The term pixel value is ambiguous because pixel values accessible to application software can be altered by the graphics subsystem on the way to the display – for example, they can be altered by the lookup table in a graphics adapter. DDL numbers are not necessarily those passed to the display panel column drivers and “glass”: Modern display equipment ordinarily incorporates signal processing – often including lookup tables (LUTs) – to compensate for the native display panel response.

average pixel level instead of pivoting at zero as is usual in video equipment and in displays. For other computer imaging applications, there are no standards; it’s often difficult or impossible to tell exactly how a particular application implements these controls.

Digital driving levels

The term digital driving level (DDL) refers to a pixel component data value (typically produced by a PC graphics subsystem, or by a consumer electronics signal source such as a Blu-ray player) that crosses an interface (typically DVI, HDMI, or DisplayPort) and drives a display device. A DDL is interpreted as an integer value from 0 to 2k - 1 (where k is the bit depth at the interface, typically 8, but potentially 10 or 12).

Computer interfaces such as DVI carry 8-bit DDLs where DDL 0 is reference black and DDL 255 is reference white.

Video interface standards such as HD-SDI in the studio and HDMI in consumer equipment allow footroom below reference black and headroom above reference white. HD-SDI is standardized with 10-bit values; interface code 64 corresponds to reference black and interface code 940 corresponds to reference white. In consumer use, eight-bit HDMI is commonly used; interface code 16 corresponds to reference black and interface code 235 corresponds to reference white.

To simplify the rest of the discussion I’ll refer to pixel values in terms of normalized DDLs (NDDLs) where reference black at the interface corresponds to NDDL 0 and reference white at the interface corresponds to NDDL 1. Pixel values in video are permitted to have modest excursions outside the reference 0 to 1 range, -15/219 to 235/219 (about -0.07 to +1.09). The NDDL range 0 to 1 corresponds to what an HD engineer might call IRE levels 0 through 100.

Relationship between signal and lightness

The sRGB standard requires an electro-optical conversion function (EOCF) comprising a 2.2-power function.

Documentation associated with sRGB makes clear that the fundamental EOCF – the mapping from pixel value to display luminance – is supposed to be a pure 2.2-power function, followed by the addition of

Poynton, Charles (2009), “Perceptual uniformity in digital imaging,” in Proc. Gjøvik Color Imaging Symposium (GCIS 2009): 102–109.

a veiling glare term. The sRGB standard also documents an OECF that is intended to describe a mapping from display luminance to pixel value, suitable to simulate a camera where the inverse power function’s infinite slope at black would be a problem. The OECF has a linear segment near black, and has an power function segment with an exponent of 1/2.4. The OECF should not be inverted for use as an EOCF; the linear slope near black is not appropriate for an EOCF.

The sRGB 2.2-power function, the de facto 2.4-power function of today’s studio reference displays, and the 2.6-power function of digital cinema all almost perfectly invert L*, as depicted in Figure 5.1. The 2.4-curve, which typifies video and HD practice, has a highly linear relationship with L* for NDDL 0.2 and above (that is, for 8-bit interface codes above 59). An NDDL of 0.2 yields an L* value of 16. The line from [0.2, 16] through reference white has slope of 105; extending that line back towards the x-axis yields an x-intercept of 0.0475, and back further, a y-intercept of almost exactly -5.

Algorithm

The effect of conventional contrast and brightness controls in video is approximated by the following

Figure 5.2 Effect of gain control (“contrast”) for nominal offset (“brightness”) setting (b = 0). Gain values 0.8, 1.0, and 1.25 are shown; these are values of m in Equation 5.1. The y-axis is tristimulus value, a linear-light quantity that is not directly perceptually meaningful.

Figure 5.3 Effect of offset control (“brightness”) for nominal gain (“contrast”) setting (m = 1). Offset values -0.2, 1.0, and +0.2 are shown; these are values of b in

Equation 5.1.

Pixel value, V

Pixel value, V

Figure 5.4 Effect of gain control (“contrast”) on lightness, for nominal bias setting (b = 0), with gain control viewed as setting the display function. Gain values correspond to values of m in

Equation 5.1.

Pixel value, normalized DDL

Figure 5.5 Effect of offset control (“brightness”) for nominal gain setting

(m = 1), with bias control viewed as setting the display function. Bias values correspond to values of b in Equation 5.1.

Pixel value, normalized DDL