J. J. McCann, "Color spaces for color mapping", J. Electronic ...

J. J. McCann,"Color spaces for color mapping",J. Electronic Imaging, 8, 354-364, 1999.Copyright SPIE

Journal of Electronic Imaging 8(4), 354-364 (October 1999).Color spaces for color-gamut mappingJohn J, McCannMcCann ImagingBelmont, Massachusetts 02478E-mail: mccanns@tiac.netAbstract. Before doing extensive c%r gamut experiments, wewanted to test the uniformity of CIE L'" a'" b* , This paper showssurprisingly large discrepancies between CIE L '" a'" b* and isotropicobselVatjon~based c%r spaces, such as Munsell: (1) L *a* b*chroma exaggerate yellows and underestimate blues. (2) The averagediscrepancy between L '" a* b* and ideal is 27%. (3) Chips withidentical L '" a* b* hue angles are not the same color. L '" a* b* introduceserrors larger than many gamut mapping corrections. We haveisotropic data in the Munsell Book. Computers aI/ow threedimensionallookup tables to convert instantly any measuredL ljI a ljl b* to interpolated Munsell Book values. We call this space ML,Ma, and Mb in honor of Munsell. LUTs have been developed forboth LabtoMLab and MLabtoLab. With this zero-error, isotropicspace we can return our attention to the original problem of colorgamutimage processing. Cl 1999 SPIE and IS&T.[5101 7-9909(99)00804-1]IntroductionThere is considerable interest in color matching betweenmonitors and printers. The problem is well documented.The color gamut of the print is very different from that ofthe monitor. The monitor has a wide variety of different,highly saturated, high-value colors near white, Prints, eventhose using high-extinction coefficient dyes, absorb toomuch light to generate these colors. Prints, however, have agreater range of colors in the low-lightness browns. Thehope is to find automatic calculations of monitor and printcolors that make them look more like each other. Beforeembarking on quantitative evaluations of these ideas, wefelt it necessary to study the color spaces used in automaticcalculations. The ideal three-dimensional (3D) color spaceis isotropic. Namely, it has the same properties in all directions,for all parts of the space. We are looking for a practicalcomputational space that has the same properties in alldirections, for all parts of the space. Any two samples thatare n units apart in a uniform color space will appearequally different, whether the separation is in hue, lightness,chroma, or any combination.This paper is a revision of a paper presented 3[ the SPIE conference on ColorImaging: Device-Independent Color, Color Hardcopy, and Graphic Arts IV. SanJose, CA. January 1999. The paper appears (unreferecd) in Proc. SPI£ 3648.Paper 008904 received Mar. 25. 1999: revised manuscript received May 21. 1999:accepted May 29. 1999.1017·99091991510.00 C 1999 SPIE and IS&T.1,1 Observations Versus EquationsThere are two different approaches to uniform color spaces.The first is direct observation. Munsell, Ostwald, OSA UniformColor Space, NCS, and ColorCurve are all examplesof extensive research using human observers to select colorsamples that appear uniformly spaced.The second approach is to use Colorimetric equations.The cornerstone of Colorimetry is the X, Y,Z 3D space. It isderived from color matching experiments and can predict iftwo samples will match based on full-spectrum measurements.Independent of X, Y,Z's ability to predict matches, itis not isotropic' and it cannot predict the sample's colorappearance.' CIELAB, CIELUV, CIECAM97 are examplesof equations that approximate the observer data.The observotion and the equation approaches are verydifferent. These two approaches may give the same renditionof color appearance, or they may not. This paper willplot L 'a*b* 's rendition of observed uniform color spaces.We will concentrate much of our discussion on Munselldata, but will include other observed spaces. Ideally, thedifferences between the observed data and their calculatedapproximations are vanishingly small.The advantage of the Munsell book (Fig. I) is that onecan see the real chips and evaluate for oneself how uniformit appears. I