0441
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`Volkswagen 1011 - Part 5 of 6
`
`

`
`CDLDIJR AND THREE DIMENSIONAL SPACE
`
`history that began with isaac Newton, but it was only in the twentieth century
`that numerical systems became important industrially.
`The answer to the question ‘why is colour specified by three numerical
`labels?‘ is that we have three different types of cone in our retinas which have
`different sensitivities to different wavelengths (Figure l5.?[a}J. Light can be spec-
`ified physically as a spectral power distribution or SPD — the oblective measure-
`ment of light energy as a function of wavelength - and we should be able to
`categorize the effect of any SPD on a human observer by three weights — the rel-
`ative response of the three different types of cone, And so it happens that we can
`visually match a sample colour by additively mixing three coloured lights. We
`can, for example, match a sample or target colour by controlling the three inten-
`sities of a red, green and a blue light. However, note the important point that in
`matching with primary colours red, green and blue we are not basing the
`labelling of an SP1) on the cone specb'al sensitivity curves, but are using the
`human vision system to match colours with a mix of primaries. To do this for all
`colours on a wavelength-by-wavelength basis leads to spectral sensitivity curves
`that our retinas would have if the cones responded maximally to these colours.
`The reason for this somewhat convoluted approach is that we can derive these
`functions easily from colour matching experiments; precise knowledge of the
`actual spectral sensitivity curves of the retina was harder to come by.
`Thus numerical specification of colour is by a triple of primary colours. Most,
`but not all, peroeivable colours can be produced by additively mixing appropri-
`ate amounts oi three primary colours (red, green and blue, for example]. if we
`denote a colour by C, we have:
`
`C=rIl+gG+I:Il!
`
`where r, g and b are the relative weights of each primary required to match the
`colour to be specified. The important point here is that this system, even though
`it is not specifying information related directly to the 51*!) of the oolour, is say-
`ing that a colour (3 can be specified by a numerical triple because if a matching
`experiment was performed an observer would choose the components r, g, b to
`match or simulate the colour (3.
`
`in a computer graphics monitor a colour is produced by exciting triples of
`adjacent dots made of red, green and blue phosphors. The dots are small and the
`eye perceives the triples as a single dot of colour. Thus we specify or label colours
`in reality using three primaries and the production of colours on a monitor is
`also specified in a similar way. However, note the important distinction that
`colour on a monitor is not produced by mixing the radiation from three light
`sources but by placing the light sources in close proximity to each other.
`Unfortunately in computer graphics this three-component specification of
`colour together with the need to produce a three-component RGB signal for a
`monitor has led to a widely held assumption that |ight—object interaction need
`only be evaluated at three points in the spectrum. This is the ‘standard’ l-iGl3 par-
`adigm that tends to be used in Phong shading, ray tracing and radiosity. if it is
`intended to simulate accurately the interaction of light with objects in a scene,
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`cotoua mo cotuwren oaatn-tics
`
`then it is necessary to evaluate this interaction at more than three wavelengths;
`otherwise aliasing will result in the colour domain because of undersampllng of
`the light distribution and obiect reflecrivity functions. Of course, aliasing in the
`colour domain simply consists of a shift in colour away from a desired effect and
`in this sense it is invisible. ["l”'his is in direct contrast to spatial domain aliasing
`which produces annoying and disturbing visual arlefa-sis.) Colours in most com-
`puter graphics applications are to a great extent arbitrary and shifts due to inac-
`curate simulation in the colour domain are generally not important. It is only in
`applications where oolour is a subtle part of the simulation, say. for example, in
`interior design, that these effects have to be taken into account.
`Given that we can represent or describe the sensation of colour. as far as
`colour matching experiments are concerned, with numeric labels, we now face
`the question: which numbers shall we use? This heralds the concept of different
`colour spaces or domains.
`it may he as we suggested in the previous section, that a calculation or ren-
`dering domain be a wavelength or spectral space. Eventually, however, we need
`to produce an image in Reflmertimr space to drive a particular monitor. ‘What about
`the storage and communication of images? Here we need a universal standard.
`RGBm1m. spaces, as we shall see, are particular to devices. These devices have
`different garnuts or colour ranges all of which are subseu of the set of perceiv-
`able colours- A universal space will be device independent and will embrace
`all perceivable colours. Such a space exists and is known as the CIE KY2.‘ stan-
`dard. A CIE triple is a unique numeric label associated with any perceivable
`oolour.
