Hoping for someone to explain some Pixelmath

Looking for some pixel math help. Mostly to just understand what I’m doing. I see what it does, and I understand the process as a whole, but just don’t know what each expression is doing. For reference I’m getting these from this website: https://www.nightphotons.com/guides/advanced-narrowband-combination/ specifically the method 1. I’ve had success doing this, but I would really like to understand more about what the pixelmath is doing because I’m pretty sure it’s not just magic.

The first expression: $T[0] - ($T[1] - med( $T[1]))

This is their last step in continuum subtraction. $T is target image I think? other than that I’m not sure.

Second is when adding the data, the expression is: $T * ~x + x * mtf(~m, (mtf(m, $T) + mtf(m, NB)))

In the above, x is the color channel, so R, G, or B. and then in the symbols part of Pixelmath it has: R = 1.0, G = 0.0, B = 0.05, m = 0.999,

What I gather from that is the number value after the R, G, or B is a percentage (I think), but what does the m value do?

You can get a pretty good idea of what does what by looking into PixelMath contextual definitions.

$T is the target image, med is a function that returns the median value of $T. So the first string returns the first image minus the difference of the second once its median value has been subtracted. (EDIT: by second is meant the second channel [G] in a RGB, with the first being the R).

As for the second if you are asking what mtf(m,x) is and does, it is the Midtones Transfer Function and the m is its strength parameter (from 0 to 1) and x is the image operand. The mtf can be thought as a basic non-linear stretching as obtained by using auto-stretching in PI. You can see that m needs not to be 1 in order for the whole expression to make sense.

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