How do a LUT actually work?

Hello there! And pleased to meet you in my wheelhouse!   😉

I work for/with/teach pro colorists on a subscription site, and have been around them for a decade now. I work in Resolve as well as Premiere, and am somewhat of an expert about Lumetri. So  .... color, oh boy! Ha.

LUT BASICS

LUTs are useful but rather "stupid" tools. As colorists say, they're "the dumbest math out there" ... as they are essentially built as a look-up table. With a limited number of "points" to the changes they make. Such as 16, 32, 64. The more "points" the more subtlety they will provide, and a bit more accuracy. In between points, an app will basically 'scale' a straight line to the next set of points. More points more 'curvy' behavior possible, fewer points ... less.

Complex LUTs are called "3D", because they can have two tables ... and the math allows for a slight bit of sliding values of one based on values in the other. Resolve and Baselight do a lot better with those, Premiere often doesn't "recognize" those LUTs. So we're left with mostly the simpler "1D" LUTs.

Premiere only creates 16 point cube (specific LUT format) LUTs. Which is something many of us have long asked to be upped to include 32/33 and 64 point LUTs. And I've seen the 16 points called 17 points someplaces, 16 others ... why? dunno. Same with 32 and 33. 

The other main process for "transform" work are algorithms, like the auto-tonemapping process in Premiere now. Algorthms are actually fully "live" mathematical calculations, with complex if-then/not-this sort of things. VASTLY superior to LUTs, so if possible, use the algorthms as the base not a LUT.

After using Premiere's new auto-log detect and auto-tonemapping options, to normalize a clip to say Rec.709/SDR, you then make your changes to get the best look for that clip possible ... just as you would have done with a LUT based normalization. Except the changes you make will of course be a little different, as the tonemapping and a LUT will not produce identical results. Trust the tonemapping though as the safest start for your pixels.

USING LUTS FOR ... ?

LUTs have three main uses:

1.  Normalization of log-encoded media to a linear timeline. Say you have some Sony log-encoded media ... (real log, not that "it looks log-ish" stuff that is like the Cinelike-D thing) which is encoded to a sort of parabolic state for values to fit more into the 'scale'. It needs to be set back to the linear math of a sequence, so you can use manual methods to increase contrast & saturation, or a LUT. Either by a manufacturer or one you make yourself to taste.
2. Transform one color space/dynamic range to another one. This is a bit more complex of an operation, and can best be done with LUTs by the software and camera companies, or LUTs you create in Lattice (Mac only) or LutCalc (PC). Those apps have the controls to make parts of the LUT perform as needed to do pretty clean transforms.
3. Provide a "show" look to the entire sequence. This is something that say most of the YouTube LUT packs are designed to do. This can do things like make the darker tones more cyan, group the mids to more orange/skin tones, and fade out the brights and shadow tones ... that sort of thing.

While at first it looks fun to get a ton of "look" LUTs, well ... the reality is, most of them can do as much harm as good. Remember the "dumbest math out there" comment? Yea, as LUTs can easily cause crushed shadows, clipped whites, saturation issues ... and artifacts like blocking or banding.

Because LUTs ... while being based on rather simple lookup tables ... are built from specific clips of media. In other words, the camera was setup with a scene, a clip or two or three recorded, and color and tonal changes made in say Resolve or something, then a LUT exported 'holding' those changes.

Which are ... X becomes Y, Q becomes R, and on. In between "points", the app provides something of a scalar process to the pixels.

So IF ... your clip is exposed pretty close to the scene the LUT was built from, with similar scene contrast and lighting ... with similar camera exposure settings ... it all works ok.

BUT ... if anything is 'off' in camera settings or scene contrast of what you shot, then ... you may well get clipping, crushing, or otherwise botched pixels. NOT ... good.

So in application, "conversion" LUTs and Look LUTs both need to be applied where you can 'trim' the clip prior to the LUT ... as in Lumetri, this would be to use the Creative tab's Look slot (no matter whether it's a log-to-Rec.709 normalization or a Look LUT) ... and then you can use the Exposure, Contrast, Saturation, Highlight & Shadow controls of the Basic tab to shape the clip into what that LUT works best with. 

AND YOU NEED TO HAVE THE SCOPES UP TO DO THIS PROPERLY!

Never trust the Mark I Eyeball ... only the Scopes! ... preferably the RGB Parade, Vectorscope, Waveform (I tend to YUV no chroma mostly) and sometimes a histogram). They tell you real data from the clip, no matter what the monitor 'shows' you.

With some practice working with Lumetri's tonal & color controls, you can watch the scopes to see what changes a LUT does to the image ... and recreate those changes without the LUTs, manually. Once you learn some of that, you can create a "Look" to taste manually far faster than sorting through 96 LUTs and testing them at various strengths.

@R Neil Haugen