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18.10 HDR displays and display mapping⧉

Tone mapping once ended with one rendition prepared for a standard screen or a print. HDR displays changed the question. Their peak luminance ranges from a few hundred to several thousand candelas per square meter, the same photograph may be seen on a phone in sunlight and on a television in a dark room, and the rendering has to be finished on the display, by the display, from information the file carries. Tone mapping becomes display mapping: compressing fourteen stops into ten is a different problem from compressing them into six, and the perceptual compensations of Chapter 18.1, Tone mapping and perception shrink as the display approaches the scene. The formats that carry the information, from radiance maps to gain maps and the PQ and HLG transfer functions, are described in Chapter 17.7, Encoding HDR images; this chapter covers the displays and the mapping onto them.

18.10.1 What a display can actually show⧉

A rendered HDR image must pass through a file format, decoder, color-management system and display. A capable panel alone is insufficient if an intermediate step strips the metadata or converts the image to standard range.

Peak luminance depends on bright-area size, duration and power limits. Visible black depends on panel emission, leakage and reflected ambient light. Some reference values give a sense of scale. Standard-range video is mastered for a reference white of about 100 cd/m², and the sRGB reference display is 80 cd/m². ITU-R BT.2408 places the reference white of HDR content at 203 cd/m², leaving the range above it for highlights. PQ encodes luminances up to 10,000 cd/m²; mastering monitors commonly reach 1,000 cd/m² or more, and recent phones advertise peaks above 1,000 cd/m² for small bright areas. Those conditions matter as much as the nominal peak; two displays with the same advertised brightness can render the same image differently (Chapter 5.6, Preparing photographs for viewing).

fig-hdr-delivery-chain
Figure 18.10.1. Interactive. One photograph, four destinations, with the same radiance map behind all of them: a standard-range screen, a phone at two thousand nits in sunlight, a reference monitor in a dark room, and a print. Each shows what the viewer actually sees, with the peak luminance, the black level and the surround stated, and a slider for the ambient light that changes all four at once and changes them differently. A second view switches the encoding between the standard transfer function, PQ and HLG, plotting code value against luminance so the reader sees where each spends its precision, and shows the banding that appears when the wrong one is used at the wrong peak. Interactive: choose the destination and the ambient light, switch the transfer function, and toggle a gain-map decode against a plain tone-mapped image.

18.10.2 HDR displays and dual modulation⧉

A bright point on a dark background tests a display differently from a full white field. A local-dimming LCD combines a spatially varying backlight with a finer panel that attenuates its light. In a simple model,

$$L(x)\approx B(x)T(x)+L_{\mathrm{refl}}(x),$$

where $B$ is the backlight reaching the pixel, $T$ the panel transmittance, and $L_{\mathrm{refl}}$ reflected ambient light. Two modulation stages can increase usable contrast Seetzen et al. 2004 (HDR display). Their nominal contrast ratios do not guarantee the same multiplication for arbitrary images.

The backlight spreads across neighboring pixels. A small highlight can therefore illuminate a broad region, and finite panel extinction leaves a halo. The controller balances highlight strength, leakage and shadow detail. Emissive pixels avoid this particular backlight mismatch but retain optical scatter, reflection and power limits. Adjacent bright and dark content, seen under the intended viewing conditions, is the real test; a specification from a dark room does not predict a sunlit screen.

Figure 18.10.2 simulates the halo.

fig-local-dimming-halo
Figure 18.10.2. Local dimming, simulated: a 1,000 cd/m² highlight on black. The backlight zones are lit to their brightest pixel and the LEDs' light spreads into a smooth backlight $B(x)$; the panel's transmittance $T(x)$ can only close to 1/1000. Their product reproduces the highlight, but around it the backlight leaks through the closed panel, a halo of about 0.7 cd/m² fifteen pixels away. An emissive OLED display has no halo; its black is set by the room's light reflected from the screen, 0.05 cd/m² here. Images on a log scale; the profile follows the dotted line through the highlight.

