WO1995010160A1

WO1995010160A1 - Method and apparatus for decoding colour video signals for display

Info

Publication number: WO1995010160A1
Application number: PCT/GB1994/002168
Authority: WO
Inventors: Ian Childs; Alan Roberts
Original assignee: British Broadcasting Corp
Current assignee: British Broadcasting Corp
Priority date: 1993-10-05
Filing date: 1994-10-05
Publication date: 1995-04-13
Anticipated expiration: 1996-04-05
Also published as: GB2282928B; GB2282928A; GB9320489D0

Abstract

A video display apparatus receives a transmitted colour video signal coded using three system primaries (Rs, Gs, Bs) and decodes the signal for display on a device using four display primaries. The four display primaries are independent, in that no display primary can be expressed as a combination of another two display primaries, and so define a quadrilateral in a chromaticity diagram. A fifth, imaginary display primary is determined as a linear combination of the third and fourth display primaries and the quadrilateral divided into triads defined respectively by the first, fourth and fifth, first, fifth and second, and second, fifth and third display primaries. The received video signal is decoded by three matrix arithmetic units (12, 14, 16), one for each triad, and drive signals for the first to fourth display primaries calculated. For each pixel, an arithmetic unit output producing no negative display drive signals is then selected and its output switched by switches (20, 22, 24) to drive a four-primary display device (2).

Description

METHOD AND APPARATUS FOR DECODING COLOUR VIDEO SIGNALS FOR DISPLAY

This invention relates to a method and apparatus for decoding colour video signals for display.

The colorimetry of television displays has been a relatively stable field, in which there have been fairly few developments since the move from black-and-white to colour in the late 1960s. Recently, however, there has been a resurgence of interest in research associated with television colorimetry, prompted by the development of new HDTV standards. A possible colorimetric coding system has been proposed in BBC Research Department Report 1990/2 published by BBC Research Department, Kingswood Warren, Tadworth, Surrey KT20 6NP, England, which describes a television system having one or more system primaries which cannot be realised in a practical display device because they are spectral or super-spectral. This system provides for a wider colour gamut and the use of true constant- luminance operation without unduly sacrificing compatibility with existing CRT (cathode ray tube) display. Thus, it would be possible to introduce a new HDTV or enhanced PAL service, operating with the improved colorimetric coding, without introducing excessive colour errors into the pictures displayed by receivers already in use.

In addition, the use of a coding method having a degree of compatibility with present-day displays results in the ability to monitor the pictures produced in the television studio while minimising the additional complexity that must be introduced into the display to achieve the necessary accuracy. A display monitor in such a system is able to reproduce accurately the range of colours coded by the new system only within the triangle defined by its display phosphors. The gamut of the system itself, however, is considerably larger than this, and embraces all of the presently- available real surface colours and a substantial proportion of the complete colour spectrum. If full advantage is eventually to be taken of this enlarged colour gamut, it will be necessary to develop new display techniques able to reproduce a wider range of colours .

The invention provides a method and apparatus as defined in the appendant independent claims . Preferred features of the invention are defined in the dependent subclaims.

In a television system having one or more system primaries which cannot be realised in a practical display device because they are spectral or super-spectral, using the method and apparatus according to the invention it may be possible to display much of the colour gamut of the system by using more independent display primaries than independent transmission primaries (independent meaning that no primary can be matched by a combination of positive multiples of the other primaries) .

At the present time, such an option could only be achieved in a CRT display by reducing the size of the mask apertures in the CRT shadow mask, and hence might be at the expense of a reduced electron-beam transmission efficiency. All other factors being equal, this could result in a lower light output; in addition, phosphors of the correct chromaticity would need to be manufactured, bearing in mind the other parameters (for example, low lag) that must be satisfied at the same time. This situation may not always persist, however. Projection displays (even those based on CRTs) are subject to different constraints to shadow-mask displays; use of four or more, rather than three, display tubes may even enhance the final brightness under these circumstances. Liquid-crystal displays, whether projection or direct-view, rely on an external source for the production of the emitted light, the colour being determined by suitable optical filtering. Illumination is either broadband or else by a series of narrow spectral lines produced by discharge lamps or phosphor excitation. Such techniques can allow a much freer choice of display colour parameters. For example, Figure 1 shows the characteristics of four colour filters which, when used to shape the wavelength spectrum produced by a normal quartz-halogen light source, are capable of producing primaries very close to the wavelengths 460, 514, 540 and 620 nm.

The selection of the colour primaries for an enhanced- colour-gamut display is only the first step in the complete process, however. It is also necessary to decode the incoming television signal into the drive signals for each of the display colours . This presents an interesting mathematical exercise, since there are only three incoming signal components - the luminance and two colour difference signals - from which it is necessary to derive, for example, four display signals. The process is therefore equivalent to solving three simultaneous equations in four unknowns and, in general, there are an infinite number of possible ways of achieving any particular displayed colour within the permissible gamut.

In order to define a unique set of display drive voltages for each incoming combination of RYB signals, therefore, it is necessary to impose an additional, somewhat arbitrary, set of constraints. A number of examples of such constraints and the solutions to which they lead are set out herein in the descriptions of specific embodiments of the invention.

Specific embodiments of the invention will now be described by way of example, with reference to the figures in which:- Figure 1 shows the characteristics of four colour filters for filtering a quartz-halogen light source to produce four primaries ;

Figure 2 is a CIE diagram showing the system primaries and white point for the HD (High Definition) Eureka system;

Figure 3 is the CIE diagram of Figure 2, also showing two green display primaries;

Figure 4 shows a block diagram of an implementation of a

4-primary display; Figure 5 is a CIE diagram showing three green display primaries, one being a linear mixture of the other two;

Figure 6 shows a decoding circuit for decoding four display drive signals;

Figure 7 is a CIE diagram showing the regions outside the colour quadrilateral of Figure 5; and

Figure 8 shows region 4 of Figure 7 in more detail .

1. Introductory theory

The three primaries of a proposed High Definition television system known as the Eureka system are shown in

Figure 2 which is a CIE 1931 chro aticity diagram, together with the spectrum locus and the balance point, D65, at which the three system primary signals are all equal to unity. The red is sited at 620 nm, blue at 460 nm. It can be seen that the "green" primary is unreal and therefore cannot be displayed by ANY means. For display purposes only this non-real transmission green may be replaced with two real greens, and the necessary four primary analysis applied to drive the four real primaries. The two greens chosen for this exercise are shown in Figure 3 as Green 1 at 540 nm and Green 2 at 514 nm. These wavelengths were chosen to maximise the displayable colour area.

The colour equation of a display using the system primaries is shown in Equation la which relates the system signals Rs Gs and Bs to the tristimulus values of the emitted light, X Y and Z. [X] [ ] [Rs] [Y] = [ Ms ] . [Gs]

[Z] [ ] [Bs] la where the values X Y and Z are the tristimulus values of the light in the CIE 1931 colour space. Any other colour space can be used, but CIE 1931 is convenient since the Y signal represents the true luminance of the colour in question.