`
`Another requirement in computer graphics is a facility that allows a user to
`manipulate and design using colour. it is generally thought that an interface that
`allows a user to mix primary colours is anti—intuitive and spaces that are inclined
`to perceptual sensations such as hue, saturation and lightness are preferred in
`this context.
`'
`
`We now list the main colour spaces used in computer imagery.
`
`[1] Chi XYZ space: the dominant international standard for colour specification.
`A colour is specified as a set of three tri-stimulus values or artificial primaries
`XYZ.
`
`[2] Variations or transfomtations of CIE KY2 space (such as Gil‘. :-ry‘r" space} that
`have evolved over the years for different contexts. These are transfonns of
`CIE KY2 that better reflect some detail in the perception of colour, for
`example. perceptual linearity.
`
`Spectral space: in image synthesis light sources are defined in this space as :1
`wavelength samples of an intensity distribution. Object
`reflectivity is
`similarly defined. A colour specified on a wavelength—by—waveiength basis is
`how we measure colour with a device such as a spectrophotometer. As we
`have pointed out, this does not necessarily relate to our perception of an
`5-PD as one colour or another. We synthesize an image at tr wavelengths and
`then need to ‘reduce’ this to three components for display.
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`0443
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`coloua mo TI-FREE-DIMENSIONM. sract
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`(E3)
`
`(4) RGB space: the ‘standard’ computer graphics paradigm for Phong shading.
`This is just a three-sample version of spectral space. light sources and obiect
`reflectivity are specified as three wavelengths:
`lied. Green and Blue. We
`understand the primaries It. (3 and B to be pure or saturated colours.
`
`RGBms.m. space: a triple in this space produces a particular colour on a
`particular display. In other words it is the space of a display. The same triple
`may not necessarily produce the same colour sensation on different
`monitors because monitors are not calibrated to a single standard. Monitor
`RG35 are not pure or saturated prlrnaries because the emission of light from
`an excited phosphor exhibits a spectral power distribution over a band of
`frequencies. If the usual three-sample approach is used in rendering then
`usually whatever values are calculated in RGB space are assumed to be
`weights in |tGBm.u.. space. if an is sample calculation has been performed
`then a device-dependent transformation is used to produce a point
`in
`Efifinhdtw space.
`
`{6} H51? space: a non-linear transfonnatlon oi RG5 space enabling colour to be
`specified as Hue. Saturation and Value.
`
`(7) YIQ space: a non-linear transformation of RGB space used in analogue TV.
`
`We will now deal with the issues surrouncllng these colour spaces. We will start
`with RGB space because it is the most familiar and easiest to use. We will then
`look at certain problems that lead us on to consideration of CIl:'. space.
`
`RGB space
`
`Given the subtle distinction between {4} and {5} above we now describe R-GB
`space as a general concept. 11iis model is the traditional form of colour specifi-
`cation io computer imagery. it enables, for example. diffuse reflecfion coeffi-
`cients in shading equations to be given a value as a triple (ll, G, B]. In this system
`(It), 0. [ll is black and (1, 1,. 1] is white. Colour is labelled as relative weights of
`three primary colours in an additive system using the primaries Red, Green and
`Blue. The space of all colour available in this system is represented by the RGB
`cube (Figure 15.2 and Figure 15.3 {Colour Plateil. important points oonoeming
`RGB space are:
`
`(1)
`
`It is perceptually non-linear. Equal distances in the space do not in general
`correspond to perceptually equal sensations. A. step between two points in
`one region of the space may produce no perceivable difference; the same
`increment in another region rnay result in a noticeable colour change. in
`other words, the same colour sensation rnay result from a multiplicity of
`RGB triples. For example. it each of RGB can vary between 0 and 255, then
`over 16 million unique RG3 codes are available.
`
`(2) Because of the non-lirrear relationship between RGB values and the Intensity
`produced at each phosphor dot {see Section 15.5}, low IIGB values produce
`
`0444
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`cotoun alto com-urea ctunucs
`
`Figure is:
`The FIGB colour solid. See
`also Figure 15.3 [Colour
`Plate).
