve: Modern computer display subsystems have hardware lookup tables (LUTs) that can be loaded dynamically with appropriate curves. However, it is

a challenge to train users to make a suitable choice. There is promise in sensors to detect ambient light, and algorithms to effect appropriate correction (largely by altering display gamma). Such schemes have been implemented commercially, but there are no standards.

When the sRGB standard for desktop computing was being developed, the inevitability of local, viewingdependent correction was not appreciated. That standard promulgates decoding with a pure 2.2-power function, but the standard also described what is apparently an encoding standard with a linear segment near black and an effective exponent of about 0.45. A close reading of the sRGB standard confirms that sRGB is display referred; the video-like definition with the linear segment is a mapping from tristimulus values at the display surface into sRGB code values. The sRGB “encode” function is not comparable to BT.709’s reference OECF. Display of sRGB material should be accomplished with the pure 2.2-power function, without any linear segment.

Video cameras, film cameras, motion picture cameras, and digital still cameras all capture images from the real world. When an image of an original scene or object is captured, it is important to introduce rendering. However, scanners used in desktop computing rarely scan original objects; they usually scan reproductions such as photographic prints or offsetprinted images. When a reproduction is scanned, rendering has already been imposed by the first imaging process. It may be sensible to adjust the original rendering, but it is not sensible to introduce rendering that would be suitable for scanning a real scene or object.

The statement is commonly made that “the human visual system is more sensitive to luma than chroma.” That statement is incorrect. It is vision’s sensitivity to information at high spatial frequency that is diminished for chroma. Chroma subsampling is enabled by poor acuity for chroma, not by poor sensitivity.

Video systems convey image data in the form of one component that represents lightness, and two components that represent colour, disregarding lightness. This scheme exploits the reduced colour acuity of vision compared to luminance acuity: As long as lightness is conveyed with full detail, detail in the colour components can be reduced by subsampling – that is, by filtering (averaging). This chapter introduces the concepts of luma and chroma encoding; details will be presented in Luma and colour differences, on page 335.

Luma

A certain amount of noise is inevitable in digital imaging systems. As explained in Perceptual uniformity, on page 8, encoding is arranged so that noise has a perceptually similar effect across the entire tone scale from black to white. The lightness component is conveyed in a perceptually uniform manner that minimizes the amount of noise (or quantization error) introduced in processing, recording, and transmission.

Ideally, noise would be minimized by forming

a signal proportional to CIE luminance, as a suitably weighted sum of linear R, G, and B tristimulus signals. Then, this signal would be subjected to a transfer function that imposes perceptual uniformity, such as the CIE L* function of colour science that will be detailed on page 259. As explained in Constant luminance, on page 107, there are practical reasons in video to perform these operations in the opposite order. First, a nonlinear transfer function – gamma correction – is applied to each of the linear R, G, and B tristimulus

The prime symbols here, and in following equations, denote nonlinear components.

CIE: Commission Internationale de l’Éclairage

See Appendix A, YUV and luminance considered harmful, on page 567.

signals: We impose a transfer function similar to

a square root, and roughly comparable to the CIE lightness (L*) function. Then a weighted sum of the resulting nonlinear R’, G’, and B’ components is computed to form a luma signal (Y’) representative of lightness. SD uses coefficients that are standardized in BT.601 (see page 131):

Unfortunately, luma for HD is coded differently from luma in SD! BT.709 specifies these coefficients:

Sloppy use of the term luminance

The term luminance and the symbol Y were established 75 years ago by the CIE, the standards body for colour science. Unfortunately, in video, the term luminance has come to mean the video signal representative of luminance even though the components of the video signal have been subjected to a nonlinear transfer function. At the dawn of video, the nonlinear signal was denoted Y’, where the prime symbol indicated the nonlinear treatment. But over the last 50 years the prime has not appeared consistently, and today, both the term luminance and the symbol Y conflict with their CIE definitions, making them ambiguous! This has led to great confusion, such as the incorrect statement commonly found in computer graphics textbooks and digital image-processing textbooks that in the YIQ or YUV colour spaces, the Y component is identical to CIE luminance!

I use the term luminance according to its CIE definition; I use the term luma to refer to the video signal; and I am careful to designate nonlinear quantities with a prime. However, many video engineers, computer graphics practitioners, and image-processing specialists use these terms carelessly. You must be careful to determine whether a linear or nonlinear interpretation is being applied to the word and the symbol.