PEER.REVIEWED ARIICTE
TheReversibility of Six Geometric Golor Spaces
Tian-YuanShih
Absttact Color coordinate systems provide a way to address, to de- Blue= (0,0, 255) C}/an= (0,255'255) scribe, and to manipulate colors. In the field of image proc- graphics, several color models in essing and computer lvlagenta= (255, A, 255) common use include RGB,HVC, HSv, HLS,and tsu' In this study, the reversibility of several color coordinate systems e = (255, 255,255) characteristicsare studied' All these and-their numerical eack= (0,0, 0 models are classifiedas user-orientedand related to the per' oe en = (0, 255, 0) ceptual color space. Red=(255,0,0) Yellow= (255, 255, 0 ) lntroduction Figure1. The RGBmodel. Color provides a rich and informative attribute for sensory and vGual communication. Color spacesprovide a method to manipulate colors. For remote sensingapplications, manipu- Iating imagesin the perceptual color spacesis efficient and In this study, reversibility is defined as the capacity o^fthe useful for image enhancementand compression(Kruse and color modei to recover the original RGBcoordinates after Raines,1984; Green, 19Bg). In the recentdevelopment of GrS transforming them into this color model. Characteristics of (GeographicInformation Systems),color spacetransforma- color model"s are assessedby transforming (256)" RGBcombi- tionJwere investigatedextensively for data fusion, either for nations to each corresponding color space and then trans- visual enhancement(Welch and Ehlersi 1987; Carper ef o/., forming back to RGB.fhe intermediate values are all scaled 1990; Harris and Murray, 1990; Chavezet al., L991i Grasso, and normalized for storage in the range 0 to 255' tggg) or to improve the accuracyof classification(Mune- chika ef d1.,1993). Both increasingapplications and the na- ColorCootdinate SYstems ture of color spaceitself deservefurther exploration. After analysis of cbmmon color models in computer g9ph-igs Early work on organizing colors into order includes Leo- and image processing, six color models were selected for this nardo da Vinci's Notebooksfrom about 1500. There are study: or to organizecolors. One many ways to define, to describe, I color bubble model [Hvc], method ii to use a three-dimensionalcoordinate system,the . hexconemodel (ssvl, color model (Billmeyer and Saltxman, 1sB1)' In a color r triangle model (tstt), model, eachcolor is addressedby a coordinatepair' Based o double hexconemodel (sls), on various guiding principles, there are severalcoordinate o usv model (Raines,1s77), and the arrangementsthat generate,in turn, color models' A color o Ius model (Pratt,1991; Niblack, 19Bo). model gener- space,a color coordinate system,and a color The eeometrv of these models and the transformation algo- ally expressthe samemeaning. rithris are summarized as follows. In addition to these six Gloss (1984)classified the color coordinate systemsas geometric color models, the hardware-oriented RGs model o obiective, such as CIEXYZ,and Xnd the cIE-L*u*v* and cIn-tHS color models are first briefly r subiective, such as the Munsell system. introduced. In this work, these two cIE models served as ref- erence. The maior differencebetween these two categoriesis the un- principle. The obiective model is basedon physical derlying RGBModel whereasthe subiectivemodel is basedon measurements, The red, green, and blue (ncs) color model, probably the perceptualfeeling. The subjectivecategory is also human most com"monly applied, is used in color cRT monitors and ;'perc-eptual,"because in perceptual color spaces,col- termed employs a Cart-esiin coordinate system. For an B-bit display than in those objective models. Hence, ors are mbre uniform rnri"*. the RGBmodel is illustrated with the color cube distancescomputed in perceptualmodels are closer to i color srrown rn lrgure r. visual differencesfor a human viewer. Among RGB'YIQ, LAB, and opponent color models, the hexcone HSVmodel provides the beli user interaction in terms of the accuracy (Schwarzef al.,1sB7). the question: This article investigates Photogrammetric Engineering & Remote Sensing' 'l'223-1232. which model providesbetter reversibilitywith the 8-bit depth Vol. ot, No. 10, October 1995, pp' limitation? 0099-111.1.2I S5161 1 0-1 2 2 3$3.00/0 Departmentof Civil Engineering,National Chiao-TungUni- @ 1995 American Society for Photogrammetry veriity, 1001Ta-Hsueh Road, Hsinchu, Taiwan, R.O.C. and Remote Sensing
PE&RS l
The backward transformation eouations for the NTSCre- ceiver primary system are ,:d;+0'201
Figure2. Colorbubble ,:#+0.461 model(Smith, 1993). 16)3 v: -1- if I* > 7.996248 # (r*
if l* < 7.996248
