Eq 4.5 Theoretical SNR limit for a k-step quantizer:

The factor of root-12, about 11 dB, accounts for the ratio between peak-to-peak and RMS; for details, see Schreiber (cited below).

Some people use the word dither to refer to the technique of adding noise prior to quantization; other people restrict the term dither to schemes that involve spatial distribution of the noise. The technique was first described by Roberts, Lawrence G. (1962),“Picture coding using pseudorandom noise,” IRE Trans. IT-8 (2): 145– 154. Roberts’ work is summarized in Schreiber, William F.

(1993), Fundamentals of Electronic Imaging Systems, Third Edition (Berlin: Springer-Verlag).

diminishes signal-to-noise ratio. The theoretical SNR limit of a k-step quantizer is given by Equation 4.5. Eight-bit quantization, common in consumer video, has a theoretical SNR limit (peak-to-peak signal to RMS noise) of about 56 dB.

If an analog signal has very little noise, then its quantized value can be nearly exact when near a step, but can exhibit an error of nearly ±1⁄2 of a step when the analog signal is midway between quantized levels. In video, this situation can cause the reproduced image to exhibit noise modulation. It is beneficial to introduce, prior to quantization, roughly ±1⁄2 of a quantizer step’s worth of high-frequency random or pseudorandom noise to avoid this effect. This introduces a little noise into the picture, but this noise is less visible than lowfrequency “patterning” of the quantization that would be liable to result without it. SNR is slightly degraded, but subjective picture quality is improved. Historically, video digitizers implicitly assumed that the input signal itself arrived with sufficient analog noise to perform this function; nowadays, analog noise levels are lower, and the noise should be added explicitly at the digitizer.

The degree to which noise in a video signal is visible – or objectionable – depends upon the properties of vision. To minimize noise visibility, we digitize a signal that is a carefully chosen nonlinear function of

luminance (or tristimulus values). The function is chosen so that a given amount of noise is approximately equally perceptible across the whole tone scale from black to white. This concept was outlined in Nonlinear image coding, on page 12; in the sections to follow, linearity and perceptual uniformity are elaborated.

Full-swing

Excursion (or colloquially, swing) refers to the range of a signal – the difference between its maximum and minimum levels. In video, reference excursion is the range between standardized reference white and reference black signal levels.

Computer graphics image data ordinarily has fullswing (or full-range), where reference black is assigned to the lowest code level and reference white is assigned to the highest code level. In desktop graphics, R’G’B’

Figure 4.3 Full-swing 8-bit quantization is depicted in this sketch. A nominally continuous input signal, here represented by values ranging 0 to 1 on the x-axis, is quantized to 8 bits – that is, 256 steps – for storage or transmission. The coding provides no footroom or headroom.

255

0

01

When the BT.601 standard was established in 1984, an engineering error was made. Luma should have been assigned interface codes from 16 to 240 to match the chroma excursion. Instead, the range 16 to 235 was chosen, for no good reason.

components typically have 8 bits each and range 0 through 255. Figure 4.3 depicts 8-bit full-swing coding.

Studio-swing (footroom and headroom)

In high-quality video, it is necessary to preserve transient signal excursions below black and above white that are liable to result from processing by digital and analog filters. Studio video standards therefore provide footroom below reference black, and headroom above reference white. Since headroom allows code values that exceed reference white, reference white and peak white refer to different signal levels.

I have described signals in the abstract range 0 to 1. When R’G’B’ or Y’ components are interfaced in 8 bits, the 0 to 1 values are scaled by 219 and offset by +16.

Eight-bit studio standards thus have 219 steps between reference black and reference white. Interface codes below 16 and above 235 are used for footroom and headroom. Unfortunately, footroom and headroom are not symmetrical. Figure 4.4 below shows the standard coding range for 8-bit R’, G’, or B’, or luma. Codes

Figure 4.4 Footroom and headroom is provided in digital video standards. For processing, reference black is considered to lie at code 0; in an 8-bit system, R’, G’, B’, and luma (Y’) range 0 through reference white at code 219. At an 8-bit interface according to BT.601, an offset of +16 is added (indicated in italics). Interface codes 0 and 255 are reserved for synchronization; those codes are prohibited in video data.

pluge: Picture line-up generator. See page 421.