have recently confirmed for myself that eachpage appears as a single hue and that the colors are isotropicallyspaced. The 40 pages appear equally spaced in hue.The advantage of CIELAB is that it has become an almostuniversal standard in imaging. It is built into manymeasuring devices for direct measurements and it uses onlythree equations to calculate L*,a',b' from X,Y,Z'L*= 116*( YI y n)'13_ 16,a* = 500*[ (XIX.) 113_ (YI Y.) '13],b* = 200*[ (YIY. ) '13_ (ZIZ.) '13].2 How Uniform is C1ELAB?Many authors use CIELAB as the space of choice for makingdecisions on the best color compromise, such as themapping of extra-gamut points in printed and displayed images.They select CIELAB because hue, lightness, andchroma are approximately uniformly spaced. Before doingan extensive set of these so called gamut mapping experiments,we became curious about the actual size of(I)354 1 Journat of Electronic tmaging 1 October 19991 Vol. 8(4)

Color-gamut mappingMunsell-------------------------------------~~jr~~----------------,--_.--------- --~~:~=:)iQuarter of solidremoved to showinterior selectionFig.l Nickerson's diagram of the Munsell color space. There are 40 planes of constant hue that sharethe vertical neutral gray axis at the center. In each plane lightness, value, and chroma are equallyspaced.CIELAB's nonunifonnities. There is abundant literaturethat straddles the line between it "does a respectable job" 3and it needs improvement, usually with more cleverfunctions.'·s The following comparisons of Munsell observationsand CIELAB calculations are an attempt to resolvethis issue.Let us define a new space called MLab 6 M is in honorof Munsell. The idea is to mimic the format and formulasof CIELAB format so we can easily compare the two.MLab just replaces the equations in L 'a'b' with isotropicdata. CIELAB lightness varies from 100 to O. Munsell notationvaries from 91 to II. By mUltiplying Munsell value by10, we get 90 to 10, more closely approximating L' . InMunsell space lightness units II are equal to chromaunitsl2. By multiplying Munsell chroma by 5 we makeMLab's chroma 10 equals MLab's lightness 10.A simple test is to look at the area of biggest concern ingamut mismatch, namely saturated yellows. A yellow Munsell5.0 Y SII4 has an expected Munsell Chroma (MC)value of 70, (14X5=70) . However, when we measure thechip we get C*=103. L*a'b' has introduced an error of.1E=33. CIELAB overestimates 5.0 YSIJ4's chroma (MC)by (33/70=47%). This is a serious problem. In yellow,L 'a'b' introduces an error of 47% compared with observerdata.Another example is Munsell lOB 6/8. Observers placethe chroma at 40 (5XS=40). CIELAB places chroma at31.9. L 'a'b' has introduced an error of .1E= S. CIELABunderestimates Munsell chroma by 20%. Both· these discrepanciesbetween observation and calculation are muchtoo large. If the entire CIELAB space has similar problems,it should not be used in gamut mapping applications becausethe space will introduce very large errors in uniformity.2.1 Real Chips in the Munsell BookThe following is a systematic study of all colors. It comparesCIELAB values with the MLab values derived fromMunsell notation. The data for CIELAB values come directlyfrom Newhall. Nickerson, and Judd's 1943 paper.'This familiar table 8 gives Y, x, y fot 2i42 chips. This setcontains both 1317 real chip data found in the Munsellbook and the remainder are defined by extrapolation to thespectrum locus· In this analysis we used only the real chipssupplied by Munsell. We used Newhall, Nickerson. andJudd (NNJ's) illuminant C as the standard iIIuminant (seeFig. 2).If we return for a moment to Fig. I, we can review thedesign of Munsell 's uniform space.There are eight horizontal lightness planes perpendicularto the gray axis.There are concentric circles of chroma, with gray atthe center.There are 40 hues that define vertical planes that areparallel to the gray axis down the center.Each plane is made of colors with constant hue.All hue planes are unifornlly spaced (360/40= 9°apart).Figure 3 plots the same data as Fig. 2 in the alb plane.Here all lightnesses are compressed into a single plane.CIELAB is irregularly spaced. Some hues, such as yellow,Journal of Electronic Imaging / Gc/obet 1999/ Vol. 8(4) / 355

