Luma and colour difference components

Imaging systems are commonly optimized for other aspects of human perception; for example, the JPEG and MPEG compression systems exploit the spatial frequency characteristics of vision. Such optimizations can also be referred to as perceptual coding.

It is a mistake to place a linear segment at the bottom of the sRGB EOCF. (A linear segment is called for in the OECF defined in sRGB, but that’s a different matter.)

Virtually all commercial imaging systems use perceptual coding, whereby pixel values are disposed along

a scale that approximates the capability of human vision to distinguish greyscale shades. In colour science, capital letter symbols R, G, and B are used to denote tristimulus values that are proportional to light power in three wavelength bands. Tristimulus values are not perceptually uniform. It is explicit or implicit in nearly all commercial digital imaging systems that pixel component values are coded as the desired display RGB tristimuli raised to a power between about 1/2.2 (that is, about 0.45) and 1/2.6 (that is, about 0.38). Pixel values so constructed are denoted with primes: R’G’B’ (though the primes are often omitted, causing confusion).

In order for image data to be exchanged and interpreted reasonably faithfully, digital image standards define pixel values for reference black and reference white. Digital image standards typically specify a target luminance for reference white. Most digital image standards offer no specific reflectance or relative luminance for reference black; it is implicit that the display system will make reference black as dark as possible.

In computing, 8-bit digital image data ranges from reference black at code 0 to reference white at code 255. The sRGB standard calls for an exponent (“gamma”) of 2.2 at the display. Reference white is

supposed to display luminance of 80 cd·m-2, though in practice values up to about 320 cd·m-2 are common.

In consumer digital video, image data is coded in 8-bit components ranging from reference black at code 16 to reference white at code 235. (In the studio, 10-bit coding is common.) Studio standards call for an exponent (“gamma”) of about 2.4 at the display. Common practice places reference white at luminance of about 100 cd·m-2, with a dark viewing environment (about 1 lx) and a dark surround (1%). Faithful display is obtained at the consumers’ premises when these conventions are followed. It is common for consumer displays to be brighter than 100 cd·m-2; consumers’ viewing environments are often fairly bright (often around 100 lx) and the surround is often dim (5%). In cases where the consumer display and viewing conditions differ from those at the studio, preserving picture appearance requires display adjustment.

In some circles, dot gain is now called tone value increase (TVI). The increase makes things darker: Printers are more concerned with ink than with light.

My definition excludes 480p, 540p, and 576p as HD, but admits 720p. (My threshold of image rows is the geometric mean of 540 and 720.)

The DVI computer display interface is defined to carry R’G’B’ values having reference range 0 through 255. The HDMI and DisplayPort interfaces also accommodate that coding, but in addition they accommodate R’G’B’ values having reference range 16 through 235, they accommodate bit depths deeper than 8 bits, and they accommodate Y’CBCR coding. The SDI and HD-SDI interfaces common in studio video accommodate 10-bit R’G’B’ or Y’CBCR values having reference range 64 through 940 (that is, 16·4 and 219·4).

Image data for offset printing is typically represented as 8-bit code values for the relative amounts of cyan, magenta, yellow, and black (CMYK) inks required at

a pixel location, where [0, 0, 0, 0] defines no ink (that is, producing the colour of the printing substrate, typically white) and [0, 0, 0, 255] defines black. Perceptual uniformity is imposed by what a printer calls dot gain. User interfaces typically present the 0 to 255 range as 0 to 100 – that is, the interface expresses percentage.

SD and HD

Until about 1995, the term television referred to either 480i (historically denoted 525/59.94, or “NTSC”) or 576i (625/50, or “PAL”). The emergence of widescreen television, high-definition television (HDTV), and other new systems introduced ambiguity into the unqualified term television. What we used to call “television” is now standard-definition television (SDTV). Video technology was and is widely used to distribute entertainment programming – historically, “television,” TV – but applications are now so diverse that I omit the letters TV and refer simply to SD and HD.

Surprisingly, there are no broadly agreed definitions of SD and HD. I classify as SD any video system having a frame rate of 23.976 Hz or more whose digital image has fewer than 1152 image columns or fewer than 648 image rows – that is, fewer than about 3⁄4 million total pixels. I classify as HD any video system with a native aspect ratio of 16:9 and frame rate of 23.976 Hz or more, whose digital image has 1152 or more image columns and 648 or more image rows – that is, a digital image comprising 729 Kpixels (about 3⁄4-million pixels) or more.

The term square refers to the sample arrangement: Square does not mean that image information is uniformly distributed throughout a square area associated with each pixel! Some 1080i HD compression systems resample to 4/3 or 3/2 pixel aspect ratio.

If you use the term pitch, it isn’t clear whether you refer to the dimension of an element or to the number of elements per unit distance. I prefer the term density.

New York Times (1995, Sep. 11), “Patents; The debate over highdefinition TV formats is resolved with a system that provides both”

Concerning the origin of the 16:9 aspect ratio, see page 5.

A 16:9 image having area of 1 m2 has dimensions 4/3 m by 3/4 m (about 1.33 m by 0.75 m) and a diagonal of about 1.53 m (60 in). Today, this size represents the largest practical consumer direct-view display.

A 16:9 image having width of 1 m has height of 0.5625 m, and area of 0.5625 m2. Its diagonal is about 1.15 m, or 45 inches; this is approximately the median size of HD receivers purchased today. At 1920× 1080,

pixel pitch is 1/1920 m, or about 520 µm; each RGB “subpixel” has dimensions roughly 174 µm by 520 µm.

Square sampling

In modern digital imaging, including computing, digital photography, graphics arts, and HD, samples (pixels) are ordinarily equally spaced vertically and horizontally – they have equal horizontal and vertical sample density. These systems have square sampling (“square pixels”); they have sample aspect ratio (SAR) of unity. With square sampling, the count of image columns is simply the aspect ratio times the count of image rows.

Legacy imaging and video systems including digital SD systems had unequal horizontal and vertical sample pitch (nonsquare sampling). That situation was sometimes misleadingly referred to as “rectangular sampling,” but a square is also a rectangle! A heated debate in the early 1990s led to the adoption of square sampling for HD. In 1995 the New York Times wrote,

HDTV signals can be sent in a variety of formats that rely not only on progressive or interlaced signals, but on features like square versus round pixels …

A technical person finds humour in that statement; surprisingly, though – and unintentionally – it contains a technical grain of truth: In sampled continuous-tone imagery, the image information associated with each sample is spread out over a neighbourhood which, ideally, has circular symmetry.

Comparison of aspect ratios

In the mid-1990s, when HD was undergoing standardization, SD and HD were compared using various measures, depicted in Figure 1.9 at the top of the facing page, based upon the difference in aspect ratio between 4:3 and 16:9. Comparisons were made of equal height,