`
`Yellow
`
`small changes in response on the screen. its many as Bi) steps may be
`necessary to produce a ‘just noticeable difference’ at low intensifies; whereas
`a single step may produce a perceivable difference at high intensities.
`{3} The set of all colours produced on a computer graphics monitor, the KGB
`space, is always a subset of the colours that can be perceived by humans.
`This is not peculiar to RGB space. any set of three visible primaries can only
`produce through additive mixing of a subset of the percelvable colour set.
`It is not a good colour description system. Without considerable experience,
`users find it difficult to give RGB values to colours known by label. What is
`the RGE value of ‘medium brown’? Once a colour has been chosen it may
`not be obvious how to make subtle changes so the nature of the colour. For
`example, changing the ’vividness' of a chosen colour will require unequal
`changes in the RGB components.
`
`(4)
`
`The Hsit‘ single hexcone model
`
`The H{ue] Siaturation Walue} or single heiccone model was proposed by A.H..
`Smith in 1998 [Smith I9.'r'8}. its purpose is to facilitate a more intuitive interface
`for colour than the selection of three primary colours. The colour space has the
`shape of a hexagonal cone or hexcone. The H51’ cone is a non-linear transfor-
`mation of the RGB cube and although it tends to be referred to as a perceptual
`model, it is still just a way of labelling colours in the monitor gamut space.
`Perceptual in this oontext means the attributes that are used to represent the
`colour are more akin to the way in which we think of colour; it does not mean
`that the space is perceptually linear. The perceptual non-linearity of KGB space
`is carried over into HSV space;
`in particular, perceptual changes in hue are
`distinctly non-linear in angle.
`
`0445
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`cotourr mo runes-om eusiomu space @
`
`It can be employed in any context where a user requires control or selection
`of a colour or colours on an aesthetic or similar basis. it enables control over the
`
`range or gamut of an RGB monitor using the perceptually based variables Hue,
`Saturation and Value. This means that a user interface can be constructed where
`
`the effect of varying one of the three qualities is easily predictable. A task such
`as make a colour brighter, paler or more yellow is far easier when these percep-
`tual variables are employed, than having to decide on what combinations of
`RGB changes are required.
`The H5? model is based on polar coordinates rather than Cartesian and H is
`specified in degrees in the range CI to 360. One of the first colour systems based
`on polar coordinates and perceptual parameters was that due to ‘ivlunsell. His
`colour notation system was iirst published in 1905 and is still in use today.
`Munsell called his perceptual variables Hue, Chroma and Value and we can do
`no better than reproduce his definition for these. Chroma is related to saturation
`— the term that appears to be preferred in oom puter graphics.
`iilunselI’s definitions are:
`
`I Hue: ‘It is that quality by which we distinguish one colour family from
`another, as red from yellow, or green front blue or purple.‘
`
`I Chroma: ‘it is that quality of colour by which we distinguish a strong colour
`from a weak one; the degree of departure of a colour sensation from that -of
`a white or grey; the intensity of a distinctive hue; colour intensity.’
`
`Value: ’lt is that quality by which we distinguish a light colour from a dark
`one.’
`
`The Munseii system is used by referring to a set of samples — the Munseli
`Book of Colour. These samples are in ‘inst discrimir1able' steps in the colour
`space.
`
`The HSV model relates to the way in which artists rnix colours. Referring to
`the difficuity of mentally imagining the relative amounts of ii, G and B required
`to produce a single colour, Srrdth says:
`
`it is not
`Try this mixing technique by mentally trarying RGB to obtain pink or brown.
`unusual to have difficulty. .
`.
`. the following [H51-"] model mimics the way an artist mixes
`paint on his palette: he chooses a pure hue, or pigment and lightens it to a tint of that hue
`by adding white, or darkens it to a shade of that hue by adding black, or In general obtains
`a bone of that hue by adding some mixture of white and black or grey,
`
`in the HSV model, varying H corresponds to selecting a colour. Decreasing
`S {desaturating the colour} corresponds to adding white. Decreasing V
`ldevaiulng the colour) corresponds to adding black. The derivation of the
`transform between RGB and HSV space is easily understood by considering a
`geometric interpretation of the hexcone. if the RGB cube is proiected along its
`main diagonal onto a plane normal to that diagonal, then a hexagonal disc
`results.