CIEL*u*v* Model In 1931, the Commission Internationalede I'Eclairage(c.t.r.) defined three standard primaries f, Y, and Z to replace red, ,yf green,and blue. Subsequently,the L*u*v* coordinatesystem , becamea c.I.E.standard in 1976.This color model providesa -0.s33748 -0.28sz8elfxl computationally simple measureof color in agreementwith 1.e10364 f -0.s84377 -0.0268181yl the Munsell color system,which is a perceptually uniform : 1.ssB3B4 I (3) | color space(Pratt, 1991). ffilL 0.058164 -O.11BO7B O,BS6B4OJLZJ The forward and backward transformationsbetween RGB and L*u*v* color modelsare definedas follows: CIEIHSModel f0.607 o.'t74 0.2011fnl In the CtE-L*u*v*color space,L* representsthe intensity,u* : (1representsthe chromaticity variation from green to red, and h L:.a::B::t ?.iiilLFI v* represents the chromaticity variation from blue to yellow. A perceptual color spaceIHS is then defined from L*u*v* with the following equations: J* - 25[1,OOY|Y]1/3- 16 ,, {,,.o.ooaBb6 I- L \/ ' / rr*x - FI: tan (:l (4) 903.3 tr < 0.008856; \LI'l _rrt I,t S:[(u*),*(v*)z1ttz ,4X u: x+15Y+32 ColorBubble Model Using a floating disk with variable radius, the color bubble, 9Y v:r*ruya32 Smith [1993) derived the representation of colors in the HVC (hue, value, chroma) system-.These three dimensions are de- u*:131*[u'-uu) fined as the dominant fiequency (hue), Iuminance (value), and the amount of color (chroma). Although the color bubble '/ : 1.3L*(l - v) (2) model can be presented on plane paper, it actually defines a three-dimensional soace. From the referencewhite in the NTSCreceiver primary sys- As illustrated in Figure 2, a floating disk (color bubble) tem, Y,,,uo, and v0are computedas 1.000,0.201, and 0.461, referred to one coordinate line has three degrees of freedom: respectively. the radius, center height, and the rotation. On this bubble, n, G, and B points are spaced evenly. The line from the center, which is normal to the horizontal axis. is the baseline. The Hue parameter is defined as the angle between the radius from the center to the green point and the baseline. The ver- tical coordinate of the center constitutes the color's Value, and the radius is considered as the Chroma. The transforma- tions between this color coordinate system and RGBare
Figure3. Hexcone V:(R+G+B)13 model. H:tan'(ffi) t5J C : (V - G)/cos(II) if lcos(F4| > o.2 C : (n - Bll(V5sin(r4)if lcos(.Fl| < o.z and
L224 PE&RS l PEER.REVIEWED ARTICTE
by addingblack, or in generalobtains a toneof thathue by addingsome mixture of white andblack, a gray(Smith, 1978). Geometricallv.the HSVmodel is the RGBcube tilted onto its back corner.it is formed by viewing the ncs color c;ube along its principal diagonal from white toward black (Figure 3). The top of this hexcone correspondsto the principal sec- tion of the color cube. For a detailed derivation, see Smith (1978).The transfor- mation describedbelow is developedaccording to Levkowitz and Herman (1993)and Foley ef 41,(1990). Let max representthe maximum value among (R, G, B), and min the minimum value, V = max; if Y: 0, then S : 0; otherwise, Figure4. Tint,tone, shade,and S:[max-min]/max; gray. if S : 0, then H in undefined; otherwise, let (7) G-8,, If R:V:max(R,G,BJ,thenH: max - mln R:v-c"orfa.?] lf G: V: max(fl,G,8),then H : 2 + -!-! . , m€x - mrn G:V-Ccos(F4 (61 l- -'l : : B:V-Ccosl H-':l" If B V: max(fi,G,a),then H 4 +ffi L 3J Then, H can be scaledto [0, 360] by multiplying by 60, or BecauseHue is measuredas an angle, a singular casearises normalized to [0, r] by dividing by 6, or scaledby multiply- when the radius of the color bubble, the chroma, is zero. ing by (255/6)to the rangeof [0, zss]. This transformation The Color Bubble model is clearly analogousto a cylin- can be reversedwith the following algorithm: drical coordinate system. If S : 0, and H is undefined; then (R,G,B): (V,V,V). Otherwise,scale Hback to [0, 6], let HexconeModel i : Floor(FI),in which i is the sectornumber of the hue "Mimicking the way an artist mixes paints on his palette," angle; (1978) Smith derived a color model based on the geometry of : H - j; in which the hue value in each sector; (Figure f /is Hexcone 3). The three primaries are named hue, sat- min: V(1 - S);mid1 : V(t - Sfl;midz: y(1 - S(1 (Hsv). uration, and value The artist's tint, shade,and tone - max : Y; then, concepts(Figure 4) are intuitively incorporated: fl); i : o, (R,G,B): {max,midr, min), He choosea purehue, or pigment,and lightens it to a tint of i : 1, (n,G,B): (midz, max, min), -- that hue by adding white, or darkens it to a shade of that hue i 2, (R,G,B): (min, max, midl),
Figure5. Trianglemodel. PEER.REVIEWED ARIICIE
i : 3, (R,G,B): (min, mid2, max), i : 4, @,G,8): (mid1,min, max), i : 5, (R,G,B): (max,min, mid2).