The system matrix [Ms] is a 3 by 3 matrix of the tristimulus values of the system primaries in CIE 1931 space, which is derived by standard means as shown below in Section 2. The relationship between the system signals and the light entering a theoretical camera using these system primaries is:

lb

The transmission matrix [Mt] is another 3 by 3 matrix, of the tristimulus values of the CIE primaries in the colour space defined by the system primaries Rs Gs and Bs .

The analysis of a four primary display is strictly insoluble, but Equation lc shows the relationships between light output and display primaries : [X] [ ] [ Rd] [Y] = [ Md ] . [Gld] [Z] [ ] [G2d]

[ Bd] lc

The matrix, [Md] , is a 3 by 4 matrix of the tristimulus values of the display primaries, again in CIE 1931 colour space. Thus Equation lc can be expanded into Equation Id: [X] [Xr Xgl Xg2 Xb] [ Rd]

[Y] = [Yr Ygl Yg2 Yb] . [Gld]

[Z] [Zr Zgl Zg2 Zb] [G2d] [ Bd] Id

The tristimulus values of the display primaries are not known at this stage , but they are linearly related to the chromaticity coordinates of the primaries in the CIE 1931 colour space , thus Equation Id expands to become

Equation le :

[X] [l*xr ml*xgl m2*xg2 n*xb] [ Rd]

[Y] = [ l *yr ml*ygl m2 *yg2 n*yb] . [Gld] [Z] [l *zr ml* zgl m2 *zg2 n*zb] [G2d]

[ Bd] le

The linear sealers l , ml , m2 and n can be found by balancing the system to its white point . In this instance the white point is illuminant D65 , thus at the balance point :

[Xw] [l *xr ml*xgl m2*xg2 n*xb] [1]

[Yw] = [l*yr ml*ygl m2 *yg2 n*yb] . [1] [Zw] [ l* zr ml* zgl m2 *zg2 n*zb] [ 1] If [ 1]

This equation presents a problem since there are four unknowns and only three equations, thus there is an infinite number of solutions. An aspect of the present invention provides a method of overcoming this problem. The method involves dissecting the colour quadrilateral into overlapping or non-overlapping triangles.

2. Standard three-primary analysis method For a conventional tri-colour system in which the system and display use the same set of primaries, the relationships between light input, transmission signals and light output are shown in Equations la and lb above. In order to derive the system matrix [Ms] it is necessary to invoke a fourth colour at which the system signals are all equal to unity (Rs=Gs=Bs=l) , thus the display equation:

[X] = [ ] [Rs]

[Y] [ Ms ] . [Gs] [Z] [ ] [Bs] becomes, at balance: [Yw] [ ] [1] [Yw] = [ Ms ] . [1] [Zw] [ ] [1] 2b where Xw Yw and Zw are the tristimulus values of the balance point or white (usually illuminant D65) . This is an expression of one of Grassman's laws, which states that any colour can be matched by linearly mixing any three other colours provided that none of these can be matched by linearly mixing the other two colours.

The display matrix [Ms] is comprised of the tristimulus values of the system primaries, as yet unknown: [Xw] [Xr Xg Xb] [1] [Yw] = [Yr Yg Yb] . [1] [Zw] [Zr Zg Zb] [1] 2c

but since the tristimulus values are proportional to the chromaticity coordinates:

[Xw] [l*xr m*xg n*xb] [1] [Yw] = [l*yr m*yg n*yb] . [1] [Zw] [l*zr m*zg n*zb] [1] 2d

where 1 m and n are unknown constants of proportionality. Equation 2d yields three equations in three unknowns and can thus be solved. The inverse of the resulting matrix gives the transmission matrix for Equation lb.

The display matrix [Ms] is made up of the tristimulus values of the display primaries, in CIE 1931 space. The middle row of the matrix defines the luminance equation for these primaries. The act of 'balancing' a practical display device to the illuminant (D65) results in the actual display primaries having luminances each proportional to the relevant value in the luminance equation. No other values will do this.

If the display primaries are not identical to the system primaries, then two solutions are required, one for the system primaries, the other for the display primaries, and a transfer matrix is derived by multiplication as shown below. For the system primaries

[Rs] [ ]-l [X] [Gs] = [ Ms ] . [Y]

[Bs] [ ] [Z] 2e

For the display primaries :

[X] [ ] [Rd] [Rd] [ ] - l [X]

[Y] = [ Md ] . [Gd] [Gd] = [ Ms ] . [Y] [Z] [ ] [Bd] [Bd] [ ] [Z ] 2 f

And the relationship between them is :

[Rd] [ ] [ ] - 1 [Rs ] [Gd] = [ Ms ] . [ Md ] . [Gs]

[Bd] [ ] [ ] [Bs ] 2g

The matrix product can be evaluated as a transfer matrix [Mx] by conventional matrix multiplication and becomes a simple 3 by 3 linear matrix to be fitted in the receiver.

Again, this matrix comprises the tristimulus values of the system primaries in the colour space defined by the display primaries. Thus if any display primary is equal to the corresponding system primary, then its column in the matrix will be linearly scaled to the appropriate column of the ident matrix, the scaling being equal to the ratio of the luminances of this primary in the two balanced conditions . If all the display primaries equal the system primaries the matrix is the ident matrix.

Any colour reproduced by this receiver, lying in the colour gamut common to the two triangles formed by the system primaries and the display primaries, will be portrayed correctly. It should be noted here that this assumes matrix operations on linear signals only; any non-linearity (gamma) must be removed and re-applied after matrix conversions. It is possible to apply matrix arithmetic to non-linear signals, but the matrices will generally be different from those described here and will only produce approximate results.

The systems described by equations 2e to 2g may each be balanced to the same illuminant, or may be separately balanced to two different colours. For example, although the standard PAL domestic system is notionally balanced to D65, it is common practice to balance studio and outside broadcast cameras to the prevailing illuminant such that the display of a neutral reflectance surface has equal system signals and hence is shown at the balance point of the display, D65. This ensures that the capability of each drive signal is fully used, whether it be a system signal or a display signal. Whenever the scene contains a colour which is mathematically equal to one of the system primaries, only that system primary signal will be non-zero and will be unity if the luminance of the scene colour is numerically equal to the relevant Y term in equation 2c. Similar arguments hold for the display. This property does not necessarily apply in the multi-primary display described below.

3. Multi-primary analysis method The multi-primary problem can be overcome by dissecting the colour gamut of the display into triangles formed by sets of three of the display primaries, and using any analysis which produces only positive drive signals. Unfortunately, not all of thew triangles thus formed will contain the balance point of the system and so the mathematics of Section 2 cannot be used directly, also it may be difficult to set up the display device in practice. For a multi- primary display there are several solutions to this.

The display may be made using three primaries at a time forming triangles which do not overlap; overlapping triangles are then required only for setting up the display. This approach, of using contiguous non- overlapping triangles, might cause some difficulties if the implementation of the following mathematics is not sufficiently accurate; noise could cause fast switching between triangles resulting in unfamiliar effects.

