What is the space of attenuation coefficients in underwater computer vision?

Underwater image reconstruction methods require the knowledge of wideband attenuation coefficients per color channel. Current estimation methods for these coefficients require specialized hardware or multiple images, and none of them leverage the multitude of existing ocean optical measurements as priors. Here, we aim to constrain the set of physically-feasible wideband attenuation coefficients in the ocean by utilizing water attenuation measured worldwide by oceanographers. We calculate the space of valid wideband effective attenuation coefficients in the 3D RGB domain and find that a bound manifold in 3-space sufficiently represents the variation from the clearest to murkiest waters. We validate our model using in situ experiments in two different optical water bodies, the Red Sea and the Mediterranean. Moreover, we show that contradictory to the common image formation model, the coefficients depend on the imaging range and object reflectance, and quantify the errors resulting from ignoring these dependencies.