TdangleModel Besidesthe hexcone model, Smith (1978)also describeda triangle-basedmodel. Utilizing the generalizedbrightness and weights generatesa family of color models. Gonzalez and Woods (r9SZ) presenteda triangle-basedmodel with derivations. Although there are some distinctions in the com- putational schemefor hue angles,this model is equivalent to the unbiased caseof the triangle model of Smith (rSzA).a Figure6. Doublehex- graphic illustration appearsin Figure 5. conemodel.
1 I:;(R+G+B).
s : 1 - and (e) - .-+E [min(n,G,B)], +(n-B)l )u^-c) O: "tr-t{- - G)'+ (R - B)(G- B)1,'l'
The Hue is undefined when S : 0, and S is undefined when 1:0. - The ISH-Io-RGBtransformation is divided into three sec- ^ fmax min) b : ;______,__-, when L S 0.5; tors: tm€x + mlnj
,d - (max - min) gqg<:-, 5:^ ----.-.whenL>0.5. ,r (z-mEIx-mln, (C-BI B:r(1- s). = * ," n rfr H : "-r=:. : '.|, - if ^R max; (11) L co'("iT'" - t)l max mrn G:3r-(fi+r1; '-! H:2 +ffi ifG = max; . n r!. 33 @-G)i H:4+ ifB=max. s.or(a - '+) max - mtn R:r(1-s),c: ,['-, - (10) cos(n Fl I' Then, scaleFI into the demandedrange. The reversetransfor- B:31- (fl + c); mation starts with rescaling the hue angles back into the 4tr-1H<2r, range [0, 6]. Then, if S: 0, His undefined;then(R,G,B): (L,L,L).Orher- wise, scaleHback to [0, 6]; let scos(a - G: 3r(1.- s),B: r[, . ? ".,(T-,n R:31 - (G + B).
DoubleHexcone Model When transforming a cylindrical coordinate system onto a cube, a double hexcone model results (Figure6). The three coordinatesof this color spaceare Hue, Lightness, and Satu- Figure7. nsv model(Rar- ration (um). The following transformationsare developed nes,1977). based on Levkowitz and Herman (1993). - Let max representthe maximum value among (R, G, B), and min the minimum value; then. r-Ilrn] t: Irngl
If max : min, then S = 0, and H is undefined. Otherwise,
L226 l
PEER.REVIEWED ARTICTE
TnerE1. Rnrucror Colon Mooers -\6 -'jl Model Para. Range Para. Range Para Range rtd
RGB R [0, 2551 G [0, 255] B [0, 2bs] CIE-L*u*v* L* lo, 72O\ D* l-976J.7071 [-117e,Bs5] (14) CIE-IHS H lo,2r) S [0,17s7] I lo,72ol Bubble H lo,2n) C [0, 170] [0,2s5] Hexcone H [0,6] s [0, 1j 1/ [o, 255] |;r Triangle H [o, zr) s [0, 1] I [0, 255] Double Hexcone H 6) S 1] L fllit [0, [0, [0,255] $ Raines[1977) H [0,2r) S [0, 2o8l lo, 4221 l: : : (FI). Pratt(1991) H lo, 2r) s [0, 233] I [0,2s5] in which % Scos (F4 and % Ssin Niblack (rseo) H lo, z1l.) s [0, 2oB] I [0,25s] For input of R, G, and B in the range[0, 255],hue: [0, eool, value: [0, 442], saturation:[o-zos]. There is a model of a sim- ilar formulation statedby Shettigara(1S92), having exactly : i Floor(F|, in which i is the sectornumber of the hue the same formulation but another baselinefor hue angle. angre; : H - i; in which is the hue value in each sector. f / IHSModel (Pratt, 199! Niblack,1986) Depending on the lightness (I) , there are two cases: Pratt (1s91)stated an tHs (Intensity,Hue, Saturation)coordi- , nate system.The transformationbetween IHSand RGBspaces if L