As an alternative, overlapping triangles can be used and the switching between triangles can then employ hysteresis to avoid these effects. It is possible to calculate an analysis for a triad which uses two real primaries and one synthetic primary, made by linearly mixing two others .

The calculation processes required to produce the matrices which connect the transmission signals with the display primaries is as described in Section 2. The concept of balancing each display primary triad individually to an illuminant is retained, even though not all of the triads contain the white point. Any triad not containing the white point will produce a column in the display matrix containing only negative numbers, and the appropriate multiplier (l,m or n) is negative. This is only a mathematical problem, and does not render the problem insoluble as is shown below.

The matrices are found as follows :

First produce the system transmission and display matrices using the method described in Section 2 above (balancing to the illuminant, D65) . This gives the matrices [Ms] and [Mt] .

3a

3b

The system matrix [Ms] is not required except for the production of the transmission matrix [Mt] , however the multipliers Is ms and ns may be of use later in the balancing of analyses together.

Then form the matrix for the real display primaries .

[X] [Xpl Xp2 Xp3 Xp4 [Y] = [Ypl Yp2 Yp3 Yp4

[Z] [Zpl Zp2 Zp3 Zp4

3c

This is actually formed, at this time, from the chromaticity coordinates and unknown sealer k.

[X] [kl*xpl k2*xp2 k3*xp3 k4*xp4 ...] [PI]

[Y] = [kl*ypl k2*yp2 k3*yp3 k4*yp4 ...] . [P2] [Z] [kl*zpl k2*zp2 k3*zp3 k4*zp4 ...] [P3]

[P4] [etc] 3d

Take sets of three of the display primaries and form a 3 by 3 display matrix [Md] from the relevant columns from the full display matrix of equation 3d, thus for example:

[X] [kl*xpl k2*xp2 k3*xp3] [PI] [Y] = [kl*ypl k2*yp2 k3*yp3] . [P2] [Z] [kl*zpl k2*zp2 k3*zp3] [P3] 3e

and balance this to the white point (D65) using the procedure of Section 2. This will give the display matrix [Mpd] for these primaries and its inverse [Mpc] .

[PI] [ ]-l [X] [P2] = [ Mpd ] . [Y] [P3] [ ] [Z]

[ ] [X]

= [ Mpc ] . [Y]

[ ] [Z] 3f

The linear sealers kl, k2 and k3 are the values 1, m and n, which are of use in relating analyses to each other. Note that if the triad of primaries does not contain the white point, then one of the sealers will be negative and its column of the display matrix will be negative. Although this appears to be an impossibility, implying that the primary must ingest light in order to produce the white point, the problem will disappear in the matching process to be described below.

Finally multiply the matrix for equation 3f by [Ms] to obtain the display transfer matrix for these primaries :

[ ] [RS] = [ Mx ] . [Gs]

[ ] [Bs] 3g

and this is the linear matrix which must be included in the display device to drive these primaries for this solution. The matrix comprises the tristimulus values of Rs Gs and Bs in the colour space defined by Pi P2 and P3.

Note that all of these matrices will result in unity display primary drives at D65 since all the sets of three primaries are balanced to D65, but that each primary triad has its own display matrix and thus requires the display to have different gain settings for each primary in each set. The separate solutions must now be modified so that there is one unified display matrix and each solution produces drive signals correctly scaled to it. This process eliminates all gain controls between each matrix output and the display, except for one master control per primary which is used to set up the display.

Let us suppose that there are two solutions (a and b) which use the red display primary, they have sealers la and lb derived from the mathematics of Section 2 and these multipliers are the sealers for the red primary. This means that solution a produces la units of light per unit of drive signal, while solution b produces lb units of light per unit drive. This problem can be resolved by moving the sealers into the transfer matrices [Mx] by multiplying each coefficient in turn by la or lb as appropriate; the red primary is now scaled to unity. The resultant matrices will no longer produce equal drives for the white point, so each primary drive can be further scaled such that no matrix ever produces more than unity drive for any displayed colour. Choice of this sealer is at the discretion of the designer; the red column of the unified display matrix will comprise the chromaticity coordinates of the red primary multiplied by this new sealer. This process can be expanded to include more than two solutions, and to match all primaries as required. It is worth noting here that if any of the primary triads do not contain the white point, the resultant negative row in the transfer matrix will change sign in this process and produce sensible numbers. Examples are given in the numerical solutions in Appendix 1.

The calculation for a triad of display primaries using two real (PI, P2) and one synthetic is as follows. To illustrate the method, the synthetic primary Pm will be taken to be a linear mix of P3 and P4 , in the ratio a:b.

First decide on the linear mix ratio and calculate the chromaticity coordinates of Pm:

xpm = ( a * xp3 + b * xp4 ) / (a+b) ypm = ( a * yp3 + b * yp4 ) / (a+b) zpm = ( a * zp3 + b * zp4 ) / (a+b) = 1 - xpm - ypm 3h

Then proceed as before to find the display matrix and its inverse for the primaries PI P2 and Pm, noting that the resulting sealers are kl k2 and km. Continue to find the transfer matrix between these primaries and the system primaries. the transfer matrix can be expanded out into a 4 by 3 matrix by copying the Pm row into the P3 and P4 rows. Thus if:

[PI] [kOO kOl k02] [Rs] [P2] = [klO kll kl2] . [Gs]

[Pm] [k20 k21 k22] [Bs] 3i

then:

[PI] [kOO kOl k02] [Rs]

[P2] = [klO kll kl2] . [Gs]

[P3] [k20 k21 k22] [Bs]

[P4] [k20 k21 k22] 3j The sealers for P3 and P4 are k3 and k4 and are given by:

k3 = km * a/ (a+b) k4 = km * b/ (a+b) 3k

This matrix and sealers can then be dealt with precisely as for the conventional 3 by 3 matrices to produce a unified display. The proof of this expansion is as follows:

The display equation for these primaries is :

[X] [kl*xpl k2*xp2 km*xpm] [PI] [Y] = [kl*ypl k2*yp2 km*ypm] . [P2 ] [Z] [kl*zpl k2*zp2 km*zpm] [Pm]

[kl*xpl k2 *xp2 k3 *xp3 k4*xp4 ] [PI ]

= [kl*ypl k2 *yp2 k3 *yp3 k4 *yp4 ] . [P2]

[kl*zpl k2*zp2 k3 *zp3 k4*zp4] [P3 ]

[P4 ] 31

From Equation 31:

km*xpm = k3*xp3 + k4*xp4

km*ypm = k3*yp3 + k4*yp4 3m

Solving these simultaneous equations in two unknowns, k3 and k4:

(xp4*ypm - xpm*yp4) k3 = km *

(xp4*yp3.- xp3*yp4)

(xp3*ypm - xpm*yp3) k3 = km *

(xp3*yp4 - xp4*yp3i 3n and substituting xpm and ypm from Equation 3h this can be simplified to produce the identity in Equation 3k. A method for determining a display colour of a point in an image can therefore be implemented, in which drive signals for generating display primaries are calculated using each of a set of triads of display primaries selected so as to encompass the required display colour gamut and the drive signals from a triad producing no negative drive signals selected as the display primary drive signals.

