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Chapter 6   Colour Models

A good understanding of colour is essential for effective use of computer graphics. The way colour is seen draws together information from such diverse disciplines as physics, optics, physiology, neurology and psychology to show that colour is an internal, subjective sensation rather than an external, objective entity. This helps explain just what colour is.

Given the biological basis of colour, how can it be measured and standardized? The CIE international standard is used to define colour. This provides the vital link between biological sensation and physical measurement.

An abstraction called a colour model is used to specify colour. The concept of primary colours leads to the many colour models that are available, each with their own particular strengths and weaknesses. A colour described in one colour model can often be converted to a description in another. The CIE standard functions as a universal yardstick in this process.

A number of guidelines for using colour exist. Rather than just an arbitrary series of rules, these guidelines follow directly from the way colour is perceived and generated.

6.1   Seeing in colour

6.1.1   The electromagnetic spectrum

Light is a form of energy. Visible light is only one form of electromagnetic energy; other forms include infrared, ultraviolet, radio waves, microwaves and X rays. Electromagnetic energy can be considered to behave like a wave, and the factor that distinguishes these many types of energy is the wavelength. This is illustrated in Figure 6.1, which uses a logarithmic scale to encompass the wide range of wavelengths. Visible wavelengths are most conveniently measured in nanometers (nm, 10-9 m).


Figure 6.1: Electromagnetic spectrum.

The range of wavelengths corresponding to the colours of the spectrum are shown in Table 6.1.
Range (nm) Colour
380 ­ 450 Violet
450 ­ 490 Blue
490 ­ 560 Green
560 ­ 590 Yellow
590 ­ 640 Orange
640 ­ 730 Red

Table 6.1: Approximate wavelengths of spectral colours.

White light consists of a mixture of all the visible wavelengths, which was first described by Sir Isaac Newton in the Optiks (1704). He found that white light could be split by a glass prism into a rainbow of colours, and combined again to form white.

6.1.2   Spectra

It could be imagined that measuring the intensity of light emitted or reflected from an object at all visible wavelengths would completely define its colour. Such a measurement will indeed define those optical properties which influence the observed colour. An example of such a measurement is given in Figure 6.2. There is no easy way to predict the visual appearance from this information. The dominant wavelength can readily be identified, but what of the contribution from the rest of the spectrum? What will the overall colour be?


Figure 6.2: Typical reflectance spectrum.

The range of wavelengths which are visible varies between species; some snakes can see portions of the infrared, and many insects can see into the ultraviolet. When white light is split by a prism, the wavelengths are separated, but it is the eye and brain that produce the sensation we call colour.

6.1.3   The eye

The function of the eye is to capture a visual image, and convert the light energy into nerve impulses to be interpreted by the brain. The overall structure of the human eye, shown in Figure 6.3, is analogous to a camera. Table 6.2 compares the functions of the eye and a video camera.


Figure 6.3: The human eye.

Eye Video Camera Function
cornea and aqueous humour primary focusing lens bend light to form image aqueous humour
lens secondary lens fine focusing
iris aperture depth of field & light level adjust
zonula auto focus move lens
conjunctiva clear daylight filter protect optics from scratches
sclera casing mechanical framework
retina photoelectric surface convert light to electrical signal
retinal blood vessels power cables supply energy to retina cells
optic nerve video signal output transmit data

Table 6.2: Comparison of the eye with a video camera.

The major optical power of the eye comes from the transparent, curved cornea, which can bend light because of the large change in refractive index between air on the outside and the liquid (aqueous humour) on the inside. This delicate component is covered by the conjunctiva to prevent scratching from small particles such as grit, dust and smoke; tears are continually secreted to wash the conjunctiva, and the combination of eyelashes, eyelids and the bony structure of the skull protect the eye against more major damage.

The iris is a muscle which, when contracted, covers all but a small central portion of the lens, blocking the majority of light and increasing the depth of field. This provides a greatly increased dynamic range of usable viewing conditions, from dim to very bright. The process of responding to a large change in overall light intensity is termed adaptation.

Focusing on objects at different distances is accomplished by the lens, which is moved by a muscle called the zonula. Some of this movement is like a camera, forwards and backwards. The lens in the eye is however pliable, and can be pulled at the edges to form a thinner, flatter shape with a longer focal length. The portion of the lens not covered by the iris looks black from the outside, and is termed the pupil.

