If I understand things correctly it's not entirely different to white balancing either, just that the difference between white balancing a monitor or camera is that you don't really have to correct for the scattering of light through air because it's negligible at the distances you're likely to work with. The trick here – again, if I understand correctly – is that this method also finds the light scattering/absorption characteristics and corrects for those as well. It might seem obvious, but I think it's more involving than it seems, because light scatters differently in different environments and I think – again, I might be wrong, this is just my understanding – this method accounts for that by using multiple images at different distances to gather the parameters to find the scattering and absorption characteristics. This is what makes it physically accurate and not just "make these colors mostly look good" which is really quite cool and useful!
If I remember correctly, the percentage of light that passes through a column of water exponentially decays with distance, like stacking a bunch of fixed-percentage optical filters on top of each other. They’re using parallax shift between multiple images to generate a depth map, so they have a measure of the amount of water obscuring each pixel.
I’m not sure how they’re finding the optical properties of the water; there’s something about using the darkest pixels in the image for calibration that I didn’t quite follow.
