HDR imaging and tone mapping

A sunlit landscape with deep shade, a backlit portrait by a window and a night street with bright signs all contain a wider range of brightness than a single exposure can record or a screen can display. High dynamic range (HDR) imaging solves the first problem by combining information from several exposures, or from many underexposed frames, into one image with far more tonal range. Tone mapping solves the second by compressing that range into something a display or print can show while keeping the scene looking natural, or deliberately stylized. This lesson measures dynamic range in stops, merges bracketed exposures into a radiance map with weighted averaging, applies the Reinhard tone curve, and explains local tone mapping, exposure fusion and the new generation of HDR displays and gain-map files that let a photo show bright highlights on capable screens.

Dynamic range in stops

Dynamic range is the ratio between the brightest and darkest values that can be recorded or shown with acceptable quality. Photographers measure it in stops, where each stop is a doubling:

A sunlit scene with deep shadows can exceed 14 to 17 stops. A single phone frame might capture around 10 to 12 usable stops, a large-sensor camera 12 to 15 at base ISO, a standard display about 8 to 10 stops of contrast in practice, and a matte print about 6 to 7 stops. These figures are approximate, depend on how "acceptable" noise is defined, and vary between devices. The mismatch at each stage, scene to sensor and sensor to display, is the reason for HDR capture and tone mapping.

Merging brackets into a radiance map

The classic approach, developed by Paul Debevec and Jitendra Malik and by others in the 1990s, takes several exposures at different shutter speeds. After converting each to linear values (raw data is already linear; JPEGs must be linearized by inverting the camera response curve), each pixel value is divided by its exposure time to estimate scene radiance. The estimates from different frames are combined with weights that favor well-exposed values and ignore clipped or very dark ones:

Here \( z_k \) is the linear pixel value in frame \( k \), \( t_k \) its exposure time and \( w \) a weighting function that is zero for clipped values and small near black. A common choice is a "hat" function peaking at mid-tones. Better weightings use the noise model: since a frame with a longer exposure has a higher SNR for the same radiance, it should get more weight unless it is clipped. The result is a floating-point radiance map with far more range than any one frame.

import numpy as np
rng = np.random.default_rng(420)
E = np.logspace(-3, 1.2, 2000)                 # scene radiance spanning about 14 stops
times = [1 / 1000, 1 / 125, 1 / 15]            # three brackets, 3 stops apart
full = 1.0                                      # sensor saturation
def capture(t):
    signal = E * t * 600                        # arbitrary sensitivity
    noisy = signal + rng.normal(0, np.sqrt(0.002 * signal + 1e-5))
    return np.clip(noisy, 0, full)
frames = [capture(t) for t in times]
num = np.zeros_like(E); den = np.zeros_like(E)
for z, t in zip(frames, times):
    w = np.where(z >= 0.98 * full, 0.0, z * t)  # zero weight if clipped; prefer long exposures (higher SNR)
    num += w * z / (t * 600); den += w
merged = num / np.maximum(den, 1e-12)
for z, t in zip(frames, times):
    ok = (z > 0.01) & (z < 0.98)
    print(f"1/{round(1 / t):4d} s: usable for {ok.mean() * 100:4.1f} % of radiances")
rel = np.abs(merged - E) / E
print(f"merged map: median relative error {np.median(rel) * 100:.1f} %, usable range {np.log2(E.max() / E.min()):.1f} stops")

1/1000 s: usable for 48.1 % of radiances
1/ 125 s: usable for 47.5 % of radiances
1/  15 s: usable for 33.1 % of radiances
merged map: median relative error 7.8 %, usable range 14.0 stops

Each bracket alone is usable for only part of the radiance range, but the merged map covers all of it, with a modest median error that is largest in the deepest shadows, where even the longest frame collects few photons. The long exposure handles shadows, the short exposure handles highlights, and the weights blend smoothly between them.

Ghosts, alignment and burst HDR

Brackets have a weakness: frames at different exposures look different, which makes alignment harder, and moving subjects appear at different positions in frames that dominate different tones, causing ghosts. Phones therefore increasingly use the burst approach from lesson 3: many identical underexposed frames, aligned and robustly merged, with the shadows lifted in tone mapping. The merged result's improved SNR in the shadows effectively extends dynamic range downward. Some pipelines add one or two longer frames to boost shadow quality, and some sensors capture multiple exposures in a single readout using dual conversion gain or staggered exposures, reducing the time gap between them and therefore ghosting. On dedicated cameras, handheld bracketing with in-camera or software merging remains common, and good HDR software includes deghosting that picks one frame for areas with motion.