Because the refractive index of the lens and aqueous humour varies with wavelength, different colours require slightly different lens positions for crisp focus. This is termed chromatic aberration, and is noticed by a blurring of focus when colours of widely separated wavelength are seen side by side.

6.1.4   The retina

Light energy is transformed to electrical impulses by the retina, a thin network of cells lining the back and sides of the eye. In some respects, this is like an array of charge coupled devices similar to that used in video cameras. It is however a more complex device than this, and it is necessary to have some idea of its action to understand how colour is perceived.

The cells making up the retina are specialized nerve cells, and are related developmentally and morphologically to the nervous tissue in the brain. Thus, some of the retinal nerve cells perform visual processing even before the signals have left the eye. Another curious consequence of the embryological development of the eye from brain tissue is that the retina seems `inside out'; light has to pass through the `wiring' of nerve cells to reach the photosensitive cells, which are at the back face of the retina.

The light sensitive receptor cells at the back of the retina face onto a black lining, the choroid, which enhances contrast by eliminating internal reflections and preventing light filtering through the front of the eyeball. Receptors are connected via bipolar cells (so called because of their double-ended shape) to ganglion nerve fibers, which pass out of the eye to form the optic nerve leading to the brain.

The retina also contains horizontal cells, which connect small clusters of receptors. When a receptor is illuminated, adjacent receptors are made less sensitive by the horizontal cells, increasing the local contrast. This is a preliminary form of edge detection, and causes an optical effect known as Mach banding. This is illustrated in Figure 6.4, which shows a series of grey rectangles. Each is a uniform shade of grey, but the edge near the darker rectangle looks lighter. Similarly, the edge near the lighter rectangle looks darker. Mach banding can be troublesome in computer graphics; if a smooth gradation in lightness is simulated by a small number of shades, ensure that the edges are ragged to reduce this effect.


Figure 6.4: Mach banding.

6.1.5   Receptor cells

There are two classes of receptor cells: rods and cones, named from their shape. They have a similar structure: a central nucleus, many mitochondria to provide chemical energy, and a stack of disks containing photo-sensitive pigment.

Rods are sensitive to very low light levels, but reach their maximum output at only moderate light intensities. Thereafter they give a constant output regardless of increases in light level. Cones are less sensitive, but can handle high light intensities.

The light sensitive pigment in rods, called rhodopsin, is a protein bound to a form of vitamin A. Absorption of a single photon of light causes a molecule of rhodopsin to change from a low energy to a high energy form. This small energy change is greatly amplified by a cascade of chemical reactions to produce a nervous signal. Unlike most nerve cells, which transmit impulses in a digital, on/off form, the receptor cells produce a graduated, analogue response to light intensity, rather like a light meter.

Figure 6.5 plots the ISO standardized luminous efficiencies of a statistically normal observer (around 96% of the population; the rest have various forms of atypical colour vision frequently but incorrectly termed `colour blindness'). This represents the perceived brightness of a light as the wavelength is varied while holding the light level constant.


Figure 6.5: Luminous efficiency.

At low light levels, when the eye is dark adapted, only the rods are active. This is termed scotopic vision, and is most sensitive in the green region, at 510nm. In brighter light, rods are overloaded and the cones are active; the maximum luminous efficiency for this photopic vision shifts to the yellow/green region at 555nm. This effect is termed the Purkinje shift.

6.1.6   Colour reception

In addition to sensing the brighter lights, cones also provide colour sensation. There are three types of cones, differing in the protein component of the visual pigment and thus in the range of wavelengths of light to which they are sensitive. Referred to as S, M and L cones (for short, medium and long wavelengths) they have maximal sensitivities at 445nm (violet), 535nm (green) and 570nm (yellow). They are also called b , g , and r cones by some authorities.

In contrast to measuring the overall luminous efficiency of a human subject, determining the response of an isolated single type of cone cell is more difficult and the precise results depend to some extent on the methods and assumptions used. Two approaches have commonly been used: experiments on subjects who lack one of the three cone types (which assumes that the other two are normal) and measurements of extracted cone pigments (which assumes that the rest of the cone cell and other retinal structure has no modifying effect).