`
`The following correspondence is then established between the six RGB
`yertices and the six points of the hexcone in the HSV model:
`
`0446
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`cDI.OUll mo comers: cults-mes
`
`RGB
`
`I100}
`(110)
`{D10}
`(till)
`(001)
`{I01}
`
`HSV
`
`{I}, 1. 1)
`{Gt}. 1, 1}
`(120, 1, 1}
`(180, 1, 1]
`i240. 1. 1}
`(300, 1, I)
`
`red
`yellow
`green
`cyan
`blue
`magenta
`
`where H is measured in degrees. This hexagonal disc is the plane containing V s
`1 in the hexcone model. For each value along the main diagonal in the RGB cube
`{increasing blackness) a contained sub-cube is defined. Each sub-cube defines a
`hexagonal disc. The stack of all hexagonal discs makes up the HS? colour solid.
`Figure 15.4 shows the H5‘! single hexcone colour solid and Figure 15.5
`(Colour Plate) is a further aid to its interpretation showing slices through the
`achromatic axis. The right-hand hali of each slice is the plane of constant H and
`the ieft—hand half that of H + 130.
`
`Apart from perceptual non-linearity another subtle problem implicit in the
`HSV system is that the attributes are not themselves perceptually independent.
`This means that it is possible to detect an apparent change in Hue. for example,
`when it is the parameter Value that is actually being changed.
`Finally, perhaps the most serious departure from perceptual reality resides in
`the geometry of the model. The colour space labels all these colours reproducible
`on a computer graphics monitor and implies that all colours on planes of con-
`stant V are of equal brightness. Such is not the case. For example, maximum
`intensity blue has a lower perceived brightness than maximum intensity yellow.
`We oonclude from this that because of the problems of perceptual non-linearity
`and the fact that different hues at maximum V exhibit different perceptual val-
`ues, representing a monitor gamut with any ‘regular’ geometric solid such
`as a cube or a hexcone is only an approximation to the sensation or colour
`and this fact means that we have to consider perceptually based colour spaces.
`
`Figure 15.4
`HSV single hexcone colour
`solid. See also Figure is.s
`(coma: Plate].
`
`3{53tiII'c'|liDI'I]
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`0447
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`cocoon, mroruuumon mo PERCEPTUAL sources
`
`A simpler way of expressing this fact is to reiterate that colour is a perceptual sen-
`sation and cannot be accurately labelled by dividing up the RG3 voltage levels
`of a monitor and using this scale as a colour label. This is essentially what we are
`doing with both the RGB and the HSV model and the association of the word
`‘perceptual’ with the HS? model is unfortunate and confusing.
`
`"(IQ space
`
`YIQ space is a linear transfonnation of RG1! space that is the basis for analogue
`TV. Its purpose is efficiency in terms of bandwidth usage (compared with the
`RG13 form} and to maintain compatibility for black and white TV {all the
`information required for black and white reception is contained in the in’
`component).
`
`‘1’
`l
`
`Q
`
`0.144
`I153?
`0.299
`= 0.596 -{L2?5 -0.321
`
`0.212 -0.523
`
`0.311
`
`R
`G
`
`5
`
`Note that the constant matrix coefficients mean that
`
`the transformation
`
`assumes that the RGB components are themselves defined with respect to a stan-
`dard [in this case an MISC definition]. The Y component is the same as the CIE
`in’ primary (see Section 15.3.1] and is called luminance. Colour information is
`‘isolated’ in the i and Qcomponents {equal RGB components will result in zero
`1 and Q values}. The bandwidth optimization oornes about because human
`beings are more sensitive to changes in luminance than to changes in colour in
`this sense. We can discriminate spatial detail more finely in grey scale changes
`than in colour changes. Thus, a lower bandwidth can be tolerated for the l and
`Q oomporients resulting in a bandwidth saving over using RGB components.
`Colour representations where the colour and luminance infomtation are sep-
`arated are important in image processing where we may want to operate on
`image stmcture without affecting the colour of the image.
`
` w -'_“§\."I.‘s‘.".'{-,U_'r':'_'fiI2'.-TE-.5!‘lH.'?'..'Il£-D‘_L'-U*!GFb i3E§ '
`
`Colour, information and perceptual spaces
`
`We now come to consider the use of perceptual spaces in computer imagery. in
`particular we shall lo-olr at the CIE XYZ spaoe — an international numerically
`based colour labelling system first introduced in 1931 and derived irom colour
`matching experiments.
