What is a LUT?

S imply put, a LUT is a Look Up Table. A LUT is used to transform a value (or a set of multiple values as in RGB) into another value or set. 1D-LUT Let’s first consider a 1D-LUT. A 1D-LUT is an array of values. For a 10-bit data system (such as the classic 10-bit Cineon Log data system), the values range from 0 to 1023, therefore, a one-dimensional array of 1024 elements can perfectly map each of the possible values into another. If the data is a 16-bit system, the array size needs to be 65536 long to accommodate all the possible input values. If for either case, the size of the array is a problem with the hardware/software, a subsampled array can be used (i.e., instead of 65536 elements for a 16-bit system, 256 can be used and the missing input values are then linearly (or another interpolation method) interpolated. On modern software systems that utilize floating point systems, i.e. OpenEXR, the data to be put through a LUT is converted to properly match the input domain of the LUT system. In modern color correction, the image is usually a three channel RGB system or some other three metric color system. One 1D-LUT can be applied to each of the three channels such as in the case of a 1D-LUT used to convert from log data to linear data. Alternatively, a separate 1D-LUT can be applied to each channel, for example, if the gain or color shift of each channel needs to change. In each case described, the channels are treated as independent, any changes in one channel does not alter any other channel. 1D-LUTs are normally used where the desired transform can adequately be described by channel independent processing (scale or RGB metric conversions, overall color changes like the ASC CDL [except for the saturation parameter]). 3D-LUT In most of the color data transformations, the three channels are dependent. Changes in one channel will alter the others. However, to use the same type of data set as a 1D-LUT, a 3-dimensional array that points to a three element set would be required. For a 10-bit system with 1024 elements, that would be an array with 1024^3 elements (1,073,741,824) each pointing to three numbers! And for a 16-bit system that would be 65536^3 (281,474,976,710,656). Clearly, these array sizes are too large to manage in today’s computers. In order to manage the system, the domain 1024, 65536 etc. is broken down into discrete intervals. There are many currently used 3D-LUT interval types used today. Some usual ones are 16^3, 17^3, 32^3, 33^3, 64^3 and 65^3. Others are possible. For a 17^3 3D-LUT in 10-bit space, each set of nodes of the three channels range from 0 to 1023 with an increment of 64. For the 65^3 3D-LUT the number of input nodes (each input point is called a node) is 65^3 (274625) which is far less than the 3D array system (281,474,976,710,656). 3D-LUTs are stored in the computer with an implied input. If one looks at a text based 3D-LUT, the numbers are the output sets and the input values are implied by the order of the list. Normally, there are two types of implied orders, the R fastest (or commonly referred to as inside) and the B fastest (most common). In order to use these 3D-LUTs, a 3D interpolation method is employed. Common ones are trilinear and tetrahedral interpolation which uses the input nodes and then linearly (occasionally other types such as cubic interpolation etc.) interpolated to obtain the output color R’G’B’ from the input RGB. Less commonly used 3D-LUT types do not have ordered nodes and are lists of input RGB to output R’G’B’ and are called cloud based systems which have their own types of interpolation methods. For these systems, the interpolation times are usually longer due to the increased processing involved. Types of 3D-LUTs Digital camera input LUT Used as a color corrector input LUT to transform the camera R G B into some desired standard or creative look. Calibration LUT One type is the film emulation LUT. These types of LUTs are derived from film negative and film print densitometry of discrete patches originating from a film recorder and a film print. These LUTs “calibrate” the display in the color correction room such that the image on the screen is a close match to a print viewed on a film projector. Post houses without their own film projectors can assure proper film out results with a quality 3D-LUT. It is possible to achieve the same look without using a LUT as long as the color correction hardware and software has the capability to process the images from the starting position to the desired position. And, of course, as long as the desired position’s look is known to the colorist. In the case of the film emulation LUT, it is probably very error prone and/or time consuming to have a colorist try to match a print on a film projector to the digital display for each scene in a consistent manner. Creative LUT Many times a creative look is desired and a specially created 3D-LUT can assure that the look is applied consistently on varied scenes. The colorist can then concentrate on minor changes from this base look provided by the LUT. Some examples are LUTs derived from older cinema systems such as Technicolor two-strip or bleach bypass etc. The output of these LUTs can then be altered by the colorist for the desired effect. I have created LUTs that desaturate all colors except reds and maintain the hue and saturation of flesh. This is a very specific LUT to create a starting point for the colorist. In some cases, the look desired by the production team stretches the ability of the controls on the color correction platform. A properly created 3D-LUT can provide the look while the color correction platform has its controls in the center positions, allowing for further creative control. Technical LUT Sometimes a 3D-LUT is used to transform a project from one type of display to another. Some examples are: P3 to Rec-709 2D P3 to 3D P3 D6500K P3 to D5500 P3 Rec-709 to P3 Transform standard display (i.e., P3) to a non-standard type such as Plasma, OLED or Laser display Technical LUTs may be provided