Fog, Light and Exposure
Fog is three coupled changes — a veil, a different light, and a camera that fights back — and simulating only the first is why augmented fog looks wrong.
Fog is the cheapest hard weather to simulate and the easiest to simulate wrongly. The equation is one line, it composites in a few milliseconds, and the result is almost always a grey wash that a human immediately reads as fake and a network immediately reads as a texture.
What is missing is never the equation. It is the three things around it: that and the airlight are physical quantities pinned to a definition, that the same weather also changes the illumination of the scene, and that a camera responds to both — with a gain, an ISO and a metering rule that were chosen without asking you. This topic goes through the render, then the light, then the camera, and ends at the question all of it exists to answer: at what distance does a machine actually lose the object?
- 01 The Koschmieder model, honestly Core 1 interactive 10′ Four symbols, three of them physical: what β, d and the airlight are actually constrained to be. Repairs Reading the fog equation as "a white overlay whose opacity grows with distance", so β, the airlight and which depth goes into the transmission are all treated as free style parameters.
- 02 Airlight is an estimate Core 2 interactive 11′ A is scattered light with a path length behind it, an estimator in front of it, and a dependence on β. Repairs Treating airlight as "white", or as a constant that has nothing to do with β, the sky, or where the camera happens to be pointing.
- 03 Fog is not one number Core 1 interactive 10′ Two fields with the same mean β are not the same fog, and the mean does not determine the mean transmission. Repairs Believing fog density is a scalar, so a model trained on uniform fog meets a fog bank and every metric was computed against a homogeneity assumption the world does not have.
- 04 The camera fights back Advanced 1 interactive 12′ Gloom is undone by the auto-exposure and paid for in noise; the veil is what the meter is trying to ignore. 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.
- 05 When does a machine lose the object? Advanced 1 interactive 12′ Meteorological visibility is one threshold. Your quantiser and your sensor impose two more, and they are shorter. Repairs Reporting "trained with fog augmentation" as one knob, when β, airlight, illumination and camera response are four independent axes — and the model is only robust to the ones that were varied.