Help for tonal stabilization of video algorithm

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Hello. I want to implement on Python an algorithm of tonal stabilization for video from the paper:
But I don’t fully understand the space color in which the author working. I understand, that I have to normalize the three RGB channel with the Luminance channel: L= R+G+B
By doing so, the author separate between Luminance and Chroma. That’s I think I get it. And here their idea, and what I don’t understand:
they represent the change at each pixel as one offset for the log luminance, i.e log(R+G+B) or log ®+log(G) + log( B) ? and two offset for the chroma, R/L and G/L ?Can you also explain to me how this represents an exposure correction ?
Moreover, to initialise the adjustment Map,they say that for the pixel which have a very few difference (say <0.05) in intensity between 2 frames, f1 and f2, the correction consist to add the corresponding difference f1-f2 to the map. Ok, but then how do I add that to the log luminance, and chroma channel ?

Sorry for my poor english and don’t hesitate to ask me for more precision in my request