Program creators routinely hire quality control (QC) contractors to vet finished programs. QC contractors have and come to believe, mistakenly, that excursions outside the 0-to-1 range are “illegal” and should be rejected. Many studios now thoughtlessly believe their QC houses instead of developing their own understanding of the issue.

having the 8 most-significant bits (MSBs) all-zero or allone 0 and 255 are used for synchronization; these codes are prohibited within video data.

Historically, there were essentially two reasons for footroom and headroom:

•It was necessary to accommodate video whose analog levels were misadjusted.

•It was very useful to preserve filter transients (undershoot and overshoot) through as much of the system as possible (even though undershoots would eventually be clipped at the display).

As use of analog decreased, the first reason vanished. The second remained important, and three additional reasons emerged:

•The footroom region enables conveyance of the pluge pattern used to set black level.

•When black is set correctly, reference black level produces luminance that is visually indistinguishable from reference black, but still nonzero. A pure 2.4-power function EOCF produces relative luminance of around 0.0003 at this point. The idealized, theoretical zero luminance occurs at a level below reference black. That level is coded in the footroom region.

•Image sensors produce noise, including noise at black. If footroom is provided, the noise averages to black. If lack of footroom clips the negative-going excursion of the noise, then the noise average rises. Provision of footroom prevents noise modulation.

So, the first reason for footroom is archaic, but the other four remain important.

Concerning headroom, reference black was originally established at a level somewhat below peak white to accommodate analog misadjustment. As digitization prevailed, that reason vanished. But reference white stands firm for digital video, and with a pure 2.4-power EOCF, peak white lies at relative luminance of (955/876)2.4, or about 1.23. A studio reference display should follow the 2.4-curve all the way to peak white. The consumer electronic industry is always keen to maximize average brightness, and that goal is routinely aided by their flattening the EOCF at the high end. The working assumption in program creation is that CE equipment will reasonably reliably display levels up to reference white, then cheat.

In consumer terminology, the footroom region is often called blacker- than-black (BTB), and the headroom region, whiter-than-white (WTW).

In digital cinema distribution according to DCI/SMPTE standards (such as SMPTE ST 431), encoding is standardized without reference to prohibited code. However, standard HD-SDI interfaces are typically used and the codes 0–3 and 1020– 1023 are prohibited. Consequently, a 10-bit interface clips to the range 4–1019 and the projector never sees codes outside that range. (In the 12-bit variants of HD-SDI, codes 0–16 and 4080–4095 are prohibited, and not seen by the projector.) The clipping is inconsequential in practice.

In interfaces having k bits (8 ≤ k), reference black and white levels are multiplied by 2k-8. For example, when R’G’B’ or Y’ components occupy 10 bits, the

0 to 1 range is scaled by 219·4 (i.e., to 0 to 876); the interface offset is +64 instead of +16.

The terms superblack and superwhite are used in the consumer arena to refer to excursions into the footroom and headroom regions respectively. In some consumer gear (e.g., PS3), Superwhite is an option that enables an interface to carry footroom and headroom codes; when not set, interface codes are clipped, and the quality of studio-standard material is liable to suffer.

I use the term studio-swing for the levels used in studio equipment; I use the term full-swing for coding that places the reference levels at the interface extremes, leaving no room for footroom or headroom. Historically, desktop graphics coding had full-swing (between 0 and 255). A realtime HD-SDI interface prohibits codes 0 and 255, or in a 10-bit system, codes 0–3 and codes 1020–1023. If full-swing coding is to be used across an HD-SDI interface, then codes 0–3 and codes 1020–1023 must be avoided.

In digital cinema acquisition and postproduction, it is common to preserve the bottom 64 codes for footroom, but use all of the headroom region up to

code 1019. Some digital cinema systems call this “extended” range; however, to my mind using the word “extended” runs the risk of suggesting that using that range is a good idea. (Who wouldn’t want “extended?”) In my view, the option should be labelled “extreme.”

Interface offset

In hardware, an 8-bit interface is considered to convey values 0 through 255. In serial digital video interfaces (SDI, or its HD variant, HD-SDI), the all-zeros and allones 8-bit codes are prohibited from data. At an 8-bit digital video interface, an offset of +16 is added to the code values shown in boldface in Figure 4.4: Reference black is placed at interface code 16, and white at 235. I consider the offset to be added or removed at the interface, because a signed representation is necessary for many processing operations (such as changing gain). However, hardware designers often consider 8-bit digital video to have black at code 16 and white at 235.