The analysis derived above can be incorporated into a practical multiprimary display device. Fig. 4 shows one implementation using, by way of example, three analyses.

Figure 4 shows a decoding circuit for a four-primary display device 2, which generates the required four display drive signals 4 from a coded transmission signal 6 from a three-primary transmission system. The transmitted signal 6 may be a conventional colour difference/luminance signal for example. The transmission signal 6 is input to a decoder 8 which decodes the signal to produce Rs, Gs and Bs system primary signals 10, and may remove any non- linearities if required. These linear Rs, Gs and Bs signals are input to three parallel matrix arithmetic units 12, 14, 16, each of which calculates linear display primary drive signals based on a respective triad of the display primaries . A logic unit 18 is connected to each matrix unit, examines the output of each and selects a set which, for each pixel, has only positive output signals (for a black pixel the choice is immaterial) . Respective matrix outputs are input to switches .20, 22, 24 controlled by the logic unit and hence via a four-way gain controller 26 and a four-way non-linearity corrector 28 for supply to the display device 2 as display primary drive signals 4.

If the triads of display primaries for the matrix analyses are contiguous but do not overlap, the logic unit only has one choice of all-positive drive signals. If the triads overlap there is ambiguity and so hysteresis can be used to reduce the frequency of switching between different triad analyses. The selected analysis operates the display device through any non-linearity needed to linearize it; each drive signal has only one gain control which is used only in the setting up procedure for white balancing.

The setting up procedure is fairly straightforward. One way to do this is to use a split-screen technique to allow the simultaneous display of overlapping analyses and adjusting the primary gains to obtain the balance point in each analysis. For four primaries two overlapping sets suffice, for five primaries three sets are required etc.

Only when each analysis is producing the chromaticity of the white point will they produce the same luminance, and at this setting the entire display is 'balanced' .

It is a curiosity of the mathematics that a practical external reference of the white point is not required since it is built into the mathematics. However, it should be noted that this analysis functions only when the display has a linear transfer characteristic, or when any display device non-linearity is fully corrected after the matrices. If the display non-linearity is not corrected, then the several analyses will not grey scale track together since the gamma correctors' will not be equally driven. Thus applying a grey scale in a split-screen arrangement as mentioned above will reveal errors of linearity and this may provide an easy way of diagnosing mistracking of the correctors.

Method of using a practical four-primary display

A set of numerical solutions is given in Appendix 1, using display primaries Rd, Bd, Gld, G2d and Md, a mixture at Rd and Bd. 5.1 Non-overlapping solutions

There are two methods using non-overlapping analyses .

The first uses the Rd Gld Bd analysis and switches to the

Gld G2d Bd analysis if Rd is negative, switching back to Rd Gld Bd if G2d is negative. The second uses the Rd G2d Bd analysis and switches to the Rd Gld G2d analysis if Bd is negative, switching back to Rd G2d Bd if Gld is negative.

5.2 Overlapping solutions

One method of using overlapping solutions is to use the Gld Md G2d solution as the default, and to switch into the Rd Gld Bd solution if G2d is negative, or into Rd G2d Bd if Gld is negative. Hysteresis can be invoked by not switching back from either of these until the appropriate green in that analysis goes negative; for example, revert from Rd Gld Bd to Gld Md G2d only when Gld goes negative, and revert from Rd G2d Bd to Gld Md G2d only when G2d goes negative.

5.3 Setting up procedure

This is the same for both contiguous and overlapping methods. Using a split-screen technique, display the equal-drive transmission signals (Rs=Gs=Bs=l) to the Rd Gld Bd and Rd G2d Bd analyses, and adjust the display primary gain controls both to produce D65 from each analysis. It is worth noting that this will not be easy, since if the mixture of red to blue is not correct, it will not be possible to get D65 in either analysis, however if that mixture is correct both analyses can produce D65 by adjustments of Gld and G2d. At white balance the two analyses not only produce D65, but they produce it at the same luminance, thus it might be possible to set up the display without external reference to D65 since that colour is generated by both analyses only when their luminances are identical, and this condition is easy to check by eye.

The resultant display is not as efficient as a conventional three primary device, since peak white can be achieved with one primary switched off. In fact, the efficiency can be calculated since the maximum luminance achievable by the display is the sum of the Y row from equation 4e and the maximum luminance of the balanced white is 1, thus the luminous efficiency is:

Eff = (0.3378 + 0.7185 + 0.6277 + 0.0386)

or 58%. A different choice of primaries would give a different result and so could produce a display with greater luminous efficiency.

Application to non-linear systems

Any non-linearity in the signal path from the display matrices to output light will result in differential level- dependant colour distortions between the several analyses, so correction for the display non-linearity must take place between the matrix outputs and the primary drives. If the overall system (light in to light out) is required to have an overall non-linear transfer characteristic then circuits having this characteristic must be interposed between the linear system signals (Rs Gs and Bs) and the inputs to the matrices .

6.1 Non-linear application of 4-primary display

In a television system which employs a constant-luminance coding system and more than three display primaries, some of the complexity of the decoder can be simplified by the adoption of YRB signal handling. In particular, since it is not necessary to decode the G signal there is no need to linearize the Y R and B before matrixing to the display primaries . All that is required is that the Y R and B signals are raised to the appropriate power for the display before matrixing. The proof is as follows:

If the system display matrix is:

[X] [ ] [Rs] [Y] = [ S ] . [Gs] [Z] [ ] [Bs]

then the luminance equation is:

Y = slO * Rs + sll * Gs + sl2 * Bs

where the coefficient suffices refer to the row and column of the matrix. Thus:

Gs = (Y - slO * Rs^'- sl2 * Bs)/ sll 6a

The transfer matrix relating the display primaries PI P2 P3... to the system primaries Rs Gs and Bs is:

Substituting Gs from equation 6a into this gives

where the matrix coefficients m are given by:

mpO = drO - drl * slO / sll mpl = drl / sll mp2 = dr2 - drl * slO / sll

where m d and s refer to the coefficients of the matrices [M] [D] and [S] respectively and suffix r deontes the row of the matrix.

Thus a linear matrix can be calculated which connects the display primaries to the transmission primaries as Y R and B, and the G signal is not required.

In a typical system the transmission power law is 0.45, driving a display with a law of 2.8 and thus having an overall law of 1.26. The Y' R' B' signals in the decoder are already raised to 0.45 by the coding system, and should be further raised to power 2.8 (1.26/0.45) before application to the matrices so that these signals are linearly related to light emitted by the display. Correction of 1/2.8 (inverse of the display) must be applied at the output of the display matrices if the several matrices are to produce identical colours in overlapping areas.

For a typical system, a power law of 0.45 is applied at the studio equipment, the display is assumed to have a power law of 2.8 and the overall system characteristic is therefore 1.26 (0.45 * 2.8). These figures are based upon standard practice with cathode ray displays. To achieve this in a multi-primary display, the input signals to the display matrices must be linearly related to the output light and thus must be related to the system signals Rs Gs and Bs by the power law 1.26. This implies that for a conventionally coded system, three non-linearities are required before the matrices and one for each display primary after matrices; for a constant-luminance coded system three non-linearities are required in the decoder, three more before the matrices and one for each display primary after the matrices.