McCann'""10_L*a*b* Uniform Color Space_.-.. __ .--"----- --- ••"-----_.- - 60iso!, ~;'""" •"soML Ma Mb Color Space" ---- '"" - -- "•20-- •"" ",,," 20 so,60" '" " " " '" '" "20Cllro .." '"soCllr._" "Fig. 2 Comparison of L· a· b* uniform color space with the proposed MLab. In both graphs chromaare plotted on the horizontal axis and lightness is plotted on the vertical axis. All hue planes arecompressed into the LlC plane. L *a*b* is not uniformly spaced in chroma.10" ," '"expand the chroma, others such as blues, compress thechroma. The distinct radial lines created by Munsell havebeen blurred. The MLab plot on the right shows a regularlyspaced array.2.2 Planes of Constant HueObservers picked the chips on a single page of the Munsellas a set of samples with the same hue. Each of these pagesis uniformly spaced around the hue circle. The values of a *and b* are derived from X, Y, and Z. Nevertheless, constanthue does not correlate with constant dominantwavelength 1 I The discrepancy between hue angle, derivedfrom a' ,b*, and observed color can be seen clearly in Fig.4. Here we look at all the chips found on the 2.5 R, 5 R, and7.5 R pages. We plot the hue angle in C[ELAB space on thevertical axis and give the name of the chip on the horizontalb'Mb120.00L*a*b*UnlfonnColor Space120.0100.0MLMaMbColor Space-80.0 -60.0o 0•-60.00.."• ••-60.080 .0qp.a.-.. ..• 40.0 ••••. .. .. . .... t· ... .. .• .*20.g..... •• •• • • ••• I ••• •• • • •··:i,All'''i'''u\·:···• • - --Q.D-.-""t-' _. J ..I •• 1 .11- --.-600:"4e0·.2~.p ''tip' ~ . rr· 4J'o- 6Q0. 80.0

Calor-gamut mapping.~ . CIO . •.•.••..••.••• -•••••••••••••••••••••.••.•.•.•.•. ••• -•••. -••.•..• -•..••.•• -•.•.. -. .. .... ..,.'J6.00.. . I'.\ •. ~" . '\. ,,·t"l . .l 1. OCUR. ~Fig. 4 The plot of hue angle on the vertical axis vs all the chips onthree pages of the Munsell book. Ideally all the L" a· b· pointsshould fall on the solid lines. A hue angle of 22° could be a light2.SA or a dark 5.0 or 7.5 A chip. CIELAB does not present the samehue in a plane parallel to the gray scale. Rather constant hue is aslanted, rippled suriace.axis. Munsell notation (MLab) places all 2.5 R hues on thesolid line at 9' . all 5 R chips on the 18' line. and all 7.5Rchips on the 27' line. CIELAB portrays a constant hueangle as drifting across three pages of the Munsell book.The drift in Fig. 3 is caused by the fact that CIELAB doesnot position chips with constant hue in a single verticalplane. It creates a slanted plane with lightness that undulateswith chroma.We have defined the expected hue angle in MLab spaceby setting 10 RP to 0' . Then. all 2.5R chips are at 9' . all5.0 R chips are at 18' .... and all 7.5 RP chips are at 351 ' .We can measure the hue error by subtracting MLab hueangle from CIELAB hue angle. Figure 5 shows this errorplotted on the vertical axis versus all the real chips in theMunsell book. Ideally. all the errors would fall close to theo line. The data, however, show that there is considerablevariability for each page in the book. as well as drift aroundthe hue circle .In order to summarize the results so far, we can reviewhow CIELAB portrays the Munsell book .• There are horizontal lightness planes perpendicular tothe gray axis. This is in excellent agreement withMunsell.There are irregular shapes instead of concentric circlesof increasing chroma.The 40 hues are not vertical planes parallel to the grayaxis.Constant hues form corrugated, slanted planes.Hue planes are nonuniforrnly spaced.Except for lightness. CIELAB distorts the fundamental designprinciples of the Munsell book. Since virtually all theerrors are in the alb planes. we can evaluate the magnitudeof the errors by measuring the distance between CIELABposition and the MLab position in the alb plane.Figure 6 defines the L * a*h* error tern! flEr. Theproceedings. 