An example of one set of measured spectral sensitivities for the three cone types is shown below in Figure 6.6. It is immediately apparent that S and M cones display significant overlap and have similar sensitivities and wavelength maxima; L cones have a much lower sensitivity.


Figure 6.6: Sensitivity curves for the three cone types.

All three cone types in fact have similar, low sensitivities in the blue and purple region, but L cones do not have the large, short wavelength sensitivity peak possessed by S and M cones.

One consequence of the marked overlap between M and L cones is that their responses to a given colour will be highly correlated. Transmitting the signals from each cone type straight to the visual cortex would therefore be inefficient. It would also require that four separate signals - S, M, L and brightness. What happens instead is a current topic of research and debate. All researchers seem to agree, however, that colour difference signals are produced.

Most researchers agree that in a second stage of colour detection, the difference of the M and L cones is used to provide a signal which discriminates between orange and bluish green.

The sum of the M and L cones is also transmitted, to provide a brightness channel. Rods, which are saturated at photopic light levels, provide a small and effectively constant input to this channel, but there seems to be no input from S cones.

A second colour difference channel is provided by a weighted combination of S, M and L cones to aid discrimination of greenish yellow from purplish blue. the exact weightings and combinations of cones, and the probable multiplexing of difference signals for transmission to the brain, are not yet known with certainty.

It is likely that there is a third stage of colour processing, somewhere in the brain, to generate three opposing pairs of colours: black/white. red/green and blue/yellow. Each of these colours is commonly seen as being in some way unique or distinct from the others. This idea of opponent colours has a long history, being described by Leonardo da Vinci and Goëthe, among others.

6.1.7   The fovea

This is a small yellowish spot on the retina, directly in line with the optical axis of the eye shown in Figure 6.3. The fovea is the area most sensitive to subtle variation in colour, and is also most sensitive to small details of lightness and shape.

It contains few rods, in contrast to the outer edges of the retina, far from the optical axis, which are rich in rods and optimized for detecting motion at the edges of vision - a clear survival advantage. Because the eye can be moved to point towards any object of interest, the small size of the fovea is not a disadvantage.

The nerves and blood vessels which cross most of the retina, and through which light must pass to reach the photoreceptors, are pushed aside from the fovea to reduce blurring. Extra large M and L cones are packed into the fovea in a hexagonal tiled pattern, to give the maximum spatial resolution for the lightness (M + L) and orange/bluish-green (L - M) second stage channels. Less than two percent of the foveal receptors are S cones, as these make no contribution to the lightness channel. A consequence of this low S density is that the spatial resolution - the amount of fine detail that can be seen - is much lower for blues and violets than for other colours.

6.2   Measuring colour

6.2.1   Colour matching

As we have seen the phenomenon of colour is a subjective one; a model of colour must take into account our knowledge of the mechanism of colour vision if it is to have any utility. The most obvious way to compare two colours for similarity is thus to look at them side by side. In the early days of colour science, this is exactly what was done.

To exactly reproduce the colour of a given object, it would at first seem necessary to have a multitude of light sources corresponding to all the different spectral colours and adjust the intensity of each one separately until the objects spectrum was precisely duplicated.

In practice, however, equivalent colour sensations can be produced by a mixture of only three colours. This is because the analytical resolving power of the eye for colour is poor, compared to the resolving power of other sense organs such as the ear or the nose; a complex light stimulus is perceived as a single sensation. For example, given a complex audio stimulus, such as a concert orchestra, it is possible to resolve the individual instruments and listen to just the violins. It is not possible, given a complex visual stimulus such as white light, to `pay attention' to just the red components. (In contrast, the spatial resolving power of the eye is much better than that of the ear).

The experimental set up for a colour matching experiment consists of lights are projected onto a diffuser so that the observer sees a uniform single colour. The unknown light to be matched is viewed side by side with the three standard lights, the intensities of which are individually varied until the colours are seen to match.

Three lights often chosen for colour matching experiments are monochromatic (single wavelength) sources at 700nm (scarlet red), 546.1nm (yellowish green) and 435.8nm (bluish violet).

The green and blue-violet lights correspond to sharp peaks in the spectrum from a mercury vapour lamp; this allows calibration and exchange of experimental data between different sites. The red light is in an area of the spectrum where changes in wavelength produce little change in perceived colour, minimizing the effect of mis-calibration.