`To deal with colour reality we need to manipulate colours in a space that bears
`sortie relationship to perceptual experience. We have already alluded to applica-
`tions where such considerations may be important. For example, in CMLD for
`interiors, the design of fabrics or the finish on such expensive consumer durables
`as cars. it will be necessary for computer graphics to move out of the arbitrary
`RGB domain into a space where colour is accurately simulated. Of course, in
`
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`cotoua mo cotutrrrrsit onartucs
`
`attempting to transmit an illusion of reality in a computer graphics simulation
`there are many other factors involved - surface texture, the macroscopic nature
`of the colour (metallic paint or ordinary gloss paint, for example) and geomct'ri~
`ca] accu racy, but at the moment in computer graphics it is the case that the RGB
`triple is the tie focto standard for rendering.
`Colour is used much in visualization applications to oommunicate numerical
`information. This has a long history. Possibly the most familiar manifestation is
`a coloured terrain map. Here colours are chosen to represent height.
`Traditionally colours are chosen widr green representing low heights. Heights
`from O to Iiitim may be represented by lightening shades of green through to
`yellow. Darkening shades of brown tnay represent the range 1000 to 3000 rn.
`Above 3i.‘l-U0 m there are usually two shades of purple, and white is reserved for
`t5DIJCIm and above.
`This technique has been used in image processing and computer graphics
`where it is called pseudo-colour enhancement. It is used most commonly to dis-
`play a function of two variables. flat, y], in two space where before such a func-
`tion would have been displayed using 'iso-f'contours.
`in pseudo-oolour
`enhanoement a deliberately restricted colour list (of, say, 1|) oolours] is dlosen
`and the value of fis mapped into the nearest oolour. The function appears like a
`terrain map with islands of one colour against a background of another.
`In computer graphics and image processing the most popular mapping of
`fix, yl into colour has been some variation of the rainbow colours with red used
`to represent high or hot and blue used for low intensity or cold — in other words
`a path around the outer edge of H51? space. One of the problems with this map-
`ping is that depending on the number of colour steps used, transitions between
`different oolours appear as false contours. Violent colour discontinuities appear
`in the image where the function f is continuous. There is a contradiction here:
`we need these apparent disoontinuities to highlight the shape of the function
`but they can easily be interpreted as transitions in the function where no tran-
`sition exists. This is particularly true in non-mathematical images which are not
`everywhere continuous to start with. Natural discontinuities may exist in the
`function anyway, say in a medical image made up of the response of a device
`to different tissue. The appearance of false contours in such an image may be
`undesirable.
`
`Thus, whether the oontours add to or subtract from the perception of
`the nature and shape of f depends in the end on the image context. The
`effect of false contours is easily diminished by adding more colours to the
`mapping but this may have the effect of making the function more difficult to
`interpret.
`The use of perceptual colour spaces in the context of numerical information
`is extremely important. if an accurate association between colours and numeric
`information is required, then a perceptually linear colour scale should be used.
`We discussed in Section 5.2.1 the perceptual non-linearity of ROB space and it
`is apparent that unless this factor is dealt with, it will interfere with the associa-
`tion ot a colour with a numeric value. There is no good reason. apart from
`
`0449
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`
`colour, inroemation mo eettceetuai. sr-aces
`
`cultural associations like the example of the terrain map coding in cartography,
`why a hue circle should be used as a pseudo-colour scale.
`The use of pseudo—colour in two space to display iunctions of two spatial vari-
`ables has been around for many years. The last ten years have seen an increas-
`ing application of three-dimensional computer graphics techniques in the
`visualization of scientific results and simulations (an area that has been awarded
`the acronym VLSC}. The graphim tech nlques used are mainly animation, volume
`rendering (‘both dealt with elsewhere in this text] and the use of pseudocolour
`in three space, which we will now examine.