7. Analysis using a fifth display colour

The constraints used to solve the problem of producing four display primaries from three system primaries in Sections 1 to 6 are not the only solution. A solution using a different set of constraints will now be described which may be more suited to an effective practical implementation requiring a reduced number of non-linear circuit components. This may allow an improvement in image quality and implementation cost.

Numerical data for the following illustrative calculation are provided in Appendix 2.

Figure 5 is a chromaticity diagram, in 1931 xy coordinates, of the improved colour coding system. This shows the spectrum locus together with the locations of the three system colour primaries Rs, Gs, Bs, and the four display colour primaries, Rd, Gld, G2d, Bd. In the colour analysis now considered a fifth display colour, G3d, is defined, formed from an approximately equal mixture of Gld and G2d. Inside the triangle formed by Rd, G3d and Bd, colours are matched by the appropriate mixture of these three primaries. Outside this triangle, colours are matched by a mixture of Rd, Gld and G3d or G2d, G3d and Bd, whichever is more appropriate.

7.1 Inside the Rs G3d Bd triangle The main function of any television system is to regenerate, at the receiver, an approximation to the colour of the original object. For the improved colour coding system considered here, if the XYZ tristimulus values of the original object were Xo, Yo and Zo, the approximation will consist of varying amounts of the transmission primaries Rs, Gs and Bs, in proportions such that the XYZ tristimulus values of the resultant mixture match those of the original colour. The chromaticity coordinates of the transmission primaries are defined in the system specification, however, so the amounts of each required to match the original object, Ars, Ags and Abs lumens respectively, can be determined as follows:

(Xrs/Yrs Xgs/Ygs Xbs/Ybs) (Ars) 1 1 1 ) . (Ags)

(Zrs/Yrs Zgs/Ygs Zbs/Ybs) (Abs) where Xrs, Yrs, Zrs are the xyz chromaticity coordinates of the Rs primary etc. Substituting the correct values into this equation gives:

I I I 2.2429 0.0000 4.8485| |Ars | I Ms I = I 1.0000 1.0000 1.0000| . |Ags| I I I 0.0006 0.0000 27.8215J |Abs|

and hence:

|Ars| I |-1 |Xo| I 0.4459 0.0000 -0.0777| |Xo| |Ags| = |Ms I . IYoI = |-0.4459 1.0000 0.0418| . |Yo| |Abs| I I I ZoI I 0.0000 0.0000 0.0359| | Zo |

Normally, the values Ars, Ags and Abs are weighted by three coefficients, Is, ms and ns respectively to form three normalised coefficients ars, ags and abs whose values are all unity at the specified white point (D65) . Substituting in the corrext XYZ values for one lumen of D65 illumination:

|Ars| I |-1 I 0.9505 | | 0.4459 0.0000 -0.0777] | 0.9505 | |Ags| = |Ms| . I X.0000 | = |-0.4459 1.0000 0.0418 | . | 1.0000 | |Abs| I I |l.089l| I 0.0000 0.0000 0.0359| |l.089l|

0.3392 I |l/ls 0.6217 I I l/ms 0.0391 I ll/ns And hence

Iars I I Is.Ars I | 2.9482 Ars |

Iags I = |ms.Ags| = | 1.6085 Ags | Iabs I |ns.Abs| |25.5548 Abs |

It is then possible to define two new matrices, such that:

|Xθ| I I I rs I |0.7607 0.0000 0.1897| |ars | |Yo| = |ms| . |ags| = |0.3392 0.6217 0.03911. | ags |

I ZoI I I Iabs I |0.0002 0.0000 1.0887| |abs | 7a

and:

Iars I | |-1 |Xo| | 1.3146 0.0000 -0.229l| |Xo | Iags I = |ms| . |Yo| = |-0.7171 1.6085 0.0672| . |Yo| I bs I I I I Zo| |-0.0003 0.0000 0.9186| | Zo|

Similar equations can be used to derive Xo, Yo and Zo in terms of the display primaries Rd, G3d and Bd (N.B. in this instance Rd and Bd are^' the same as Rs and Bs, but this has not been reflected in the analysis, in order to keep it more general) . Thus:

|Xo| I I |ard | |0.6615 0.1126 0.1763| |ard | |Yo| = |md| . |ag3d| = |0.2950 0.6687 0.0364 | . | ag3d| I ZoI I I |abd | | 0.0002 0.0774 1.0115 | |abd |

and:

|ard I | |-1 |Yo| | 1.6193 -0.2411 -0.2736| |Xo | |ag3d| = |md| . |Xo| = |-0.7172 1.6086 0.067l| . |Yo| |abd I I I | Zo| | 0.0550 -0.1238 0.9847| | Zo | 7b

The weighting coefficients, Id, md, nd in this case are given by: |ld| I 3.3904| |md| = I 1.4955| |nd| I 27.5055 I 7c

Equations 7a and 7b can be combined to yield the relationship defining the display drive signals ard, ag3d and abd in terms of the decoded transmission signals ars, ags and abs :

|ard | | |-l | | | ars | | 1.1500 -0.1499 0.0000| |ars| |ag3d| = |md| . |ms|. |ags| = | 0.0000 1.0000 0.0000 | . |ags | |abd I I I I I |abs| | 0.0000 -0.0766 1.0766| | abs |

7d

7.2 Inside the Rd G3d Gld triangle

For colours falling inside the triangle formed by the Rd, G3d and Gld primaries, the value of abd calculated from equation 11 above will be negative. Because it is not possible to generate negative light in a display, it is necessary to use an alternative method of colour analysis if colour reproduction errors are to be avoided. In this instance, it would seem sensible to match Xo, Yo and Zo with mixtures of Rd, G3d and Gld, rather than Rd, G3d and Bd as in the previous section. By following the same procedure as that given in the previous section, therefore, it is possible to derive the revised set of display drive signals, a'rd, a'g3d and a'gld:

|a'rd | | 1.1500 -0.3700 3.0942| |ars | |a'g3d| = | 0.0000 -0.2457 17.5128 | . | ags | |a'gld| | 0.0000 1.3386 -18.819θ| |abs | 7e

(N.B. In this instance the weighting coefficients Id, md and nd have not been recalculated from the values used in section 2.1. This is in order to avoid the need for different gains in practical realisations of this method. The factor md has been applied to both the a'g3d and a'gld signals - in this case nd is not required. It should be noted, however, that equal drive signals a'rd, a'g3d, a'gld will no longer match to D65) .

By inspection of equations 7d and 7e it can be noted that:

a'gld = -17.4804 abd 7fl a'rd = ard + 2.8741 abd 7f2 a'g3d = ag3d + 16.2671 abd 7f3

It should also be noted that:

a'bd = 0 = abd - abd 7f4

Thus the above operation is equivalent to subtracting a signal of abd from the blue primary and adding signals of 2.8741 abd, 16.2671 abd and -17.4804abd to the red, green3 and greenl primaries respectively.

