Pareidolia, but underwater: What is under the green paint?

[Jorge_Stolfi]

it helps if the result can be independently reproduced via a simple (ideally linear, or maybe polynomial) combination of channels.

That will not be the case, because Bayesian classification with Gaussian distributions is inherently non-linear, and usually extremely so.

For instance, imagine that you have only two Gaussian classes (plus "OTHER"), where class A has a very broad spherical  distribution centered at middle gray (0.5,0.5,0.5) and class B has a much narrower one centered at slightly darker gray (0.4,0.4,0.4).  Bayesian classification will assign class A to colors inside the A sphere, except within a small region around the darker gray, where it will say B.   A linear classifier will be unable to delimit even the A sphere, much less the B hole inside it.  

That is why linear vector classifiers are usually applied to non-linear functions of the inputs, the (improperly) so called "kernels".  Which requires the user to come up with suitable kernels.  If one tries to use as kernels all polynomials on the input coordinates up to degree (say) 4, one gets so many kernels that the classification will probably be garbage. 

That is also a danger if one uses "magical" non-linear classifiers with zillions of internal parameters, like neural networks...

All the best, --stolfi