I.M - LUTs¶

The acronym LUT comes from Lookup Table.

M.1 - Description¶

As its name suggests, it is a simple array of values, allowing to match some input values with other output values. In computing, it is a convenient way to replace complex mathematical functions, the result of time-consuming calculations, with a simple search in the array, which can greatly improve performance: instead of having to recalculate, you already have the results in memory.

We keep the use in colors; it is a simple way to match a color in input to a different color in output: it is therefore a table that allows to retouch the colors or convert color spaces, describing them, color by color.

The main interest of a LUT is that any program can easily use them and thus convert from and to color spaces which are not provided for at the base by the program; instead of having to “know” the mathematical functions which define a color space (in particular the transfer curve), the program has only to read the results in the mapping table without having to carry out the calculation. It is a utility tool, for conversion.

They are also a way to “save” any colorimetric adjustment; even if an adjustment is made using multiple effects in an application (levels, curves, saturation…), it can be described and saved as a single LUT and then reapplied easily, and in any application capable of reading a LUT. In this case, it is an artistic and practical use.

Here is an example of a few lines of values from a LUT, which is really just a text file containing such an array of values:

R	G	B
0	0	0
0	0	298
0	0	596
0	0	894
0	351	0
0	326	260
0	302	558
0	278	856
381	3784	0
282	3760	0
184	3736	117
85	3712	415

A LUT does not describe all possible color matches, but a selection of colors; to obtain a color that is not in the table, it is necessary to perform interpolation. Normally, the application using the LUT proposes different interpolations which will change the way these colors are obtained (by rounding, linear interpolation, etc.).

The quantity of values contained in a LUT is thus very important for the quality of the output image: being only a table of limited values, there can be a loss during the conversion and the result can more or less differ from a true mathematical operation. However, the difference is not discernible in the case of LUT with many values, such as those used by OCIO + ACES for its conversions for example. See Chapter N - OCIO, ACES.

M.2 - Use¶

There are many different file formats for LUTs, depending on applications, developers, etc. Here are some examples (formats supported by FFmpeg):

Extension	Name, publisher, application…
3dl	Discreet / After Effects / Autodesk
cube	Iridas / Resolve
dat	DaVinci
m3d	Pandora
csp	cineSpace
spi1d, spi3d	Sony Pictures Imageworks

It can be useful to convert between different LUT formats; OCIO includes a command line conversion tool, for which the media encoder DuME provides a graphical interface.

There are two main types of LUT: LUT 1D and LUT 3D.

• 1D LUT

1D LUT work only on the luminance and do not modify the colors. Having only one dimension, they are lighter and simpler than the 3D LUT and are useful for the conversions of gamma*, for example between two colorimetric spaces which would have the same primaries*. See chapter L - Transfer curves, linear space and gamma.

• 3D LUT

The 3D LUT work on the three channels red, green and blue. They therefore allow detailed retouching of both luminance and hues as well as saturation. They allow artistic effects as well as conversions from and to any color space.

Whatever the type of LUT, these conversion tables offer only a simple correspondence of value, each LUT is designed for a precise space and colors in entry and cannot be used indifferently on any image!

For example, a LUT that converts to the Rec.2020 color space is certainly intended to be applied to an image in another specific color space, e.g. Rec.709; in this example, it cannot be used on an sRGB image, unless it has first been converted to Rec.709.

This is also true for LUTs that are for artistic use, not utilitarian. It is necessary to know on which space and which type of image each LUT is supposed to be applied. Depending on the application, the choice of workspace is therefore important when using LUT, or at least you must be aware of it in order to make any conversions prior to using LUT (which means that they are not as simple as they seem).

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Sources & References

• Lookup table on Wikipedia
• 1D vs 3D LUTs by James Ritson on Affinity Spotlight¹