'O with an earlier version of this paper. includesa list of flE, and flE" C for all the real chips in theMunsell book. The rows report data for a particular hue andlightness. The colunms report values for different chromas.A verages are presented at the end of the table. The Munsellchip 2.5R9/2 has a flE, of 5.0. flE,IC is 50%. 2.5RS/2, 4.6 have flE,s of 4.4, 6.4. 8.8 and flE,ICs are 44%, 32%.29%. averaging 35%. The average for all the chips on 2.5Rpage is 23%. The average of the eight R pages is 25%. TheY, G. B, P page averages are 36%. 19%. 14%. and 29%.27 .0018.009.000.00- 9.00~ ~ ~ ~"! "1 > >'" ... '" "!>'""Q."1'"'" '" 0 ~Q. Q. Q. Q.0; "1N-- 18.00Fig. 5 The error in hue angle introduced by CIELAB. The vertical axis is the difference [CIELAB hueangle - MLab hue angle]. The horizontal axis comprises all the real chips in the Munsell book. InL· a'" b '" space Munsell red samples vary from 00 to + 18° discrepancy from the ideal angle. Greensfall between +9° and - 14°. Blues and purples fall between 0° and +20°.Journal of Eleclronic Imaging / Oclober 1999 / Vol. 8(4) / 357

McCann+bDistribution of Directions of Hue Errors~ ~ :: ~ ; ::: :: ~ ; :;:: ~ ': ~ ~ ! '; ; ; ; ! Ii E S S ! c i 5 i Ui ~ 5 5 : aAngle o1J:.r with raspect 10 Angle Co oFig. 8 Histogram of the angle of i::J. E, with respect to the angle of C.If the problem in L:II a'" b* could be fixed by an overall decrease insaturation, then all the errors would fall at 180°, If the problem inL * a* b* could be fixed by overall increase in saturation, then aU theerrors would fall at 0°. These data demonstrate that there is noapparent simple relationship between observed hue shift data(MLab) and calculations (L "' a* b"' ). The error in hue angle is distributedin virtually aU directions from the point (Ma,Mb).Fig. 6 The (Ma,Mb) coordinates show the location in MLab space.The (a* ,b* ) coordinates show the location in CIELAB space. Theline C is the distance from the origin to (Ma,Mb). The line a Er is themagnitude of the error introduced by CIELAB. It is the distance between(Ma,Mb) and (a*, b* ). We evaluated each chip in the Munsellbook as a percentage error by the ratio of tJ.Er to C. Further, weresolved uE, into its components 6C and tJ.H to evaluate the relativesizes of chroma and hue errors.The average of all 91 chips is 42%, 81 chips is 38%, 71 chipsis 32%, 61 chips is 29%, 51 chips is 25%, 41 chips is 22%, 31chips is 21 %, 21 chips is 20%. The average of all 12 chips is30%,14 chips is 26%, 16 chips is 24%, 18 chips is 24%, 110chips is 26%, 112 chips is 31%, 114 chips is 31%, and 116chips is 33%. Studying these data suggests that the patternof these discrepancies is quite complex.Figure 7 shows the histogram of /!, E,I C for all chips inthe Munsell book. On average CIELAB distorts Munselldata by 27% of chroma. Figure 8 plots the direction of hueerrors.Figure 9 shows the breakdown of the Munsell book distancesinto component vectors, /!,H and /!, C (see Fig. 6).The /!,H graph on the left shows that hue discrepancies aresignificant. The middle /!, C graph shows that chroma discrepanciesare somewhat larger. The resultant !:::. Er error isshown in the right graph." Here we see that both /!,H and/!,C are each significant contributors to /!'E,. [n the diagramon the left we see 0 /!,H at the point of normalization(90°). [n the reds the errors range from - 5 to +20. [n this...."Hlstogram"Er I C_._ • ., •• " .. 111111 III III tI" III .. 1111" ... l1li ....... 111- .. .. ~::!'!~:::::G:e;;:;:;;~;~;~~~;:~;;?~;e::::;::Fig. 7 The histogram of .6. E,I C for all 1731 real chips in the Munsellbook. The maximum error is 82%; the minimum is 0.01 %. The meani::J.E,IC is 27%, the standard deviation is 13%, and the median is24%., , ~color region the /!, C increases from - 5 to + 5. Combined,the /!' E, varies from 0 to 30 L*a*b' units. In the yellowregion the /!,H errors range from +20 to -25. Here /!, Cvaries from + 5 to +30 to + 5. Combined the /!'E, variesfrom 0 to 30 L' a * b * units. [n the green region the /!, Herrors range from 0 to - 10. In this color region the /!, C isthe smallest and varies from - 5 to O. Combined, the /!'E,varies from -5 to +5 L*a*h* units. In the blue region the/!,H errors range from 0 to -10. Here the /!,C varies fromo to -10. Combined, the /!'E , varies from 0 to IS. [n thepurple region the /!,H errors range from 0 to 5. Here /!, Cvaries from 0 to -10. Combined, the /!'E , varies from 0 toIS. The green to blue section of color space is best representedby L 'a*b' . The reds suffer from hue angle distortion;the yellows suffer from chroma exaggeration; and theblue-purples suffer hue angle distortion in the opposite direction.Putting the whole story together, we see a very complexpattern of local variations between L *a*b' and observerappearance. Figure 7 shows a histogram mean at 27%/!' E,IC. Figure 8 shows that these errors are in all directions.Figure 9 showed that /!,H is a slightly smaller contributorthan /!'C. Nevertheless /!,H is significant. On averagethe /!'E, IC val ues are greater for higher lightnessesthan for lower ones. Figure 9 shows that the smallest errorsfall in the green-blue region.3 L * a* b * Portrayal of Other Uniform ColorSpacesSo far we have seen that Munsell book observer data andL * a * b' calculations do not agree. The L * a' b * portrayalof Munsell colors agrees in lightness, but is markedly differentin both chroma and hue. If these distortions are commonto all uniform color spaces, then we can conclude thatthe equation set fails to model color appearance. [f theabove observed overestimation of chroma in yellow and itsunderestimation in blue are found in many color spaces,then it is a L *a*b* problem. If, however, these propertiesare unique to Munsell space, then we cannot find fau lt withL *a*h*.We can compare Munsell with other color spaces suchas Ostwald, NCS, and OSA Uniform Color Space and ColorCurve.First, we need to identify sources of colorimetricdata for each space. OSA data are documented in Mac-358/ Journal of Electronic Imaging / October 1999 / Vol. 8(4)

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McCannprinter. Digits used to make printing plates were sent to thefilm recorder. The color transform board stored map coefficientsderived from the press and film calibrations. Theinput digits were sent to the lookup table. All combinationsof the most significant five digits were prestored in theboard. Using prestored information from all nearest neighborswe interpolated the best output in the least significantbits. The hardware board calculated the LUT output valuemuch faster than the film recorder could read image datafrom the magnetic disk. A more complete description canbe found in a U.S. Patent entitled Method and Apparatusfor Transfonning Color Image Data on the Basis of anIsotropic and Uniform Colorimetric Space. 24Kotera and his colleagues 25 - 29 have used 3D LUTs in awide variety of applications, including high speed videoapplications. The 3D LUTs techniques are used to makeaccurate color reproductions of paintings 30 Here the LUTsare used to remove the characteristic sensitivity functionsfound in films 31 These reproductions have a slope 1.0 relationshipwith the painting throughout the entire colorspace. Many commercial products use 3D LUTs as themost efficient way to calculate accurate information in realtimeapplications. For more information on 3D LUTs, seeRef. 32.If we think of the uniform color space problem as acandidate for 3D LUTs we have:AdvantagesAll 1317 Munsell chips have zero error(they are table lookups) .All intermediate values are computed from all theirnearest neighbors.RequirementsRequires a computer program and LUT.Size of program = 80 KBytes.Size of LUT=806 KBytes.Run time = I s for all 1317 chips in the Munsell book.DisadvantagesDifficult to do with a slide rule.There are no disadvantages for anyone using a computer.The lookup table function has been possible for manyyears, first by using the Newhall, Nickerson, and Judd,table as originally designed. The real-time conversion fromMunsell notation to L*a*b* and the inverse interpolationcan be done with a Munsell conversion program sold byMunsell of Grey tag Macbeth. It can be found on the web athttp://munsell.comIDownload.htmMunsell notation is far from ideal in format. L * a * b *, sfannat was chosen so that the one can calculate distancesand