In some cases, a match can only be obtained by adjusting the unknown colour; this is done by adding a proportion of one or more of the standard lights using a second set of standard lamps This is equivalent to a negative quantity of one or more lights being required. The specification of a colour in terms of the amounts of energy required from each of the three lights to match it is termed its tristimulus value.

The colour resulting from two coloured lights can be exactly predicted; it is the sum of the tristimulus values of the two lights. The tristimulus value of a 50-50 mixture of two lights is thus the average tristimulus value.

This important property, termed additivity, allows the colour of a mixture of an arbitrary number of lights to be predicted. Considering the spectrum of a colour to be made of a large number of wavelength bands allows the tristimulus value of any object to be calculated as the additive mixture of these bands.

If the predicted tristimulus value of a mixture is positive, it can be mixed with the colour matching apparatus described. This is true even if one of the components of the mixture has negative tristimulus values.

Based on a series of matching experiments, a standard observer was defined in 1931 by the International Lighting Committee (Committee Internationale de l'E'clairage, CIE). This is a set of data which defines three primary colours for colour measurements and states, for each wavelength interval, the amount of these primaries which would be required to match a spectrally pure colour for a statistically normal (non `colour blind') observer. A graph of the matching functions is shown in Figure 6.7.


Figure 6.7: CIE colour matching functions.

The three primaries are called X, Y and Z. A graph of the amounts of each CIE primary required to match any pure spectral colour is called the matching function, and is shown in Figure 6.7. To match a particular colour, a vertical line is drawn at that colour's wavelength and the quantities read off from the intersections with each matching function. For example, to match the blue/violet colour of wavelength 450 nm requires 0.33 units of X, 0.04 units of Y and 1.77 units of Z.

In mathematics, many problems are made easier by the use of imaginary numbers, which contain the square root of minus one. Similarly, the X, Y and Z primaries used to define the standard observer are `imaginary' colours, in that they do not correspond to visible colours. They have the property of being considerably more saturated than real colours, so that no real colour requires a negative contribution from any of the primaries for a colour match. X is a super- saturated purplish red; Y is a supersaturated form of the real spectral green of wavelength 520nm, and Z is a supersaturated form of the real spectral blue of wavelength 477nm. Also, the spectral matching function of the Y primary was chosen to exactly match the CIE standard photopic luminous efficiency function shown in Figure 6.5. It therefore carries all the luminance information about the colour.

The assumptions made in defining this observer were that the colour subtends a visual angle of 2° or less and the illuminant is not too dissimilar to daylight. These are easy conditions to meet in practice. The restriction on angular size is so that the image of patch of colour on the retina falls on the fovea, the area most sensitive to small changes in colour. This is the usual situation when looking at a coloured object.

Because the standard observer is a mathematically defined set of functions, the results of colour matching experiments can be simply calculated without actually having to do the experiment. Colour measurement can thus become an automated process.

6.2.2   Calculating tristimulus values

The colour of a light source is defined by the quantities of X, Y and Z primaries which would be required to match it. To calculate these quantities, the visible spectrum of 380 to 730nm is divided into a number of wavelength intervals and the intensity of the sample measured for each interval to produce its spectrum. A 10nm interval is commonly used. Then, for each primary in turn, the height of the sample spectrum is multiplied by the height of that primary's matching function. These products are summed across all wavelength intervals to calculate the overall quantity of that primary required for the match.

The resulting value (X, Y, Z) may be plotted on a 3D diagram, and will fall in the positive (XYZ) quadrant within the cone-shaped solid shown in Figure 6.8. Notice that the coordinate axes are not inside this solid; the XYZ primaries are imaginary colours. Black, corresponding to the lack of light, is at the origin. The curved boundary represents the tristimulus values of pure spectral colours. Because these are of a single wavelength, they represent the maximum attainable saturation. This boundary is called the spectral locus; all visible colours are inside or on it.


Figure 6.8: The CIE 1931 XYZ diagram.

Wavelengths from 400nm (violet) to 700nm (red) are shown; note that the wavelength spacing is not at all even. The straight line connecting the ends of the spectral locus corresponds to additive mixtures of the red nearest infrared and the violet nearest ultraviolet to produce purple.

In practice, the process of measuring the spectrum of a light source and obtaining its tristimulus values is automated. An instrument called a spectroradiometer measures the brightness at each wavelength interval with a photocell, and has the values of the standard observer matching functions at each wavelength interval stored internally. A small microprocessor performs the calculations, and readout is directly in the form of X Y and Z tristimulus values.

