Colour gamut mapping

The range of colours that can be produced by a given medium is also specific to that medium, a feature that remains after device characterisation. This range, or colour gamut, is device- or medium- dependent owing to differences in the imaging process and colorants used by different media, or to differences in their physical properties. Gamuts will differ in size between different media and devices. Referring to the definitions given earlier, a gamut can be the set of colours contained in an image, or the colours that are reproducible by a given device or medium. A colour gamut is also specific to a given set of viewing conditions, and these conditions must be specified (Morovic, 2003).

Gamut differences present a problem for colour reproduction in that some of the original colours might not be able to be displayed or produced by the reproduction unless suitable modifications are made to these original colours. The process of altering colours in the original image, and replacing them with ‘ones that a given medium is capable of reproducing’ (Morovic, 2003) is called colour gamut mapping. Colour gamut mapping is a necessary part of transcribing

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display images to hard-copy print, because RGB gamuts are larger than CMYK gamuts (Grey, 2004; Nate, 2004) . RGB colours outside of the CMYK gamut are said to be out-of gamut. In colour gamut mapping, for practical reasons, gamuts are treated as continuous volumes in colour space, rather than as a set of discrete colours (Morovic, 2008). Two properties of these volumes require definition before mapping can take place; these are the CIE colour space for mapping and the colour gamut boundary, which are discussed below.

2.5.3.1.Colour appearance spaces: CIELAB and CIECAM97s

Gamut mapping needs to take place in a device-independent space which also needs to take into account the conditions under which the original, and reproduction, are viewed. This intermediate colour space should therefore be a colour appearance space that is based on a

colour appearance model. As defined by CIE Technical Committee 1-34, a colour appearance

model is

“Any model that includes predictors of at least the relative color appearance attributes

of lightness, chroma and hue. For a model to include reasonable predictors of these

attributes, it must include at least some form of a chromatic adaptation transform.

Models must be more complex to include predictors of brightness and colorfulness or to

model other luminance-dependent effects such as the Stevens effect or the Hunt effect”

(Fairchild, 2005).

Chromatic adaptation refers to the ability of the human visual system to adjust to changing

conditions of illumination, resulting in the colours of objects appearing more or less the same under, for example, daylight and incandescent illumination (Fairchild, 2005).

While CIELAB is unable to predict luminance-dependency (such as the increase in

colourfulness and contrast with luminance), or the effects of background and surround

(Fairchild, 2005), it is considered a colour appearance model on the basis of its lightness, hue and chroma predictors and incorporated chromatic adaptation transforms. Strictly speaking however, CIELAB was originally designed as a uniform colour space for the specification of

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colour differences between colours of identical size, shape and viewing conditions. Also, CIELAB can lack accuracy in its chromatic adaptation transforms and in its ability to predict hue in different parts of the colour space. The latter feature however, is shared by other colour appearance models (Morovic, 2003).

Another example of a colour appearance space is the one based on the CIE colour appearance model (1997), CIECAM97s, which has correlates for the appearance attributes brightness, colourfulness and saturation, as well as for lightness (denoted J), chroma (C) and hue (h). The space also uses the coordinates J,a,b (Fairchild, 2005). The choice of which appearance attributes to use for gamut mapping depends on the specified contribution of the light source under which the original is viewed, and on the properties that are desired in the reproduction, as specified by a rendering intent (Morovic, 2003). Rendering intents are discussed in Section 2.5.3.3 below.

2.5.3.2.Gamut boundary computation and gamut sampling

The formal CIE definition of a colour gamut boundary is ‘a surface determined by a colour

gamut’s extremes’ (Morovic, 2008). Being able to describe this boundary, in the form of a

computed gamut boundary descriptor, or GBD, allows gamut mapping lines (as well as their direction, centre of gravity, and their intersections with the boundary) and mapping distances to be established. In the case of colour printing, GBDs are needed for the original image and reproduction medium gamuts. GBDs can be either generic, or medium-specific. Generic GBDs are comprised of the points that from a convex hull or alpha shape around the gamut, or the points which are the maxima of evenly divided spherical segments of the colour space. This type of GBD is suitable for image gamuts or palettes of spot colours (Morovic, 2008). In this respect, the image gamut refers to the gamut of all the image pixels; this will differ to the

perceived gamut of the image because not all pixels will be perceptible, or pixels will occur

infrequently in an image. Perceived image gamuts require a different approach which is yet to be firmly established (Morovic, 2003). Medium-specific GBDs can be computed from a characterisation model, as the “the gamut of the device is implicitly quantified” during device

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characterisation (Sharma, 2007). One method for computing medium-specific GBDs is based on the Kubelka-Munk equations (Morovic, 2003).