angles. The ideal case is to use Munsell information tocalculate a MLab space and use it as we would CrEL*a*b* To be effective we need 3D LUTs to convertL *a*b* to MLab and MLab to L *a*b*5 LabtoMLab And MLabtoLab Working 3D LUTThe best source of data for a 3D LUT is the data fromNewhall, Nickerson, and Judd (NNJ)7 Here they list Munsellnotation colors that are uniformly spaced in appearance.The foundation is a very large study of real papersselected by extensive observer experiments. They interpolatecolors out to the spectrum locus. There is another advantageto the Munsell data. In situations in which therange of colors exceeds the set of reflectance papers, wecan use the rest of the NNJ table to reach the total range ofall possible colors. This simply means that the 3D LUT has2742 input chips, instead of 1317.They provide an atlas of all possible colors that are uniformlyspaced. First we need to make a 3D table of equivalents.We used the NNJ Y, x, y data to calculate L *a*b* inilluntinant C for each chip. The MLab designation was calculatedfrom Munsell notation as follows:Hue angle for 10 RP was set to 0°.A table of the 40 hue pages was spaced 9°.2.5R=9°, 5.0R=18°, ... 7.5RP=351°.H = hue angle from the above table.ML= 10* value notation.MC = 5 * chroma notation.Ma = MC* cos H.Mb=MC* sinH.With Gary Dispoto and Michael McGuire of HP Labs wecreated a pair of 3D LUT LabtoMLab and MLabtoLab andtwo programs to use them. The input and output channelsof the LUTs are scaled to 8 bits. The tables are 65 x 65x 65 x 3 planes, 824 Kbytes which means the six most significantbits are looked up and the two least significant bitsare interpolated. The programs do the transform in eitherdirection, depending on the table used. One program makessingle calculations, with input and output in normal units.The other program is for transforming TIFF images anduses the standard representation of L * a * b * The programsare console applications for Win NT or WlN95/98.All programs ran on an HP Kayak PC with a 300 MHz.'processor. ThI:.LabtoMLab table is 806 KBytes. The programaccepts either a triplet of L *a*b* values, or an arrayof them, and calculates the MLab values for all inputs. Theprogram's size is under 80 KBytes and it takes less than Isecond to convert a 512X512 array of L*a*b* to MLab.The second set of LUTs makes the inverse estimation. Itreads in MLab data and puts out L *a*b* The MLabtoLabcalculation has roughly the same sizes and speeds. Thismeans that anyone concerned with working in a truly uniformcolor space can do so by taking advantage of 3D LUTtechnology. [t takes only a second to get there.Gabriel Marcu presented a recent paper using the sameapproach 33 He used a 3D LUT to convert L*a*b* toMLab. He optintized portions of an out-of-gamut image inMLab space. He got improved pictures by interpolating inMLab space.We are very fortunate these days to have such a widevariety of reliable colorimetric equipment. Many of thesedevices provide direct L*a*b* measurements of high ac-362/ Journal of Electronic Imaging / October 1999/ Vol. 8(4)

Color·gamut mappingcuracy and reliability. The problem is not the devices, butthe L * a * b * space. as seen above. In the future we canspeculate that these devices will include MLab LUTs. Untilthen, pairs of efficient 3D LUT computer programs caneasily transform our data into and out of the uniform Munsellcolor space.6 When Do We Care?Any time that we need to compare two colors and we wantto express that information as a distance we imply an isotropiccolor space. If the colors vary only in lightness, thenL * is perfectly appropriate. If the colors vary in hue angleand chroma, then L * a * b * will introduce on average a 27%error at each end of the color difference. A numerical colorspace must conform to color appearance experiments incolor appearance.7 DiscussionL * a * b * calculations designed to create a uniform colorspace do not correspond to observer data found in Munsell,Ostwald, NCS, OSA , and ColorCurve spaces. The extentand direction of the discrepancies between observer andequation are complex and vary