The visual appearance of a white surface, such as a piece of paper, varies slightly when seen under different illuminants, but still looks white. In contrast, the measured spectrum and tristimulus values will vary considerably. This phenomenon is termed colour constancy and is due to complex visual processing in the brain which tries to correct for slow changes in overall light level and quality. This is dependent on the overall state of adaptation of the eye. For example, a white sheet of paper will look white under the orangish glow of a tungsten light bulb or the bluish glare of a fluorescent striplight. This is because the illuminant fills the whole field of vision and provides the dominant adaptive stimulus. If a photograph is taken of the paper under tungsten light, there will be a marked orange tint to the white paper when the print is developed. This is because the amount of light reflected from the photograph is a small fraction of the total light entering the eye, which does not therefore adapt to it.

To account for this phenomenon, it is customary to define a white point which is taken to be the colour currently accepted as white. For emissive colour, this is one of the standard `white' illuminants.

6.3   Chromaticity

6.3.1   The CIE 1931 (xy) diagram

If a given colour is increased in brightness, the amount of light required from each primary to match the colour increases. The increases will be in proportion, so the ratio X:Y:Z remains constant as the colour moves away from the origin.

It is often useful to examine the colour of a sample separately from its brightness. To do this, the tristimulus values are normalized:
x =
X
X+Y+Z
y =
Y
X+Y+Z
z =
Z
X+Y+Z

Clearly, x+y+z=1 in all cases. It is therefore customary to drop the z coordinate and produce a 2D plot of x against y. This is equivalent to projecting the XYZ colour solid onto the X + Y + Z = 1 plane, which is shown in Figure 6.9.


Figure 6.9: The X + Y + Z = 1 plane on the CIE 1931 XYZ diagram.

The resulting diagram is called the CIE 1931 chromaticity diagram, and is shown in Figure6.10. It represents the perceptual attributes of hue and saturation, separated from luminance.


Figure 6.10: The CIE 1931 chromaticity diagram.

Chromaticity (x,y) values are sometimes encountered together with a Y value (xyY) to allow conversion back to XYZ.

One problem with this diagram is that it is not perceptually uniform. In other words, the distance between two colours which are just noticeably different varies across the surface of the diagram.

6.3.2   CIE 1976 uniform chromaticity scale (UCS)

Investigation of the perceptual uniformity of the 1931 chromaticity diagram, by plotting the size of a just noticeable colour change in various parts of the diagram showed that the portion at the top of the curve, in the green region, showed little variation in colour compared to the blue violet portion. This perceptual discrepancy has been likened to the distortions on flat maps of the world, in that it cannot be removed entirely by a linear projection of the 1931 chromaticity diagram. However, some projections will be better than others. One such projection was recommended by the CIE in 1976, the uniform chromaticity scale (UCS).

Also known as the u'v' diagram, from the labels on its axes, this is a projection of CIE 1931 XYZ space designed to produce much less distortion than the xy diagram.The axes are calculated as follows:

u' =
4X
X+15Y+3Z
  =
4x
-2x+12y+3
v' =
9Y
X+15Y+3Z
  =
9y
-2x+12y+3
The resulting diagram, shown below in Figure 6.11, is of the same general shape as the 1931 chromaticity diagram but stretched to give a more uniform distribution of colours.


Figure 6.11: The CIE 1976 uniform chromaticity scale diagram.

6.3.3   Putting chromaticity diagrams to work

Chromaticity diagrams have a variety of uses. They all share the property that an additive mixture of two colours will lie along the line connecting them. This can be used to calculate colourimetric data such as the dominant wavelength and excitation purity of a colour.

Dominant wavelength is determined by constructing a line from the white point, through the colour in question, to the spectral locus and reading off the wavelength. This is shown in Figure 6.12. Regardless of the spectral composition of the original colour, an equivalent colour sensation will be obtained by mixing monochromatic light of the dominant wavelength with the specified white. The excitation purity gives the proportions of this mixture. In this example, the excitation purity is 40%.


Figure 6.12: Dominant wavelength calculation.

In other words, the sample colour is made from the additive mixture of 40% spectral light of wavelength 540nm, and 60% of D65 white at the same luminance.