Global tone mapping

A radiance map cannot be displayed directly: its values span thousands to one, while a display spans perhaps a few hundred to one in practice. Tone mapping compresses the range. A global operator applies the same curve to every pixel based only on its value. Erik Reinhard and colleagues proposed a widely used simple operator in 2002. After scaling the image so that its log-average luminance maps to a chosen middle gray, each luminance \( L \) is compressed by:

Dark values (\( L \ll 1 \)) pass almost unchanged, while bright values approach 1 asymptotically, so highlights are compressed but never clip. An extended version adds a white point \( L_w \), the smallest luminance that maps to pure white:

Global curves are fast and preserve the overall order of brightness, but compressing a large range globally reduces local contrast, making images look flat. Filmic curves used in games and some raw converters add an S-shaped toe and shoulder to imitate film's response.

import numpy as np
L = 0.18 * 2.0 ** np.arange(-6, 7, 2)              # scene luminances from -6 to +6 stops around mid-tone
key = 0.18
Ls = L / 0.18 * key                                 # already keyed to the mid-tone
simple = Ls / (1 + Ls)
Lw = Ls.max()
ext = Ls * (1 + Ls / Lw ** 2) / (1 + Ls)
for l, a, b in zip(L, simple, ext):
    print(f"scene {l:8.4f} -> simple {a:.3f}  with white point {b:.3f}")
print(f"contrast ratio in: {L.max() / L.min():.0f}:1, out (white point): {ext.max() / ext.min():.0f}:1")

scene   0.0028 -> simple 0.003  with white point 0.003
scene   0.0112 -> simple 0.011  with white point 0.011
scene   0.0450 -> simple 0.043  with white point 0.043
scene   0.1800 -> simple 0.153  with white point 0.153
scene   0.7200 -> simple 0.419  with white point 0.421
scene   2.8800 -> simple 0.742  with white point 0.758
scene  11.5200 -> simple 0.920  with white point 1.000
contrast ratio in: 4096:1, out (white point): 357:1

The output shows the compression: a 4,096:1 scene range is squeezed into a few hundred to one, with the brightest value reaching exactly 1.0 when a white point is used. Shadows keep roughly their relative steps, while each stop of highlight occupies less and less of the output range.

Local tone mapping and exposure fusion

Local operators let the curve vary across the image, so a dark interior and a bright window can each keep good contrast. The simplest idea is to separate an image into a smooth base layer containing large-scale brightness and a detail layer containing texture, compress only the base, and add the detail back. Using an ordinary blur to find the base creates halos, bright or dark fringes along strong edges, because the blur crosses the edge. Edge-preserving filters such as the bilateral filter, guided filter and local Laplacian filters avoid this. The over-processed "HDR look" of the late 2000s, with glowing halos and gray skies, came from aggressive local operators.

Exposure fusion, introduced by Tom Mertens, Jan Kautz and Frank Van Reeth in 2007, skips the radiance map altogether. It blends the differently exposed frames directly, weighting each pixel by contrast, saturation and well-exposedness, and blends them across a Laplacian pyramid so that transitions are smooth at every scale. The result looks natural and needs no tone curve. Many phone pipelines use ideas from exposure fusion: Google's HDR+ described synthesizing a short and a long "virtual exposure" from the merged burst and fusing them. Today, neural networks often predict local tone curves or adjustment grids from a low-resolution version of the image, an approach known from research on deep bilateral learning, then apply them at full resolution quickly.

Semantic tone mapping and the phone look

Modern phones adjust tone by content. Face detection keeps skin at a pleasing brightness; sky segmentation darkens and saturates skies; and different rules apply to foliage, food or text. This semantic processing is why many phone photos look bright and evenly lit, with shadows lifted and highlights held, sometimes described as flat or "HDR-ish". Critics argue that it removes the drama of light and shadow; manufacturers have responded with styles and more natural options. For professional work, choosing computational raw or a natural style and doing your own tone mapping keeps the creative decisions yours.

HDR display and gain maps

For most of digital photography's history, the final image was standard dynamic range (SDR): diffuse white was the brightest the display could show. HDR displays, now common on phones, laptops and televisions, can show highlights several times brighter than diffuse white. Video has HDR standards such as HDR10, HLG and Dolby Vision. For still photos, the industry converged on gain maps: a file stores a normal SDR image plus a secondary map recording how much brighter each region should be on an HDR display. Viewers that do not understand the gain map show the SDR image normally; capable viewers apply the map. The ISO 21496-1 standard for gain maps, published in 2025, aims to unify earlier formats such as Google's Ultra HDR JPEG and Apple's adaptive HDR approach, and Adobe and others support gain maps in editing and export (status at the time of writing; check software support). This changes tone mapping: rather than compressing everything into SDR, the pipeline can keep bright specular highlights and sunsets genuinely bright on screens that can show them.

For photographers delivering work, HDR output raises new questions: clients viewing on SDR screens see the base image; print cannot reproduce the headroom; and social platforms handle gain maps inconsistently. Proof both versions and keep the SDR rendition strong on its own.