7.3 Inside the G2d G3d Bd triangle

Colours falling in this region have negative values of ard. Following a similar procedure as in previous sections, and matching the input colour by mixtures of G2d, G3d and Bd therefore:

|a''g2d| |-7.4446 0.9707 0.0000| |ars | |a''g3d| = | 7.9301 -0.0340 0.0000 | . | ags | |a''bd I I 0.4001 -0.1257 1.0766| | abs | 7g

As in section 7.2, the weighting coefficients used in equation 7g are the same as those used in equation 7d. By inspection of equations 7d and 7g:

a''g2d = -6.4739 ard 7hl

a''g3d = ag3d + 6.8961 ard 7h2 a''bd = abd + 0.3479 ard 7h3

a''rd = 0 = ard - ard 7h4

7.4 Forming final combined display drive signals

The final display drive signals for the Rd and Bd primaries are formed by combining the signals of equations 7d, 7f and 7h:

a'''rd = ard - ( ard ) ard≤o + 2.8741 ( abd ) abd≤o a'''bd = abd - ( abd ) abd≤o + 0.3479 ( ard ) ard≤o

In order to form the Gld and G2d drive signals, account must also be taken of the value of the G3d primary. In section 7 above, it was stated that the G3d primary was formed from approximately equal proportions of Gld and G2d. The exact proportions were adjusted so that the chromaticity coordinates of G3d were exactly mid-way between those of Gld and G2d; i.e. the relative luminances are mixed in the ratio 0.7543 : 0.8029 - the ratio of their y chromaticity coordinates. Thus a given amount, Ag3d lumens, of the G3d primary may be matched by Agld lumens of Gld added to Ag2d lumens of G2d, where:

Agld = 0.7543 . Ag3d = 0.4844 Ag3d 2 * 0.7786

Ag2d = - 0.8029 . Ag3d = 0.5156 Ag3d 2 * 0.7786

Since the weighting factors applied to Gld, G2d and G3d are all equal, the same equations can be applied to the normalised values agld etc:

agld = 0.4844 ag3d ag2d = 0.5156 ag3d Adding together the various contributions, therefore:

a'''g3d = ag3d + 6.8961 ( ard ) ard≤o + 16.2671 ( abd ) abd≤o

And hence:

a' ''gld = 0.4844 a'''g3d - 17.4804 ( abd ) abd≤o

= 0.4844 ag3d + 3.3405 ( ard ) ard≤o - 9.6006 ( abd ) abd≤o

a'''g2d = 0.5156 a"'g3d - 6.4739 ( ard ) ard≤o

= 0.5156 ag3d - 2.9182 ( ard ) ard≤o + 8.3873 ( abd ) abd≤o

A method for determining a display colour of a point in an image can thus be implemented. This method in more general terms uses four display primaries, i.e. first, second, third and fourth primaries lying in sequence at consecutive, adjacent corners of a quadrilateral in a chromaticity diagram, and comprises the following steps:

(A) a fifth, imaginary, display primary is determined, being a linear combination of the third and fourth display primaries,

(B) signals for generating first, second and fifth display primaries are calculated using a triad of display primaries comprising the first, second and fifth display primaries ,

(C) if the signals calculated in (B) are all either zero or positive, the signals for the first and second display primaries are used to form display primary drive signals, and drive signals for the third and fourth display primaries are calculated by using the signal for the fifth display primary to calculate drive signals for the third and fourth display primaries according to the linear relationship between them, (D) if the signal calculated for the first display primary is negative, display primary drive signals are initially calculated as in (C) , and then the second and fourth display primary drive signals so calculated are modified by the addition of predetermined multiples of the first display primary drive signal thereto and the first display primary drive signal is set to zero. (E) if the signal calculated for the second display primary is negative, display primary drive signals are initially calculated as in (C) , and then the first and third display primary drive signals so calculated are modified by the addition of predetermined multiples of the second display primary drive signal thereto and the second display primary drive signal is set to zero.

8. Implementation in hardware

Figure 6 shows a circuit which might be used to decode the four drive signals in practice.

Incoming ars, ags and abs signals 30, which may be derived from transmitted colour difference/luminance signals, are input to a matrix arithmetic unit 32. Any non-linearity in these signals may need to be removed, for example on prior decoding of a transmitted signal. In practice, there will probably be no need to first decode the ars, ags and abs signals, ard, ag3d and abd probably being formed directly from transmitted Y,R-Y,B-Y signals; this has little effect on the decoder circuit however.

The matrix arithmetic unit calculates display primary signals for Rd, G3d and Bd, i.e. ard, ag3d and abd. These signals are then applied to outputs 34 of the decoder circuit to form portions of the a'''rd, a' ''gld, a'''g2d, and a'''bd display primary drive signals respectively. The ard and abd signals from the matrix unit are however also applied to an 'ideal diode' circuit 36 and the resultant rectified signals combined at the circuit outputs 34 with the signals output directly from the matrix unit to form contributions to the final decoded a'"rd, a' ''gld, a'''g2d and a' ' 'bd. Two factors are worth noting on this circuit. The first is that the diodes are being used simply as switches, and not as calibrated non-linearities. This should make the circuit easy to duplicate. The second factor to note is that the diode outputs are added into all four of the output colour channels. This is equivalent to matching negative values of Rd by the appropriate values of Gld, G2d and Bd. The circuit is therefore quasi-linear in operation, in that there is no internal clipping involved. The only clipping that is present is in the display itself - negative values of a'''rd etc cannot be reproduced, and are hence clipped to black. This quasi-linear response is largely responsible for the well-behaved response to colours outside the reproducible gamut - see following section.

9. Performance outside the realisable gamut

The circuit of Figure 6 is capable of accurately reproducing any colour occurring within the colour gamut set by Rd, Gld, G2d and Bd. It is important, however, to also consider what happens to colours outside this gamut; the system should "fail gracefully" under such conditions, and should not behave in an unacceptable manner.

As can be seen from Figure 7, the complete colour spectrum outside the reproducible gamut can be split into four identifiable regions. In region 1, a'''g2d is negative. Since negative values of G2d cannot be produced, the colour is displayed as if it were mixed with a sufficient amount of G2d to bring it to the line GldRd. In region 1 the colours thus move towards G2d. In regions 2 and 3, the colours cannot be reproduced by the coding system itself (ags or ars becomes negative) ; the display system introduces no further errors, and the displayed colours are distorted towards the Gs or Rs primaries respectively. Region 4 is more complex, however, and must be further sub¬ divided into three areas, depending on the relationship of the colour being transmitted to the lines RdG3d and BdG3d.

These sub-regions of region 4 are shown enlarged in Figure 8. In sub-region 4a, abd is negative and ard is positive. The operations of equation 16a, however, result in a value of a'''rd which is negative (a'''bd becoming zero) . Thus the displayed colour shifts towards the Rd primary.

Similarly in sub-region 4c,abd is positive and ard is negative. The corrections of equation 16b result in a zero value of a'''rd and a negative value of a'''bd. The colour moves towards the Bd primary.