18.10.3 Display mapping: rendering for the display at hand⧉

HDR video is mastered on a reference display, often with a peak of 1,000 or 4,000 cd/m², and encoded with the PQ transfer function, whose code values stand for absolute luminances (Chapter 17.7, Encoding HDR images). A consumer display with a lower peak cannot show the brightest codes and must map them into its own range. Clipping them would flatten every highlight above the display's peak; scaling everything down would darken the whole picture. The ITU's report BT.2390 describes a reference electro-optical transfer function, the EETF, that does what a tone curve does at the top of the range: below a knee it leaves the signal unchanged, and above it a Hermite spline rolls the remaining range off smoothly to the display's peak, all in the PQ domain, so the compression is roughly uniform in perceived steps; a similar adjustment lifts the bottom of the range for a display whose black is not zero (ITU-R BT.2390).

To place its knee, the display needs to know what the content contains. Static metadata, carried once per program, describes the mastering display, its primaries, white point and luminance range (SMPTE ST 2086), and the content's maximum and maximum frame-average light levels, MaxCLL and MaxFALL. HDR10 uses PQ with static metadata only, so one curve serves a whole film, its darkest scene and its brightest. Dynamic metadata, in Dolby Vision and in HDR10+ (SMPTE ST 2094), carries a tone-mapping curve or its parameters per scene or per frame, chosen when the content was graded, so the display can compress a bright scene and leave a dark one untouched. Hybrid log-gamma takes the other route: it carries no metadata, and the display applies a system gamma that depends on its own peak, the Stevens compensation written into BT.2100 (Chapter 18.1, Tone mapping and perception).

Figure 18.10.3 plots the EETF and HLG's alternative.

fig-eetf-curves
Figure 18.10.3. Mapping HDR content onto a dimmer display. Left and center, the BT.2390 reference EETF for content mastered at 4,000 cd/m², onto displays of 600, 1,000 and 2,000 cd/m² peak, in PQ code values and in luminance on log axes. Each curve follows the identity up to its knee, at 229, 499 and 1,417 cd/m², then rolls off along a Hermite spline to land exactly on the display's peak. Right, HLG's system gamma $1.2 + 0.42 \log_{10}(L_W/1000)$ against the display peak $L_W$: without metadata, the display adapts its own gamma instead.

18.10.4 Gain maps on displays of different headroom⧉

For photographs, the gain map plays the role of dynamic metadata, per pixel rather than per scene. The file carries a standard-range rendition and a map of the gains that turn it into an HDR rendition, together with the range of display headroom over which the full gain applies (Chapter 17.7, Encoding HDR images). The display computes its current headroom, the ratio of its peak to the luminance it uses for standard white, which changes with its brightness setting and the room, and applies a fraction of the gain. In Adobe's specification, the weight is the position of the display's headroom between the file's minimum and maximum capacity on a log scale,

$$w=\operatorname{clamp}\!\left(\frac{\log_2 H_\text{display}-\log_2 H_{\min}}{\log_2 H_{\max}-\log_2 H_{\min}},\,0,\,1\right),$$

so a standard display shows the base rendition (Chapter 17.7, Encoding HDR images shows the renditions at several weights), a display with the full headroom shows the HDR rendition, and displays in between show an interpolation, in log space, between the two (Adobe gain-map specification). The photographer's choices are preserved at both ends, since both renditions were made deliberately, and the display does only the interpolation, which is the division of labor of the whole part: the look belongs to the author, the adaptation to the display.

18.10.5 Inverse tone mapping⧉

The reverse problem is growing. Most existing photographs and video are standard range, and an HDR display shows them either as they are, wasting its range, or expanded. Inverse tone mapping expands standard-range content to use the display's headroom: it has to decide which regions were highlights clipped or compressed by the original rendering, expand them toward their likely brightness, and leave skin and midtones where they were. Simple methods apply an expansive curve to the highlights; the local Laplacian filter with an edge slope above one expands large-scale contrast while keeping detail (Chapter 10.4, Local Laplacian filters); learned methods predict the missing highlight content from examples (Chapter 17.5, Single-shot range and inverse tone mapping). None can recover what clipping destroyed; they can only make a plausible guess, which is why the growth area is also a place for careful evaluation.