`Figure 13.1 (Colour Plate) illustrates an application. It shows an isosurface
`extracted from a Navier—Stoites simulation of a reverse flow pipe oombustor. in
`this simulation the primary gas flow is from leit to right. Air is forced into the
`chamber under compression at the left, and dispersed by two fans. Eight fuel
`iets, situated radially approximately halfway along the combustor, are directed
`in such a way as to send the fuel mixnire in a spiralling path towards the iront
`of the chamber. Combustible mixing takes place in the central region and thrust
`is created at the exhaust outlet on the right. The isosui-faces shown connect all
`points where the net flow along the long axis is zero - a zero velocity surface.
`Such an lsosu rface can be displayed by using conventional three-dimensional
`rendering techniques as the Illustration demonstrates. In the second Illustration
`we have sought to superimpose a pseudo-colour that represents temperature. A
`spectral colour path, from blue to magenta, around the circumference of the
`HSV cone is used.
`
`Thus, in the same three-dimensional image we are trying to represent two
`functions simultaneously. First, the shape of an isosurface and, second. the tem-
`perahire at every point on the iscsurface. Perceptual problems arise in this case
`because we are using colour to represent both shape and temperature, whereas
`nonnally the colour is experienced as an association with a single phenomenon.
`For example, it tends to be difficult in such representations. to Interpret the
`shape of the isosurface in regions at rapidly varying hue or temperature.
`Nevertheless representational sche_mes like this are becoming commonplace in
`visualization techniques. They represent a ltind of summary of complex data
`that, prior to the use of threedimensional computer graphics, could only be
`examined one part at a time. For example, the simulation in the illuslration may
`have been investigated by using a rotating cross-section. This leaves the difficult
`task of building up a three—dimensional picture of the data to the brain of the
`SHEWEI.
`
`CIE KY2 space
`
`We have discussed in previous sections that we need spectral space to try to simu-
`late reality. This implies that we need a way of ‘reducing’ or converting spectral
`space calculations for a monitor display. Also, we saw that we need perceptual
`colour spaces for choosing mappings for pseudocolour enhancement. Another
`
`
`
`*"I-'-:5..i-+_---'-1'.-I.._=’r_.’.-e...-.1.‘-.5‘.-.-=~_—<-.:-Ini.'._'.._
`
`
`
`
`
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`cotourr mo coinvurea can-arcs
`
`ttrisovr dlirre for perceptual colour spaces in computer graphics is for the storage and
`the communication of files within me computer graphics community and for
`oommunication between computer gr-aphicists and industries that use colour.
`The CD5 standard allows a colour to be specified as a numeric triple (X, Y, Z).
`CIE KY2 space embraces all colours peroeivable by human beings and it is based
`on experimentally determined colour matching functions. Thus, unlike the
`three previous colour spaces, it is not a monitor gamut space.
`The basis of the standard, adopted ir1 1931, was colour matching experinlents
`where a user controls or weights three primary light sources to match a target
`monochromatic light source. The sources used were almost monochromatic and
`were I1 = ?iIiO nm. I3 = 546.1 nm and B 2 435.8 nm. In other words the weights in:
`C=rIl+gG+bIi
`
`are determined experimentally.
`The result of such experiments can be summarized by colour matching func-
`tions. These are shown in Figure 15.d{b] and show the amounts of red, green and
`blue light which when acitiitively mixed will produce in a standard observer a
`monochromatic colour whose wavelength is given by it. That is:
`
`Ca. = [UL] + gilt) + bill
`
`For any colour sensation C which exhibits an SPD Plitl, r, g and b are given by:
`r = it IPl?-Jrilidlll
`
`s = ifi[Pl.1l3llldi3tl
`
`1* = K!‘ Pillbilidfll
`
`Thus, we see that colour matching functions reduce a colour C, with any shape
`of spectral energy distribution to a triple rgb. At this stage we should make the
`extremely important point that the triple rgb bears no relationship whatever to
`a triple RGB specified in the aforementioned (computer graphics} system. .-‘is we
`discussed in Section 15.2, computer graphic-ists understand the triple RGB to be
`three samples of the SPD of an illuminant or three samples of the rellectivity
`function of the object which are linearly combined in rendering models to pro-
`duce a calculated RGB for reflected light. in other words, we can render by work-
`ing with three samples or we can extend our approach to working with rt
`samples. In contrast the triple rgb is not three samples of an SPD but the values
`obtained by integrating the product of the SPD and each matching function. In
`other words, it is a specification of the SPD as humans see it (in terms of colour
`matching} rather than as a spectrophotometer would see It.