In sub-region 4b, however, both ard and abd are negative. The corrected values of a'''rd and a'''bd are therefore also both negative. The final displayed colour is still on the line joining Gld and G2d, therefore, but its exact position on that line is harder to determine. In general, as the original colour moves along any particular arc AB, the displayed colour will move along the corresponding line A'B' . As the arc of colours becomes more saturated (e.g. the arc CD) , so the length of the corresponding line CD' becomes longer. In general, therefore, saturation changes in the incoming colours can produce hue changes in the reproduced colour. Nevertheless, it can be seen from Figure 8 that these hue changes are relatively minor (similar in magnitude to the hue changes that might be produced by saturation effects in present-day coding systems) . Thus the performance of the four-primary display is unlikely to produce unacceptable colour errors in any part of the visible spectrum. APPENDIX 1

Four-primary display: Numerical Solutions

This Appendix contains the numerical results for a four primary display designed for the Eureka set of primaries The system and display primaries are listed below:

y=0.3083 U'=0.4538 v'=0.5081 y=1.0000 u'=0.0000 v'=0.6000 y=0.0297 u'=0.1877 v' =0.0871

y=0.7543 u'=0.0792 v'=0.5856

y=0.8029 u'=0.0104 v'=0.5749

Md (7Rd+9Bd)/l6 x=0.3835 y=0.1516 u'=0.3787 v'=0.3367

Balance D65 x=0.3l27 y=0.3290 u'=0.1978 v'=0.4683

Xw=0.3127/0.3290*1.0000=0.9505 Yw=1.0000 Zw=(1-0.3127-0.3290) /0.3290*1.0000=1.0891

1. Solution for the transmission system

Denormalising gains:

Rs (1) 1.1001 Gs (m) 0.6217 Bs (n) 1.3176 Al.1

Matrix equations :

[Y] [ 0.7607 0.0000 0.1897] [Rs]

[Y] = [ 0.3392 0.6217 0.0391] . [Gs] [Z] [ 0.0002 0.0000 1.0887] [Bs] A1.2 A1.3

Denormalising gains:

Rd 0.7877 Gld 0.9525 Bd 1.2992 A2.1

Matrix equations :

[X] [ 0.5447 0.2187 0.1870] [ Rd

[Y] = [ 0.2429 0.7185 0.0386] . [Gld] [Z] [ 0.0001 0.0153 1.0735] [ Bd] A2.2

A2.3

Transfer matrix:

[ Rd] [ 1.3967 -0.3967 0.0000] [Rs]

[Gld] = [ 0.0000 1.0000 0.0000] . [Gs] [ Bd] [ 0.0000 -0.0142 1.0142] [Bs] A2.4

3. Solution for display, Rd G2d Bd

Denormalising gains

Rd 1.0954 G2d 0.7818 Bd 1.1621 A3.1

Matrix equations:

A3.3

Transfer matrix:

[ Rd] [ 1.0043 -0.0043 0.0000] [Rs]

[G2d] = [ 0.0000 1.0000 0.0000] . [Gs]

[ Bd] [ 0.0000 -0.1337 1.1337] [Bs] A3.4

Solution for display, Rd Gld G2d

Denormalising gains:

Rd 3.7066 Gld •8.0834 G2d 7.4151 A4.1

Matrix equations:

[X] [ 2.5632 -1.8561 0.2434] [ Rd]

[Y] = [ 1.1429 -6.0975 5.9546] . [Gld]

[Z] [ 0.0006 -0.1297 1.2181] [G2d] A4.2

0.6592] [X]

1.0324] . [Y]

0.9306] [Z] A4.3

Transfer matrix:

[ Rd] [ 0.2968 -0.0955 0.7987] [Rs]

[Gld] = [ 0.0000 -0.1337 1.1337] . [Gs] [G2d] [ 0.0000 -0.0142 1.0142] [Bs] A4.4

5. Solution for display, Gld G2d Bd

Denormalising gains:

Bid 3.3910 G2d -2.0013 Bd 1.6497 A5.1 Matrix eσuations:

[X] [ 0.7786 -0.0657 0.2375] [Gld]

[Y] = [ 2.5579 -1.6069 0.0490] [G2d] [Z] [ 0.0544 -0.3287 1.3632] [ Bd] A5.2

[Gld] [ 1.3233 -0.0070 •0.2303] [X]

[G2d] = [ 2.1205 -0.6381 ■0.3465] . [Y]

[ Bd] [ 0.4585 -0.1536 0.6592] [Z] A5.3

Transfer matrix:

[Gld] [ 1.0043 -0.0043 0.0000] [Rs]

[G2d] = [ 1.3967 -0.3967 0.0000] . [Gs] [ Bd] [ 0.2968 -0.0955 0.7987] [Bs] A5.4

Solution for display, Gld Md G2d

Denormalising gains:

Gld 0.4404 Md 2.1786 G2d 0.4204 A6.1

Matrix equations

[X] [ 0.1011 0.0138 0.8355] [Gld]

[Y] = [ 0.0071 0.0690 1.0128] . [ Md] [Z] [ 0.3322 0.3375 0.3303] [G2d] A6.2

[Gld] [ 7.1178 0.9753 -6.1901] [X] [ Md] = [ 0.4585 -0.1336 0.6592] . [Y]

[G2d] [-7.4543 2.1532 5.4473] [Z] A6.3

Transfer matrix:

A6.4 Denormalising gains:

Rd 0.9531 (=2.1786*7/16) Bd 1.2255 (=2.1786*9/16) A6.5

Transfer matrix:

A6.6

For arbitrary reasons, the display matrix will use as denormalising gains, Rd and G2d from solution 3 (Rd G2d Bd) , Gld and Bd from solution 2 (Rd Gd Bd) . Each row of each transfer matrix is then multiplied by the ratio of the denormalisers for that colour in its own solution and for the unified display matrix.

Denormalising gains:

A7.1

Unified display matrix equation:

[X] [ 0.7576 0.2187 0.0257 0.1870] [ Rd]

[Y] = [ 0.3378 0.7185 0.6277 0.0386] [Gld] [Z] [ 0.0001 0.0153 0.1284 1.0735] [G2d] [ Bd] A7.2

Transfer matrices

Solution 2 (Rd Gld Bd)

A7.3

Solution 3 (Rd G2d Bd)

[ Rd] [ 1.0043 -0.0043 0.0000] [Rs]

[Gld] = [ 0.0000 0.0000 0.0000] . [Gs] [G2d] [ 0.0000 1.0000 0.0000] [Bs]

[ Bd] [ 0.0000 -0.1196 1.0142] A7.4

Solution 4 (Rd Gld G2d)

[ Rd] [ 1.0043 -0.3231 2.7025] [Rs]

[Gld] = [ 0.0000 1.1347 -9.6207] . [Gs] [G2d] [ 0.0000 -0.1347 9.6207] [Bs]

[ Bd] [ 0.0000 0.0000 0.0000] A7.5

Solution 5 (Gld G2d Bd)

[ Rd] [ 0.0000 0.0000 0.0000] [Rs]

[Gld] = [ 3.5754 -0.0155 0.0000] . [Gs]

