[Udik]

> so you need to have a depth map to recover the true colors

Isn't the blue shift of a known color already a measure of the amount of water between the object and the camera- and therefore its distance? Knowing the true color of a fish, a seaweed or the sand isn't already enough to infer distances and color-correct?

[OskarS]

I've only skimmed the paper, but it's more complicated than that. There's both an light attenuation effect (the "blue shift" you're talking about), as well as a separate back-scatter effect, which use different coefficients based on depth. It seems to me that the hard part is figuring out a function to color correct based on both these factors for a large range of depths using a limited number of reference points (as well as getting an accurate depth map, of course).

[rocqua]

Not everything in the image is at the same distance from the camera as the color chart. You still need depth information for the other parts.

[Udik]

I'm sorry, but I don't get it. I mean, if what you want is an accurate color reconstruction, for scientific purpose, then yes, you probably need depth information. If what you want is simply to colorise an image inferring the correct colors from a mix of residual color, blue shift, and a general knowledge about the object itself (the color of a seaweed, a starfish, etc.) then you can probably do it pretty well from a single image. There are neural networks that can colorise a b&w picture with zero color data available(1), and in this case you just want to enhance existing colors, so it should be much easier. Of course you'll get a representation with no claim of accuracy, but it should be fine for many purposes.

(1) often with pretty bad results, but consider the variety of scenes and object above water compared to the average underwater scenario.

[Scaevolus]

Yes, but how do you know the true color of a fish, seaweed, or sand? That's the unknown part!

[Udik]

> how do you know the true color of a fish, seaweed, or sand

I am pretty sure that in most cases those colours are well known.

[afwaller]

I, personally, have picked up sand, shells, even seaweed from the ocean, and lifted it out of the water and looked at it with my eyes. I have released this technique to the world, patent free.