considerably in local regionsof the space. Although these observer based spacesare all different because of their design, they all show similardiscrepancies with L*a*b*'s portrayal of uniformity.The convenience of using L * a * b * made us all use it beyondits experimental definition. No one I know has eversaid that L • a * b * is proven to be sufficiently accurate forthe delicate rearrangement of complex scenes required incolor-gamut mapping. Nevertheless, it is almost universallyused in the evaluation of images and in instrumentation.Whenever we report a separation between two colors as adistance (!J.E), we imply an isotropic space. Whenever weuse L * a * b *, each point has an average isotropic discrepancyof 27%.All the problems of complexity disappear with the use of3D LUTs. The user of the LabtoMLab tables does not noticethe increased computational load between the LUT anda fonnula. They both report their answers in an instant.However, the LUT takes into account all the local variationsfound in the observer data. The LUT has zero errorfor all chips in the Munsell book.We reviewed the selection of Munsell space as the datafor a 3D LUT. The Munsell space shares the same goals asOstwald, NCS, OS A, and ColorCurve spaces. They all attemptto provide a set of colors that are uniformly spaced inhue, chroma, and lightness. The experiments that definedthese spaces were different and therefore the data are somewhatdifferent. Nevertheless, Munsell, NCS , and Ostwaldshow similar properties when compared in L * a * b * space.In OSA space, j and g have a specific relationship definedby the equations 34 and are described by CIE 1964 Tristimu­Ius values. ColorCurve used a * and b *. These hue planeplacements are different from those of Munsell, NSC, andOstwald.1 3The decomposition of the distance between (a * ,b*) and(Ma,Mb) into!J.H and I1C shows that hue distortions introducedby L ' a'b* are substantial, but somewhat smallerthan those introduced by chroma. Lightness discrepanciesare very small.Munsell space remains the preferred space for a uniformcolor 3D LUT. It is unique in that it provides data out to thespectrum locus. It is the compilation of 3 million observationsthat is most highly relevant to the problem. Therecould possibly be some errors in the hue plane placement,but it is not obvious how to improve the data collectingprocess.8 ConclusionsThis paper describes the substantial discrepancies betweenobserved uniform color spaces and calculated L' a * b *.The discrepancies are complex and apparently unique ineach subsection of color space.We recommend the use of 3D LabtoMLab LUT to convertcolorimetric measurement (X,Y,Z or L *a*b') to isotropicMLab. Distances in color space can be accuratelyand conveniently calculated in MLab. When required inverseMLabtoLab LUTs can accurately return values toCIE notation.Calculations that involve finding minimal error in hue,chroma, and lightness, such as color-gamut mapping, willbenefit from analysis in an isotropic space with zero errors.AcknowledgmentsThe author wishes to thank Gary Dispoto and MikeMcGuire for their work on the very fast 3D LUT running inWindows. He also wants to thank Gunilla Derefeldt forproviding colorimetric data on NCS and Peter Engledrumand Max Satzman for leads to NBS work in the 1960s, andto John Meyer, Gabriel Marcu, and Mary McCann for theirthoughtful discussions and comments.ReferencesI. G. Wyszecki and W. S. Stiles. Color Science: Concepts and Metlwds,QII(llItitative Data and Fonnulae. 2nd ed .. pp. 306-330. 506- 513,Wiley, New York (1982).2. E. H. Land and 1. 1. McCann. "Lighlness and rctinex theory," J. 0p"Soc. Am. 61. t (1971).3. M. D. Fairchild. Color Appearance Models, p. 221. Addison Wesley.Reading, MA (1998).4. M. D. Fairchild. "Refinement of the RLAB color space" Color Res.Appl. 21 (5), 338-346 (1996).5. F. Ebner and M. D. Fairchild, "Gamut mapping: Evaluation ofchroma clipping techniques for three destination gamuts," Proc. 6thIS&TISID Color Imaging Conf, p. 57, Scottsdale, Arizona (1998).6. J. J. McCann and M. Slokes. "Color spaces and image quality."Proc. IS&T PieS, pp. 14O-t44 (1998).7. S. M. Newhall, D. Nickerson. and D. B. Judd. "Final report of theO.S.A. subcomminee on spacing of the Munsell colors." J. Opt, Soc.Am. 33. 