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ETTR vs LUT-based HDR

I just read about Exposing to the Right as a way to compensate for the way the dynamic range bracketing works. This roughly re-maps intensity values so that more "shades" of shadows are captured, but somewhat less "shades" of highlights.

But if a camera uses a LUT to spread the captured information more evenly onto the 8/10/12/etc -bit space, then a similar effect should be achieved - albeit for LUTs, the resulting image, when viewed without being post-processed, has a very specific look, with reduced contrast and range peaking around the mid-tones (unless I'm mistaken).

I guess ETTR would yield a (pre-post-processing) reduced-contrast image with histogram peaking closer to the highlights. But in this sense the two would achieve similar effects, and are employed for similar purposes. It's just the transformation function that is essentially the same (if I understand it right).

However, I'm curious about two things:

  1. What are the advantages and disadvantages of using one over the other?

  2. Is there a way to use both techniques to obtain a greater benefit over using just one approach?  (For example, shooting with an HDR camera that can do a log-based LUT recording and expose the image to the right somehow.)

My intuition says that the disadvantage comes from the non-logarithmic (?) nature of ETTR. The advantage of ETTR is its being a technique that can be easily employed on cameras without HDR/LUT capabilities. Combining the two would not help in any way (assuming an idealised scenario; e.g., one where we're not overexposing to compensate for lack of light).