1、1 ScopeThis practice is intended to define the numerical pro-cedures for deriving basic color equations for colortelevision and other systems using additive displaydevices. These equations are first, the normalizedreference primary matrix which defines the relation-ship between RGB signals and CIE t
2、ristimulus valuesXYZ; then, the system luminance equation; andfinally, the color primary transformation matrix fortransforming signals from one set of referenceprimaries to another set of reference primaries or to aset of display primaries.2 Normative referenceThe following standard contains provisi
3、ons which,through reference in this text, constitute provisions ofthis practice. At the time of publication, the editionindicated was valid. All standards are subject torevision, and parties to agreements based on thispractice are encouraged to investigate the possibilityof applying the most recent
4、edition of the standardindicated below.CIE Publication 15.2 (1986), Colorimetry3 Reference primary matrix3.1 Input data3.1.1 For television systems, reference white forboth reference camera and display is CIE illumi-nant D65. The chromaticities of D65, rounded tofour significant digits (CIE 15.2), a
5、re:x = 0.3127y = 0.3290Other displays may utilize other white points. The CIEcoordinates of some other standard CIE illuminantsare:(A more complete discussion of reference white andoperating white is given in annex A.)3.1.2 The chromaticity coordinates of the systemreference primaries or display pri
6、maries shallbe specified to a minimum of three significantdigits using the 1931 CIE system of colorimetry(x, y coordinates). More precision may be usedin the starting data if available. If the primarychromaticities are provided in the CIE 1976uniform chromaticity coordinate systems (u,v),then they m
7、ust be transformed to the 1931 CIEx, y chromaticity coordinates using the transfor-mation given below (see annex D (1).x = 9u12 + 6u 16vy = 4v12 + 6u 16vShould the primary chromaticities be provided in theobsolete 1960 UCS system (u,v), these values shouldfirst be transformed to the 1976 system and
8、then tothe 1931 x,y values.u = u; v = 1.5 v.3.1.3 In the event that starting data are not avail-able as chromaticity coordinates for a whiteRP 177-1993SMPTE RECOMMENDED PRACTICEApproved November 1,1993Copyright 1993 by theSOCIETY OF MOTION PICTURE AND TELEVISION ENGINEERS595 W. Hartsdale Ave., White
9、 Plains, NY 10607(914) 761-1100x yD550.3324 0.3474D500.3457 0.3585Ill C0.3101 0.3162Derivation of BasicTelevision Color EquationsPage 1 of 4 pagesREAFFIRMED 2002point or display primaries, they should becomputed from the spectral power distributionsusing the colorimetric integration tables and pro-c
10、edures given in CIE 15.2.3.2 Output dataThe numerical coefficients of the output matrix mustbe computed accurately to four decimal digits. Toavoid effects of rounding and truncation errors andto ensure this accuracy in the final result, it is recom-mended that all computations be carried out to 10-d
11、igitaccuracy with the output matrix being derived directlyfrom the chromaticity coordinates of the RGBprimaries and reference white with no rounding ortruncation of intermediate results. The final 10-digitresult is rounded to the required 4-digit accuracy. A setof example computations accurate to 10
12、 digits is givenin annex B to aid in checking computational equip-ment.3.3 General procedureThe general procedure for deriving the matrix relatingnormalized linear RGB signals to CIE XYZ tristimulusvalues is described in this clause and an examplederivation is given in annex B. The RGB signals areno
13、rmalized such that reference white has the valuesR=G=B=1.0. The step-by-step process is as follows:3.3.1 Obtain the CIE x y chromaticity coordi-nates of the reference white (D65for television)and of the RGB primaries.3.3.2 Compute the z coordinate for the referencewhite and each of the RGB primaries
14、:z = 1 (x + y)3.3.3 Form the following matrix and columnvector from the x y z numerical values of thereference primaries and white:P = xRxGxByRyGyBzRzGzBW = xw yw1 zw ywNote that the W vector, representing the referencewhite, has been normalized so that white has a lumi-nance factor of 1.0; i.e., Y
15、= 1.0. This is necessary soas to cause the video reference white signal(R=G=B=1) to produce the reference white with aunity luminance factor.3.3.4 Compute the coefficients Ci on the left sideof the equation below by multiplying the W vectorby the inverse of the P matrix. Note the notationP-1indicate
16、s the matrix inversion operation.These coefficients are normalization factorswhich normalize the units of the RGB primariessuch that a unit amount of each combine toproduce the white point chromaticities with aluminance factor of 1:CRCGCB= P1 W3.3.5 Form the diagonal matrix from the coeffi-cients Ci
17、computed in 3.3.4:C = CR000CG000CB3.3.6 Compute the final normalized primary ma-trix NPM as the product of the P and C matrices:NPM = XRYRZRXGYGZGXBYBZB= P C3.3.7 This matrix, NPM, is the final result andrelates television linear RGB signals to CIE XYZtristimulus values as follows:XY Z = XRYRZRXGYGZ
