Advanced 12 min 4 of 5

The camera fights back

Gloom is undone by the auto-exposure and paid for in noise; the veil is what the meter is trying to ignore.

What this repairs

Simulating fog by compositing a grey veil onto a sunny image — producing sunny shadows in foggy air, and missing that the real cost of gloom is noise, not darkness.

Assumes

Exposure is a decision, not a measurement · The Camera Pipeline
Photons, electrons, and why σ is not a constant · The Camera Pipeline
The Koschmieder model, honestly

A foggy day is not a sunny day with a veil in front of it. The same water that scatters light into your line of sight is also between the sun and the scene, so the illumination is lower, flatter and bluer before any of it reaches a surface. Composite a veil onto a sunny frame and you get a picture with hard shadows in thick fog — which is the tell that no human can name and everyone can see.

The pipeline models this as a radiance scale applied to the scene before the fog render:

$\text{scale} = \max\!\left(2^{-\text{EV}},\, s_{\min}\right), \qquad \text{EV} = \text{EV}_{\text{global}} + \text{EV}_{\text{near}}\,e^{-d/\lambda} + \text{EV}_{\text{fog}}\big(1 - e^{-\beta d}\big).$

Three terms, because gloom is not uniform: a global level, a near-field term that decays with distance, and a term proportional to the local fog opacity, so the parts of the scene that are deepest in the fog are also the parts that are receiving the least light.

Pitfall The two EV conventions point in opposite directions

This is the sign error waiting for every reader, and it is not a bug — it is two stages of the same pipeline using the same unit for opposite intents.

Scene illumination uses EV to darken: the scale is $2^{-\text{EV}}$ , so a positive value means a gloomier scene. It is describing light being taken away from the world.
Exposure compensation, later in the same pipeline and inside the sensor, uses EV to brighten: the gain is multiplied by $2^{+\text{EV}}$ , so a positive value means a brighter picture. It is describing a photographer's thumb on the meter.

Same unit, one pipeline, opposite directions. An inverted sign in either place produces an image that looks entirely plausible and is wrong, so read the sign off the stage, never off the name — and when both appear on one screen, label the controls by their effect ("gloom, in stops" and "exposure compensation, in stops") rather than by their config key.

What two stops of gloom actually cost

$J \rightarrow \eta\,J, \qquad \eta = 2^{-\text{EV}} = 0.25 \quad (\text{EV} = 2)$

Two stops of gloom: the scene radiance entering the fog render is quartered, before anything about the camera is involved.
$g_{\text{auto}} = \frac{L_{\text{target}}}{L_{\text{meter}}} \approx \frac{1}{\eta} = 4$

The meter sees a quarter of the luminance and asks for four times the gain, because the metering rule targets a fixed level and knows nothing about why the level fell.
$\text{ISO} = \text{ISO}_0\left(\frac{g_{\text{auto}}}{a}\right)^{k} = \text{ISO}_0\left(\frac{4}{1.2}\right)^{0.85} = 2.78\,\text{ISO}_0$

The gain pressure resolves an ISO nearly three times the configured one — this is the step where a lighting change becomes a sensor change.
$N_e = \frac{\text{full well}}{\text{ISO}/\text{ISO}_0} \;\Longrightarrow\; N_e \rightarrow \frac{N_e}{2.78}$

And ISO is a divisor on the well capacity, so the same normalised signal is now measured against 2.78 times fewer electrons.
$\sigma_{\text{shot}} \propto \sqrt{\frac{s}{N_e}} \rightarrow \sqrt{2.78}\,\sigma_{\text{shot}} = 1.67\,\sigma_{\text{shot}}, \qquad \sigma_{\text{read}} \rightarrow 2.78\,\sigma_{\text{read}}$

The result at the end of the loop: the delivered image is at the same brightness it started, with 1.7 times the shot noise and 2.8 times the read noise. Gloom did not make the picture darker; it made it noisier.

Insight The meter is deliberately ignoring the fog

Left to itself, a meter looking at a foggy scene reads the veil — the brightest, largest and least informative thing in the frame — and under-exposes the road into the shadows. The fog-aware metering mode exists to stop that: it down-weights pixels the sky mask marks, pixels whose fog opacity is high, and pixels whose depth is large, so the reading comes mostly from the near road surface.

That is the correct engineering decision and it has a consequence worth stating plainly. The delivered image of a foggy scene is not systematically darker than a clear one. The camera has spent its dynamic range keeping the near field at the target and paid for it in ISO. Any heuristic that expects fog to look dark — a brightness threshold, a mean-luminance feature, an exposure-based domain gap check — is looking for something the camera removed.

The loop does not continue forever, and the places it stops are as informative as the loop itself.

The gain is clamped, and the ceiling is a multiplier rather than an offset, so the compensation available is $\log_2 g_{\max}$ stops above unity gain — $0.85$ of a stop at the shipped ceiling of $1.8\times$ , $1.4$ stops at the $2.6\times$ the geometry module defaults to. Past that the requested gain is unavailable and the picture does start to get darker, so the response has two regimes: noisier at constant brightness first, then darker and noisier. The ISO is clamped too, at a ceiling far below what a real camera would reach, which quietly limits how bad the simulated noise is allowed to get. And the radiance scale itself has a floor, so no amount of gloom EV renders a black frame.

Three clamps, three places where the augmentation's parameter stops mapping linearly onto what the image does. Sweeping gloom EV past any of them produces a robustness curve with a knee that belongs to the configuration and not to the weather.

Check yourself

You add two stops of gloom to a fog scenario and the delivered images are barely darker than before. Is the augmentation broken?

Show answer

No — that is the pipeline behaving exactly as a camera would, and it is the point of the concept. The auto-exposure absorbed the illumination change into gain, and the gain pressure pushed the ISO up, so what actually changed is the noise: about $1.7\times$ the shot noise at the same brightness, plus a proportionally larger read-noise floor. Verify it by looking at the resolved gain and ISO rather than at the mean level, and if the noise did not move either, check whether the gain hit its clamp — in which case the images should be darker and something else is wrong.