[G2d] [-3.5754 1.0155 0.0000] [Bs] [ Bd] [ 0.3769 -0.1212 1.0142] A7.6

Solution 6 (Gld Md G2d)

[ Rd] [ 0.2583 -0.0831 0.6949] [Rs] [Gld] = [ 2.6560 0.2803 -2.4740] . [Gs]

[G2d] [-2.6960 0.7197 2.4740] [Bs] APPENDIX 2

Colorimetric data for the four-primary system

System primaries:

Rs 620 nm x= 0.6915 y= 0.3083 (u' = 0.5203 V = 0.5219) Gs x= 0.0000 y= 1.0000 (u'= 0.0000 V = 0.6000)

Bs 460 nm x= 0.1440 y= 0.0297 (u' = 0.1877 V = 0.0871)

Display primaries

x = 0.6915 y = 0.3083

X = 0.2296 y = 0.7543 x = 0 . 0328 y = 0 . 8029 x = 0.1312 y = 0.7786

x = 0.1440 y = 0.0297

Balance white point :

D65 x = 0.3127 y = 0.3290 x = 0.9505 y = 1.0000 z = 1.0891

Claims

1. A method for decoding a signal defining a video image in terms of n independent system primaries to produce a display signal using m independent display primaries, where m>n.

2. A method according to claim 1, in which at least one of the system primaries is spectral or super-spectral.

3. A method according to claim 1 or claim 2, in which for each colour to be displayed, display primary drive signals are calculated in terms of a triad of three display primaries selected from the available m display primaries, or from one or more additional imaginary display primaries each calculated as linear combinations of two of the m display primaries, a triad comprising three display primaries of which none can be formed from a linear combination of the other two.

4. A method according to claim 3, in which more than one triad of display primaries is required to calculate display primary drive signals for all colours within an available gamut of display colours .

5. A method according to claim 4, in which the triads of display primaries are selected so that each colour to be displayed can only be defined in terms of the display primaries of one of the triads.

6. A method according to claim 4, in which the triads of display primaries are selected so that they overlap, so that at least one of the colours to be displayed can be defined in terms of the display primaries of two or more triads.

7. A method according to any of claims 4 to 6, in which four display primaries lie at the corners of a quadrilateral on a chromaticity diagram.

8. A method according to claim 7, in which n = 3, the three system primaries lying at the corners of a triangle on a chromaticity diagram, first and second display primaries are approximately matched to first and second system primaries respectively, and third and fourth display primaries lie in the chromaticity diagram on or near sides of the triangle defined by the system primaries between the first and third system primaries and second and third system primaries respectively.

9. A method according to claim 7 or claim 8, in which at least the third system primary is spectral or super-spectral .

10. A method according to any of claims 4 to 9, in which four display primaries are used (m=4) , the first, second, third and fourth display primaries lying at corners taken in order around the circumference of a quadrilateral in a chromaticity diagram, the method comprising the following steps to determine a display colour of a point in an image;

(B) signals for generating first, second and fifth display primaries are calculated using a triad of display primaries comprising the first, second and fifth display primaries,

(C) if the signals calculated in (B) are all either zero or positive, the signals for the first and second display primaries are used to form display primary drive signals, and drive signals for the third and fourth display primaries are calculated by using the signal for the fifth display primary to calculate drive signals for the third and fourth display primaries according to the linear relationship between them, (D) if the signal calculated for the first display primary is negative, display primary drive signals are initially calculated as in (C) , and then the second and fourth display primary drive signals so calculated are modified by the addition of predetermined multiples of the first display primary drive signal thereto and the first display primary drive signal is set to zero,

(E) if the signal calculated for the second display primary is negative, display primary drive signals are initially calculated as in (C) , and then the first and third display primary drive signals so calculated are modified by the addition of predetermined multiples of the second display primary drive signal thereto and the second display primary drive signal is set to zero.

11. A method according to any of claims 4 to 9, in which to determine a display colour of a point in an image, drive signals for generating display primaries are calculated using each of a set of triads of display primaries selected in order to encompass the required display gamut and the drive signals from a triad producing no negative drive signals are selected as the display primary drive signals.

12. A method according to claim 11, in which at least two of the selected triads overlap, the principle of hysteresis being used to control drive signal selection for __ the colours of neighbouring points in an image or the colours of the same point in successive images to limit the frequency of switching between triads for the generation of drive signals.

13. Video display apparatus comprising; inputs for receiving input signals coded using n system primaries; display means for displaying an image using m display primaries, where m > n, and; decoder means coupling the inputs and the display means for decoding the input signals to produce display primary drive signals.

14. Apparatus according to claim 13 , in which for a colour to be displayed the decoder means evaluates display primary drive signals in terms of at least one triad of three display primaries selected from the available m display primaries or from one or more additional imaginary display primaries determined as linear combinations of two of the m display primaries, each triad comprising three display primaries of which none can be formed from a linear combination of the other two.

15. Apparatus according to claim 14, in which more than one triad of display primaries is required to display all colours within an available gamut of display colours .

16. Apparatus according to claim 15, in which the triads of display primaries are contiguous and do not overlap.

17. Apparatus according to claim 15, in which the triads of display primaries overlap, the decoder means employing hysteresis to reduce switching between triads.

18. Apparatus according to any of claims 15 to 17, in which the decoder means comprises; matrix arithmetic means for calculating display primary drive signals from the input signals based on each selected triad of display primaries,- logic means coupled to the arithmetic means for detecting the presence of negative drive signals calculated by the arithmetic means; and switch means connected to the output of the arithmetic means and responsive to the logic means to switch to the display means only selected display primary drive signals based on one of the triads for which all the drive signals calculated are positive.

19. Apparatus according to claim 18, in which the logic means comprises means for using hysteresis to control drive signal selection of the colours of neighbouring points in an image or the colours of the same point in successive images to limit the frequency of switching between drive signals generated using different triads.

20. Apparatus according to any of claims 15 to 17, in which the display means uses four display primaries (m=4) which lie at the corners of a quadrilateral in a chromaticity diagram, the first, second, third and fourth display primaries lying at corners taken in order around the circumference of the quadrilateral, and an imaginary fifth display primary which is a linear combination of the ,third and fourth display primaries, and in which the decoder means comprises; a matrix arithmetic means for calculating first, second, and fifth display primary signals using a triad defined by the first, second and fifth display primaries; means for apportioning the fifth display primary signal into signals for the third and fourth display primaries; means for multiplying the signals generated by the arithmetic means for the first and second display primaries by predetermined fixed coefficients and for sensing the sign (positive or negative) of the signals; and means for adding the multiplied first and second display primary signals, depending on their sign, to the first, second, third and fourth display primary signals to produce four display primary drive signals for driving the display unit.

21. Apparatus according to any of claims 13 to 20, comprising a non-linearity decoder for substantially removing non-linearity from the input signals received before they are input to the decoder means.

22. Apparatus according to any of claims 13 to 21, comprising a non-linearity coder coupled between the decoder means and the display means for applying any required non-linearity to the display primary drive signals.