18、GXBYBZB RGB 3.3.8 The luminance equation for this set of pri-maries is the second row of the NPM matrix:Y = YR(R) + YG(G) + YB(B)In some cases, the NPM matrix values rounded to fourdigits may result in a luminance equation whose termsdo not sum to 1.0. In that situation, the NPM matrixshould be colu
19、mn normalized to force the second rowto sum to 1.0.3.3.9 Computations of color-difference signal co-efficients should use all 10 digits of the luminanceequation as determined above. These datashould be multiplied by applicable scaling factorsbefore rounding. Round to four decimal placesRP 177-1993Pa
20、ge 2 of 4 pagesand/or four digits, whichever extends thenumber further.In some cases, the coefficients of the color-differ-ence equations may not sum to zero after rounding.In that situation, the coefficients should be renor-malized to force the coefficients of each equation tosum to zero.4 Transfor
21、mation between primary sets4.1 Input dataThe input data consists of the normalized primarymatrices for a source system (NPMS) and for adestination system (NPMD). Ideally these matricesshould have been generated directly from the 3-digitprimary chromaticities and 4-digit reference whiteand, therefore
22、, be of 10-digit accuracy. However,normalized reference primary matrices rounded tofour digits may be used. It must be recognized thatthis will result in a lower precision transformation (seeannex D (2).4.2 General procedure4.2.1 Given the normalized primary matricesfor the source (NPMS) and destina
23、tion(NPMD) systems, the following equationsrelate CIE tristimulus values to the linearRGB signals in both source and destinationsystems:XYZ = NPMS RSGSBSand XYZ = NPMD RDGDBDThe inverse relationships, predicting RGB from XYZ,may also be written:RSGSBS= NPMs1 XYZ and RDGDBD= NPMD1 XYZ Again, the (-1)
24、 notation of the NPM matrices indicatesmatrix inversion.4.2.2 The objective is to determine a matrixwhich transforms RGB signals from the sourcesystem into appropriate signals for the destina-tion system. Start from the source, using its NPMto predict XYZ values from source RGB signalvalues as shown
25、 in the left equation below. Thenwrite the equation predicting the destinationRGB signals from XYZ values as shown in theright equation below:XYZ = NPMS RSGSBSand RDGDBD= NPMD1 XYZ Since the values of XYZ should be the same for bothsource and destination systems, the XYZ vector onthe right side of t
26、he right equation can be replacedwith the entire right side of the left equation:RDGDBD= NPMD1 NPMS RSGSBS4.2.3 The desired transformation matrix TRA isthe product of NPMDinverse and NPMS:TRA = NPMD1 NPMSandRDGDBD= TRA RSGSBSRP 177-1993Page 3 of 4 pagesAnnex A (informative)Reference white and RGB si
27、gnal valuesThe role of the reference white, in this practice, is simplythat of normalizing the units of the R G B primaries. Thatis, the relative video signal levels R=G=B=1 correspond tothe reference white in the scene or on the display. All currenttelevision systems specify CIE illuminant D65 for
28、bothsource and display. The signal processing on televisionsignal sources is based on this white-point assumption. Inpractice, television cameras are used to produce imagesunder a wide range of lighting conditions ranging from tungstento very high color temperatures, and CIE illuminant D65 isprobabl
29、y rarely encountered. The television camera is al-ways white balanced so that a white object always pro-duces R=G=B regardless of the color quality of the studiolight. In effect, television systems have always tacitlyassumed that the color reproduction goal is to reproduce allcolors as though they h
30、ad been illuminated by CIE illuminant D65.Annex B (informative)Example derivation of normalized primary matrixB.1 Given the reference white chromaticities:x = 0.3127 y = 0.3290and a set of reference primaries:B.2 The following values of Ci are derived:CR = 0.6443606239CG = 1.1919477979CB = 1.2032052
31、560B.3 The values for the NPM matrix before rounding to fourdigits are:NPM = 0.41239079930.21263900590.01933081870.35758433940.71516867880.11919477980.18048078840.0721923154 0.9505321522B.4 The luminance equation is:Y = 0.2126390059(R) + 0.7151686788(G) + 0.0721923154(B)and rounded to four digits:Y
32、= 0.2126(R) + 0.7152(G) + 0.0722(B), in which the coeffi-cients sum to 1.0.Annex C (informative)Example derivation of primary transformation matrixC.1 Given a source NPM:NPM S= 0.56711818590.27932686770.00000000000.19032106630.64346646240.07250326340.19301667480.07720666991.0165544874and a destinati
33、on NPM:NPM D= 0.41239079930.21263900590.01933081870.35758433940.71516867880.11919477980.18048078840.07219231540.9505321522 C.2 The resulting transformation matrix TRA before round-ing is:TRA S D= 1.4085805665.0256675666.0254274151.40858056671.0256675666.04403087200.0000000000.00000000011.0694582872Annex D (informative)Bibliography1) Hunt, R.W.G. Measuring colour. London: Elis HorwoodLimited; 1987.2) Sproson, W.N. Colour science in television and displaysystems, p21. Bristol: Adam Hilger Ltd; 1983.xR = 0.640xG = 0.300xB = 0.150yR = 0.330yG = 0.600yB = 0.060RP 177-1993Page 4 of 4 pages