Chromaticity diagrams may be used to pick complementary colours by selecting points opposite to each other across the white point, and to design continuous colour scales by tracing straight or curved paths across the diagram. In general, however, a three dimensional colour model is used for this task so that the brightness of the colours can also be altered.

6.4   Colour models

Given the complexities of colour perception, it is useful to define a simplified, abstract method of succinctly specifying colour with a small number of parameters. Typically, the tristimulus theory is used so there are three parameters. There may be other underlying assumptions too. Often colour models are defined in terms of three primary colours, from which all others are obtained by mixture. In other cases, the three parameters represent more readily understood attributes such as lightness or saturation.

Considering the three parameters to be orthogonal axes produces a geometric colour space. The geometric position of a colour in this space can be used to see its relationship with other colours.

6.4.1   Primary colours

The choice of `primary' colours depends on a number of factors:

If the primaries can be negative and are not constrained by hardware, any primaries can be used. A single primary is represented by a point on a chromaticity diagram; it can only produce that one colour at varying intensities. Two primaries produce a line segment on a chromaticity diagram. Any colour on that segment can be produced by a non-negative mixture of the two primaries. If negative values for primary colours are allowed, the line segment can be extended out from each primary to the spectral locus.

Three primaries define a plane, and so any visible colour can be specified with any arbitrary choice of primaries provided negative values are allowed. If primaries cannot take negative values, only colours within the central triangle can be produced. In this case, it makes sense to maximize the area of this triangle by aligning it with the broadly triangular shape of the chromaticity diagram. This gives one primary somewhere near the far red corner, one in the green corner and one near the far violet corner.

Another way to increase the range of colours is to use more primaries. For example, with five primaries all colours within the pentagon can be produced, and in more than one way. Removing any one primary reduces the number of colours that can be produced.

6.4.2   Colour models

6.4.2.1   CIE 1931 XYZ

This colour space has already been discussed; it is the primary colour space for colourimetric measurement and the basis for other CIE colour spaces. It has the advantage of being rigorously defined, and an international standard. Whilst good for presenting a description of an existing, measured colour, it is not particularly easy to use for specifying new colours. This is because the primaries are not visible colours; while they are always positive, the axes lie outside the range of visible colour.

6.4.2.2   1976 CIELUV

If the luminance of a colour is divided by that of some reference white, a relative luminance scale from 0 to 100% (black to white) is obtained. Measured luminance, however, does not correspond well to perceived lightness; the scale looks markedly non uniform, with all the dark colours bunched up at one end. The CIE has recommended a non-linear formula for lightness, L* , which corresponds more closely to the perceived sensation. The medium, 50% grey occurs at L*=50 .

L*= ì
ï
í
ï
î
116(Y/Yw)
1
3
 
 for  Y/Yw>0.008856
903.3(Y/Yw) for  Y/Yw£ 0.008856
Yw is the Y tristimulus value for the reference white, in other words that white to which the eye is adapted. For most purposes, a standard illuminant such as D65 is used as the reference white.

The CIE has recommended a uniform, 3 dimensional colour space called the CIE 1976 (L*u*v*) colour space. It is commonly referred to as CIELUV, and may be considered a uniform version of the CIE 1931 XYZ space.

The formulae are:

u* = 13L*(u'-uw')
v* = 13L*(v'-vw')
where uw' and vw' are the UCS coordinates of the chosen reference white. These formulae correspond to translating the origin of the UCS diagram to the white point and scaling the relative chromaticity coordinates by the lightness so that the geometrical distance between two colours is reduced as they are made darker. This takes account of the fact that dark colours look more alike than light ones, even when the chromaticities are the same. The resulting colour space therefore forms a cone-like solid. Black, at L*=0 is thus a single colour at the apex of this cone.

6.4.2.3   CIELCH

As the spectral colours form a loop around the origin, it is possible to define a hue angle huv which specifies hue with a single numerical value. The positive u* axis is defined to be 0° , and angles are measured anti-clockwise.
huv=arctan (
v*
u*
 )

An advantage of this is that hue is a readily understood concept. The colours of the rainbow are arranged in a circle. The distance from the achromatic L* axis may then be used as a measure of chroma, or colourfullness:
Cuv*=(u*)2+(v*)2

Lightness, chroma and hue angle define an alternative, polar form of CIELUV. This is easier to use for mixing colours than CIELUV.

