1D LUTs
As an example the start of a 1D LUT could look something like this:
Note: strictly speaking this is 3x 1D LUTs, as each colour (R,G,B) is a 1D LUT

R, G, B
3, 0, 0
5, 2, 1
7, 5, 3
9, 9, 9

Which means that:
For an input value of 0 for R, G, and B, the output is R=3, G=0, B=0
For an input value of 1 for R, G, and B, the output is R=5, G=2, B=1
For an input value of 2 for R, G, and B, the output is R=7, G=5, B=3
For an input value of 3 for R, G, and B, the output is R=9, G=9, B=9

Which is a weird LUT, but you see that for a given value of R, G, or B input, there is a given value of r, G, and B output.

So, if a pixel had an input value of 3, 1, 0 for RGB, the output pixel would be 9, 2, 0...

If the R input value changes to 2, but G and B stay the same, only the R output value changes, with the output pixel values being 7, 2, 0.

Make sense?

This can be shown graphically, like this:

3D LUTs
3D LUTs are a little bit more complex, and are based on a three-dimensional Cube with the ability to alter a given single R, G, or B output value based on a single R, G or B input value change.

This is probably best shown graphically, like this:

Hopefully, you can see that as the colour 'planes' move away from the origin point (0, 0, 0) in the direction of their individual axis they will increase in their respective colour, as indicated.

1D vs. 3D
So, 3D LUT are way better than 1D then?

Looking at this 1D vs. 3D comparison you'd think so, wouldn't you?.

Well, this is not always the case...

A 1D LUT tends to have values for each and every input to output value, so they are very accurate within their 1D conversions.

If a 3D LUT were to have values for each and every input to output combination the LUT would be very, very large indeed - so large as to be impossible to use...

So, most 3D LUTs use 17 point cubes, which means there are 17 input to output points for each axis, and the values in between these points have to be interpolated, and different systems do this do different levels of accuracy, so the exact same 3D LUT used in two different system will, in all probability, produce a subtly different result.

The following image show the difference between two well know display system that use 3D LUTs working with the exact same LUT:

Move cursor over image to see the difference

It is very rare to get two systems working with the same 3D LUT to show the exact same result!

The way 3D LUTs are written can also be rather confusing.

There are still usually three columns of numbers, R, G, and B, but usually with Blue changing fastest, then green, then red.

The following is the first few lines from a 'default bypass' 3D LUT - output is equal to input:

R, G, B
0, 0, 0
0, 0, 64
0, 0, 128
0, 0, 192
0, 0, 256
0, 0, 320
0, 0, 384
0, 0, 448
0, 0, 512
0, 0, 576
0, 0, 640
0, 0, 704
0, 0, 768
0, 0, 832
0, 0, 896
0, 0, 960
0, 0, 1023
0, 64, 0
0, 64, 64
0, 64, 128
0, 64, 192
0, 64, 256
0, 64, 320
0, 64, 384
0, 64, 448
0, 64, 512
0, 64, 576
0, 64, 640
0, 64, 704
0, 64, 768
0, 64, 832
0, 64, 896
0, 64, 960
0, 64, 1023
0, 128, 0
0, 128, 64
0, 128, 128
0, 128, 192
0, 128, 256
0, 128, 320
0, 128, 384
..., ..., ...

What can be seen is that Blue goes through its 17 point cycle, quickly, Green is updating its cycle once for 17 of Blue's cycles, and Red will update once during the whole length of the LUT, which is equal to Green going through 17 cycles...

These 42 lines continue for a total of 4913 lines...

Easy!

Ok, not so easy... Think of it this way:

In the above 'cube' diagram the Red plane starts in the first of its 17 points (positions).
The Green plane is also at its first point, as is Blue.
The output value for this position is recorded as the fist line of the LUT (0, 0, 0).
The Red plane stays where it is, as does the Green, and Blue moves to its second position.
The output value for this position is recorded as the second line of the LUT (0, 0, 64).
This continues for all 17 points (positions) for Blue.
Then Green is moved to its second point, and Blue goes through its 17 points again.
When Green has been through all 17 of its points, Red is moved to its second point, and the cycle begins again...

Make sense now?

So, for a LUT that isn't a bypass LUT, the position of each 'plane' is altered for each of the 17 points to generate the desired output value.

The first few lines from a real 'calibration 3D LUT' would therefore be something like:

R, G, B
0, 0, 0
0, 0, 36
0, 0, 112
0, 0, 188
0, 0, 261
0, 0, 341
0, 0, 425
0, 0, 509
0, 0, 594
0, 0, 682
0, 0, 771
0, 0, 859
0, 0, 955
0, 0, 1023
0, 0, 1023
0, 0, 1023
0, 0, 1023
0, 32, 0
0, 28, 28
0, 28, 96
0, 24, 172
0, 24, 252
0, 20, 333
0, 20, 417
0, 12, 501
0, 12, 586
0, 8, 674
0, 4, 762
0, 4, 851
0, 0, 943
0, 0, 1023
0, 0, 1023
0, 0, 1023
0, 0, 1023
0, 92, 0
0, 88, 20
0, 88, 88
0, 88, 164
0, 84, 244
0, 84, 321
0, 80, 405
..., ..., ...

And this is actually the first part of the LUT used for the comparison image above.

What A LUT Does
So, in essence, what a LUT does is take an input value and generate a new output value...

In general (and totally ignoring what I said above about the accuracy of 3D LUTs vs, 1D), 1D LUTs have their uses, but 3D LUTs can be a lot more accurate, specifically as they can alter saturation (a 1D LUT cannot show a black & white image from a colour one for example), and a 1D LUT is capable of only altering a single output colour value based on a single input value, so has no cross colour component, which can be critical in accurate calibration... In the real world a change in Red value will often cause a (smaller) change in Green and Blue, etc...

Next Page - 1D vs. 3D LUTs