Rather than to base the computation of GBDs on entire sets of colours, which can number into the tens of thousands (for the colours in an image) or hundreds of thousands (for media gamuts), it is more practical to use a smaller sample. Samples can be taken from the entire gamut volume, or from the gamut surface only (Morovic, 2003). Indications are that a subset of around 1,000 colours is needed for volume sampling of image colours, referring to an example given in Morovic (2003). Sampling is not required for smaller sets of colours, such as the 1,114 colours of the Pantone Formula Guide® (Morovic, 2008). In certain situations, a denser sampling is required (see below) which, for imaging media, means that the size of the sample is in the order of the size of the population gamut (Morovic, 2008).

The GBD represents the combined effects of the size of the sample and whether the GBD algorithm results in a ‘tight’ or ‘loose’ gamut boundary. Morovic (2008) gives a detailed discussion on the contributions of these effects, and on the implications for the relationship between sample-derived gamut boundaries and those of the colour population from which the samples are drawn. Briefly, sample-derived gamut boundaries could either under- or over- estimate the population gamut, which itself can be small or large (Morovic, 2008), with consequences such as population colours remaining out-of-gamut even after mapping, colours being mapped unnecessarily, or regions of gamuts not being used. The best estimation of a population gamut boundary will come from a combination of dense sampling and a ‘tight’ boundary.

2.5.3.3.Gamut mapping algorithms and rendering intents

In the process of altering colours in the original image, and replacing them with ‘ones that a given medium is capable of reproducing’ (Morovic, 2003) it is not only the difference between the gamuts of the original and reproduction (the source and destination gamuts respectively) that need to be taken into account. Within these constraints, the properties that are desired in

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the reproduction, relative to the original, also need to be specified. Broadly speaking, either an

accurate or a pleasant reproduction will be aimed for, and within each there are various sub-

types (Morovic, 2003). These objectives are referred to as rendering intents. An accurate reproduction specifies that the reproduction be as close as possible to the original, whether it is pleasant or unpleasant (Morovic, 2003), and both are compared side-by-side as in a copying environment (Braun et al., 1999). A pleasant reproduction aims to be pleasant, irrespective of the pleasantness of the original (Morovic, 2003), and is not compared to the original, as in a printing environment (Braun et al., 1999). The rendering intent decides the set of appearance attributes that are the focus of mapping. The combination of lightness and chroma are used if the appearance of an original is taken to be its appearance relative to a reference white, while brightness and colourfulness are used in situations such as art reproduction where the conditions of the original surroundings are more important (Morovic, 2003).

Typically it is accurate reproduction that is aimed for, because these are the better understood, and the more straightforward to achieve (Morovic, 2003). There are two main types of mapping algorithm that are used to achieve an accurate reproduction: clipping algorithms and compression algorithms. Clipping algorithms are applied to out-of-gamut original colours only, which are replaced by those on the surface of the destination gamut boundary, with the aim of maintaining overall accuracy. Compression algorithms transform all colours, whether within or out-of-gamut, and are replaced by colours inside the destination gamut, thereby preserving relativity. Clipping and compression algorithms are usually hue-preserving, that is, they take place within a plane of constant hue angle; colours are clipped or compressed along pre-defined lines (for example, towards a ‘centre of gravity’ on the lightness axis, Figure 2.10), or clipped along the line with the shortest distance (minimum ΔE clipping), toward the reproduction gamut boundary. Alternatively, there are minimum ΔE clipping algorithms which do not preserve hue (Morovic, 2008).

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2.5.3.4.Quality (evaluation) of reproduction: print

The evaluation of the reproduction is made against the rendering intent, and will apply only to the image and media that are involved (Braun et al., 1999; Morovic, 2003). However no established model exists for quantifying the appearance of complex images or for quantifying the difference between original and reproduction (Kang, 2006). Braun et al. (1999) used panels of individuals (with various levels of experience) to judge reproductions of colour images that were made using various gamut mapping algorithms. Clipping algorithms were overall the better performing when the reproduction was compared to the original. Contrast-boosting algorithms newly developed by the authors did better than clipping algorithms when images were ranked in order of preference in the absence of the original. The latter result highlights the influence of lightness or darkness in source image content (Morovic, 2003); the contrast- boosting algorithms may have lightened images that were dark to begin with (Braun et al., 1999).

Figure 2.10 An illustration of colour gamut clipping (top) and colour gamut compression (bottom) towards a centre of gravity, E, on the lightness axis (Morovic, 2003).

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