385 (1943).8. G. Wyszecki and W. S. Sliles, Color Science: Concepts and Methods.Quamitative Data and FormuLae, 2nd ed., pp. 840-852. Wiley , NewYork (1982).9. D. L. MacAdam, "Maximum visual efficiency of colored materials,"J. Opr. Soc. Am. 25, 36t (1935).10. J. J. McCann, "Color gamut measurements and mapping: The role ofcolor spaces." in Color Imaging: Devict! independem Color. 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McCann17. P. Hung and R. S. Berns, "Oetennination of constant hue loci for aCRT gamut and their predictions using color appearance space,"Colo, Res. Appl. 20(5),285-295 (1995).18. ClEo Technical Report ClE No. 11 6 (1995).19. P. Glatz and E. Luebbe, "Colour gamut transformation using visuallyassessed colour difference form ula," Proc AIC, Vol. 1. p. 586, Kyoto(1997).20. F. Ebner and M. D. Fairchild, "Finding constant hue surfaces in colorspace," Pmc. SPIE 3300, 107- 117 (1998).21. Braun and Fairchild. " Color gamut mapping in a hue-linearizedCfEtAS color space:' in Proc. 6Th IS&T/SID Color Imaging Cont,p. 163, SconsdaJe, Arizona (1998).22. M. D. Fairchild. " Refinemem of the RLAB color space," Color Res.Appl. 21(5),338-346 (1996).23. w. C. Rheinboldt and 1. P. Menard .. 'Mechanized conversion of coloimetricdata ro Munsell renolaions," 1. Opr. Soc. Am. 50, 802-807(1960).24. M. Abdulwahab, 1. L. Burkhardt, and 1. 1. McCann, "Method andapparatus for transforming color image data on the basis of an isotropICanrm colorimetric space:' U.S. Parent, Application No. 4,839,721(filed Jun. 13, 1989).25. K. Kanamori, H. Kawakami, and H. Kotera, ,. A novel color transformationalgorithm and its applications." Proc. SPIE 1244. 272-281(1990).26. K. Kanamori and H. Kotera. . 'Color correction teChnique for hardcopies by 4-neighbors interpolation method," 1. Imaging Sci. Technol.36(1), 73-80 ( 1992).27. K. Kanamori. H. Kotera, O. Yamada. H. Mommura, R. likawa, and T.Fumoto: " Fast color processor with programmable interpolation bysmall memory (PRISM)," 1. Electron. Imaging 2(3). 2 13-224(1993).28. H. Kotera, K. KaDamon, T. Fumoto. O. Yamada, H. Motomura, andM. Inoue: " A single chip color processor fo r device independentcolor reproduction." in Proc. First CIC. pp. 133-137 (1993).29. T. Fumoto, K. Kanamori. O. Yamada. H. Motomura. and H. Kotera:"SLANTIPRlSM Convertible structured color processor MN55 15."Pmc. ],d CIC, pp. 101-105 (1995).30. 1. J. McCann, "High resolution color photographic reproductions,"Proc. SPIE 3025, 7 (1 997).31. 1. 1. McCann. "Color imaging systems and color theory: Past presentand future," P,oc. SPIE 3299,38- 46 (1 998).32. H. Kang, "30 lookup table with interpolation," in Color Technologyof Electronic Imaging Devices, Vol. 28, SPIE Press, Bellingham, WA(1997).33. G. Marcu, "Gamut mapping in munsell constant hue sections." inProc. 6th IS&TISID Color Imaging Conf, p. 159. Scottsdale, Arizona(I 998).34. G. Wyszecki and W. S. Stiles, Color Science.' Concepts and Methods,Quantitative Data and Formulae, 2nd ed., pp. 506-513. Wiley. NewYork (1982).John J. McCann has studied color andcalculated sensations since college. As afreshman at Harvard he started to workpart-time for Edwin Land and Nigel Daw atPolaroid. He did an undergraduate thesisunder John Dowling on human adaptationmechanisms. He is co-author of Retinextheory and has written more than 50 paperson color in complex images, colorfrom rods and long-wave cone interactions,spatial-frequency response of the eye, visibilityof gradients, and lightness. He has written a dozen patents onimaging. At Polaroid he managed the Vision Research Laboratory,Large Format Photography, and the Polaroid Replica Collection, adigital reproduction service for fine art, until he retired in 1996. Henow consults and continues his research on color, lightness, andcalculated color sensations. John was elected fellow of 18& Tin 1984and is past president of 15& T.364 / Journal of Electronic Imaging / Oclober 1999/ Vol. 8(4)