6.4.2.4   RGB (Red, green, blue)

It is sometimes convenient or customary to specify colour directly in the native colour space of a particular device. In the case of devices which use emitted light, such as colour monitors, an additive geometrical space can be produced.

This colour space is commonly used, and corresponds to the input data for a specific colour CRT computer monitor. The three primaries are the particular colours emitted by the three phosphors. It is therefore highly device specific; the same colour will be specified as two different sets of numbers on two different monitors. The parameters are the quantities of red, green and blue light to emit, generally in the range 0 to 1.

One strength of the RGB colour space is that it is a unit cube, and thus all possible values of R,G,B correspond to realizable colour. This makes it convenient from a programming point of view, in that range checking is straightforward.

A major weakness is that colours specified in RGB space are not at all perceptually uniform, and it is not sensible to measure colour differences in RGB space.

If the chromaticity coordinates of the monitor phosphors are known, and also both the chromaticity and luminance of the white produced by equal quantities of red, green and blue, it is possible to inter-convert between RGB and the CIE colour spaces.

RGB colour space is widely used in computer graphics. It is adequate for use in situations where producing different colours is more important than portability or reproducibility.

6.4.2.5   HSV (Hue, saturation, value)

Saturation is calculated from:

S*=
C*
L*
Chroma is clearly seen as independent of lightness.

Specifying colour is more convenient if hue, chroma and lightness are separate parameters. There are two transformations of RGB space used to achieve this: HLS and HSV.

The major diagonal of the RGB cube, from black at (0,0,0) to white at (1,1,1) forms an achromatic axis or gray scale. If the cube is rotated so that the white corner points towards the viewer and the black corner points away, as in Figure 34, a hexagon is seen with hues radiating around the achromatic axis. The HSV colour space uses this concept to define a hue angle, saturation and a third parameter, value, which broadly corresponds to lightness. HSV is thus a polar coordinate model, and these terms are analogous to, but not identical with, the similarly named terms in the LCH model.

The space is a cylinder centered on the achromatic axis. Value is the distance along this axis, saturation is the radial distance from it. Hue is an angular measure with 0 representing red and 180 representing cyan (a greenish blue).

Because HSV uses saturation rather than chroma, the perceived change in colour as saturation varies between 0 and 1 is less for dark (low value) colours than for light (high value) colours. To compensate for this, the HSV colour space is often shown distorted to form a cone rather than a cylinder. Other diagrams show HSV as a hexcone, to reinforce the link with RGB. However, saturation still ranges from 0 to 1 regardless of value or hue so these changes do not represent the geometric space accurately.

Being a transformation of RGB space, HSV shares the advantage that all possible values of H,S and V correspond to displayable colours. In addition, it is easier to mix colours than in RGB because the three parameters correspond more closely to perceptual attributes. On the other hand, HSV is just as device specific as RGB so descriptions of colours in HSV are not portable. Like RGB, only displayable colours can be specified.

Unlike CIELUV, HSV space is not perceptually uniform. Equal increments of hue angle do not produce smooth changes of perceived hue. Also, the three parameters are not independent. For example, a pure yellow and a pure blue both have S=1, V=1 yet the yellow will have a significantly higher luminance and be perceptually lighter than the blue.

6.4.2.6   HLS (Hue, lightness, saturation)

Similar to HSV, this colour model has a lightness axis rather than a value axis. Pure colours have a saturation of 0.5, rather than 1.0 in HSV. HLS may be considered a simple deformation of HSV produced by moving the white point as far above the pure colours as the black point is below them. Like HSV, it is a cylindrical colour space but is often drawn as a cone - in this case, a double ended one.

HLS, like HSV, is simply another representation of RGB space.

6.4.2.7   CMY (Cyan, magenta, yellow )

CMY is sometimes presented as a colour space, and corresponds to the input data for colour printing. However it deals with the proportions of real pigments rather than abstract colours. Furthermore, mixing two colours is not additive, which makes the representation of CMY as a geometric solid of little value. Specification of colours in CMY, even when the CIE tristimulus values of the inks are known, is complicated by a great many factors. A variation of CMY adds black ink, and is called CMYK. (Black is referred to as K rather than B to avoid confusion with blue in RGB).

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