`There is, however, a problem in representing colours with an additive primary
`system which is that with positive weights, only a subset of perceivable colours
`can be described by the weights it, g. b]. The problem arises out of the fact that
`when two colours are mixed the result is a less saturated colour. it is impossible
`
`0451
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`

`
`Figure ms
`The ‘evolution’ of the cue
`mlmlr matching l'1.|m:|iaI11.
`
`_
`_
`_
`Speclral 3-l‘ll5Il1\"Il')" curves
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`to form a highly saturated colour by superimposing colours. Any set of three
`primaries forms a bounded space outside of which certain perceival:-le highly
`saturated colours exist. in such colours a negative weight is required.
`To avoid negative weights the CIE devised a standard of three supersaturated
`(or non-realizable} primaries X, Y and 2., which, when additively mixed, will pro-
`duce all peroeivable colours using positive weights. The three corresponding
`matching functions xii], y(.'i.] and zit.) shown in Figure 15.5-{ct are always posi-
`tive. Thus we have;
`
`X = *1‘ Pfllxilldill
`
`1’= if I Piklrilldlll
`
`z = t _[1=(i.:rz{i.,ian.)
`where:
`
`it = 63!] for self—luminous oblects
`
`The space formed by the li‘i"Z values for all perceiirahle colours is CIE XYZ space.
`The matching functions are transformations of the experimental results. In addi-
`tion the i-{A} matching function was defined to have a oolour matching function
`that corresponded to the luminous efficiertc}-t characteristic of the human eye, a
`function that peaks at 550 nm [yellow-green}.
`The shape of the CIE KY2 colour solid is basically conical with the apex of the
`cone at the origin (Figure 15.?,i. also shown in this space is a monitor gamut
`which appears as a parallelepiped. If we compare this space to H5? space we can
`
`i’
`
`Figure 15¢
`{ai CIE KY1 solid.
`lb) #1 typical monitor
`gamut in EiE iii’: space.
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`View the solid as distorted H55.-' space. The black point is at the origins and the
`l-ls‘! space is deformed to embrace all colours and to encompass the fact that the
`space is based on perceptual measurements. if we consider, for example, the outer
`surface of the deformed oone, this is made of rays that emanate from the origin
`terminating on the edge of the cone. Along any ray is the set of colours of
`identical chromaticity [see the next section}.
`If a ray is moved in towards
`the white point, situated on the base of the deformed cone then we desaturate
`the set of colours specified by the ray. Within this space, the monitor gamut
`is a deformed (sheared and scaled) cube, forming a subset of the volume of
`perceiuable colours.
`
`CIE ity"l" space
`
`An alternative way of specifying the (K, Y, 2) triple is [1, y, Y] where {x, y) are
`known as chromaticity coordinates:
`
`LX
`
`+Y+Z
`
`Ix:
`
`- ._L
`V‘
`:~;+r+z
`
`Plotting it against y for all visible colours yields a two—dimensional fa, yjl space
`known as the CIE chromatlcity diagram.
`‘l'he wing-shaped CIE. chromaticity diagram (Figure 15.8] is extensively used
`in colour science. it encompasses all the perceivable colours in two—dimensional
`space by ignoring the luminance Y. The locus of the pure saturated or spectral
`colours is formed by the cunred line from blue [-iilil nm) to red Uflfi nm}. ‘The
`straight line between the end points is known as the purple or magenta line.
`Along this line is located the purples or magentas. These are colours whose per-
`ceiyable sensation cannot be produced by any single monochromatic stimulus,
`and which cannot be Isolated from daylight.
`Also shown in Figure 15.8 is the gamut of colours reproducible on a computer
`graphics monitor from three phosphors. The monitor gamut is a triangle formed
`by drawing straight lines between three KGB points. The RGB points are con-
`tained within the outermost curve of monochromatic or saturated colours.
`
`Examination oi the emission characteristics of the phosphors will reveal a spread
`about the dominant wavelength which means that the colour contains white
`light and is not saturated. When, say, the blue and green phosphors are fully
`excited their emission characteristics add together into a broader band meaning
`that the resultant colour will be less saturated than blue or green.
`The triangular monitor gamut in CIE icy space is to be found in most texts
`dealing with colour science in oomputer grap