by the camera manufacturer for certain purposes. For example, a LUT may be provided to transform the camera data to ACES data for ingest into the color corrector. Post house engineering staff, color scientist, can create specific technical LUTs for a variety of purposes. P3 to Cineon DPX LUT Some post houses use as their workflow a digital cinema P3 data-centric system. This is due to the deliverable to the production is mostly for digital cinema venues and they do not want to limit the image to a film print. Other display types that are common, such as Rec-709 can be created from the P3 data (with some mild gamut remapping of the larger color P3 system into Rec-709). In these cases, it is desired to use a 3D-LUT to transform the P3 data into Cineon 10-bit DPX data for film out if a small number of film prints are requested by the production. The generation of an accurate 3D-LUT for this purpose is very complex. The P3 data can be out of the film print’s color gamut and needs to be gently remapped. I have developed a sophisticated computer model to create these types of LUTs. The film out results is exceptional. Viewing LUT (Show LUT) The Viewing LUT is what the colorist uses in the normal viewing of the digital data in the suite. It depends on what the data metric of the source is. If it is a digital camera, then the LUT will convert it to P3 directly, or if the camera LUT is a camera to Cineon DPX LUT then that LUT can be combined with the Calibration LUT (which converts Cineon DPX to P3) to get the Viewing LUT. So, the Viewing LUT is whatever LUT that can take the source data metric and convert it to the metric used for the digital projector (usually normal P3 but can be Rec-709, P3 @ 6000K white point or P3 @ 6500K white point etc.). Float conversion LUT The Float conversion LUT can be useful, however very few LUT interpolation algorithms can effectively work with the implied data range of EXR. For example, a normal Cineon DPX 0-1023 log data set is roughly to -0.05 to 13.5 in linear EXR. But, the "usable" EXR range for display is 0 - 1.0. Which means that the LUT must convert the EXR range into a viewable range. Commonly, since the LUTs can only handle an implied range of 0 - 1.0, the data is manipulated by the colorist to take the wider EXR range and artistically compress it into the domain the LUT can handle. One problem with the EXR metric is that it is normally linear. Linear data going through a LUT is not efficient. For an EXR linear range of -0.05 to 13.5, that is a 14.0 range and if the displayable range is 0 - 1.0 that is only ~7% (1.0/14.0 = 0.0714). That means that for the size of the LUT in nodes (33^3, 65^3 etc.) only 7% is used and interpolation artifacts can show up. For a 33^3 LUT, there are 33^3 = 35937 nodes and 7% is only 2567 nodes used, the rest are not used. Schemes such as introducing a gamma or log on the data can effectively compress it for LUT conversion, but it takes some color expertise to create the LUT. On most modern color correction platforms when they use the LUT conversion, the system re-scales the data to 0 - 1.0 LUT input to interpolate through the LUT. Mathematically other domains are possible, but typically all positive values are used. Inverting a LUT Whether the LUT used is a 1D-LUT or a 3D-LUT, the process of going backwards is possible but plagued with some problems. If the transform going forward through the LUT gives the same output for multiple inputs, then it is not possible to “guess” which of the inputs produced the output. Further, the output domain of the LUT may be different from the input domain. For example, it is common to want the RGB triad that gives a specific XYZ on a display. Going forward from RGB to XYZ is relatively simple since we can pass a set of patches on a display and measure the XYZ values and create a 3D-LUT. However, the domain of the XYZ is limited by the gamut of the RGB primaries and white point of the display. The inverse 3D-LUT needs to accommodate the full XYZ range possible and complex gamut mapping techniques need to be applied to be able to produce an operationally correct 3D-LUT. Even with these techniques, proper statistically sound results are achieved that may not be entirely accurate. There are certain LUTs that cannot be inverted. For example, a LUT that creates Black and White (or some tone like sepia) from a color image. A color image cannot be derived from a single black and white image. The creation of LUTs Many techniques are used to create LUTs. 1D-LUTs and 3D-LUTs may be created by applying a mathematical transform to a unity LUT. In the case of a 1D-LUT, a unity LUT is an array where the values are the indices (for example, a unity 1D-LUT give 233 output for a 233 input etc.). A unity 3D-LUT has the output R G B set equal to the input RGB. Some examples of LUTs that are created mathematically are Rec-709 to linear, linear to sRGB and gamma (2.6 gamma for digital cinema) to linear XYZ. LUTs that are created from non-equation systems are from measured data derived from actual color patches (either on film or on measurements from values sent to a display device) or very complex system computer models. For the systems from measured data derived from actual color patches, usually only a small portion of the total color space of the LUT is measured and the nodes not measured are interpolated via conventional techniques. Systems like Truelight (from Filmlight) utilize a bit over 1200 film patches (via an auto-reading densitometer) and where the measurements are done from displays many more patches can be measured depending on the characteristics of the measuring device. A larger number of patches usually reduces error in the created 3D-LUT. Certain 3D-LUTs, i.e. P3 to Cineon DPX LUT, benefit from large patch sets. Typically, I use 9000-10000 film patches to create these 3D-LUTs. If less than the actual number of nodes in the 3D-LUT is measured, some error is introduced by the interpolation method. Mitch Bogdanowicz

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