y, : : Accordingto Pratt (1991),the element(2, z) of the transfor- if 0, H is undefined; otherwiseA t""-t ( $). ' vt' mation matrix in Equation 16 has a positive sign. Because the transformationmatrix in Equation 16 is actually the in-
PE&RS PEER.REVIEWED ANTICIE
TneLE2. ExrReveMrscrosunes ur'l Positive Negative t
AR AG AB AR AG AB ttel CIE-L*u*v* 2.79782.3088 2.8611 -2.8229 2.3276-2.9053 CIE-IHS J.+6 / 3 2.5365 4.6143 -3.5463 -2.5203- 4.6659 Color Bubble 2.2226 2.2226 2.2226 -2.1960 - 2.1960- 2.1960 'nfl -3.0829 -3.0829-3.0829 H Hexcone 3."12783.1.2783.1278 Triangle 4.7626 4.1.6264.'t626 -4.3404 - 4.3404- 4.3404 -3.5764 - ffl Double Hexcone 2.9882 2.5882 2.5882 3.9764- 3.5764 Raines(1977) 1.8631 1.8631 1.8631 -1.9066 -1.9066-1.9066 _o.408248 Pratt(1s91) 2.71.842.1239 2.2233 -2.7625 -2.7\87 -2.2120 -0.408248 _i33r,12] Niblack (1986) -3.0685 -3.13s0-1.2059 3.1479 3.11291.1958 ,,' 0.816497 | lil verse of the transformationmatrix in Equation 15, the ele- in which % : Scos (.FI and % = Ssin (14. ment (2, 2) in Equation 16 should have a negative sign. The detailed derivation of this color model was not Dro- Relative to the HSV model developed by Rairies (1972), the vided by Pratt (1991).Background work revealed that it may elements in the first row of the transformation matrices indi- also have been derived from cylindrical geometry.Following cate another scale choice. The transformation matrix in Niblack (1986),the ll : G : B axis is taken as the intensity Raines (1977) model is an orthogonal matrix, whereas the coordinate.The vector V, is defined as orthogonalto inten- one developed following Niblack (rOaO) scheme is not. sity axis l and lies in the plane of l and the blue axis B. The third axis V, is the crossproduct of l and V,. the resulting Range,Singular Points, and the Validation transformations are BecauseB bits is the image depth commonly used, the do- main selectedfor this work is a set of integersbelonging to [0, 2551.The final ranqe used is also the same for eaih coor- r ! ! dinate. In order to have an appreciation of rounding errors 1.l.., during this scaling process,the original rangesof each color spaceare summarizedin Table 1. For the L*, u*, v* and I S 07of cIn models and S of the Niblack (1986)model, the ranges frll*++llgl are rounded to the nearestinteeer. Lnl In all six models, there is i common sinsular situation, oJ-' When saturation is zero, the hue anqle is undefined. When LT + the intensity is zero,both saturation-andhue are undefined. In the practical implementation, there are different condi- tIons. :lr,;::ru (1) Color Bubble Model (Hvc) s;ffi#] - If R + B : 2G, then (V G) would be zeto. Together +,;::;l: - : lal with.R B 0, the singular situations occur when R :G:8. (2) Hexcone Model (usv) When r? : G : B, S is zero, then H is undefined. t:(tt*rr)''' (3) Triangle Model (tsu) The saturationreaches zero when (rt + G + B) : 31-itt @, G, B)1.This set includes all casesfor which R : G if V, :0, H is undefined;otherwise, H : tan ' (+) :8. (4) Double Hexcone Model (Hr-s)
Tnsre3. CooRornnrEsor ExrRevEMrscrosuRes
Positive Negative
AR AG AB AG
CIE-L*u*v* 1255,255,242) 12s2,247, 24o) 1241,2s1,252) 1255,244,248) (252,254,23O) (2s2,23s,2s2) CIE.IHS 1250,238,2) 1228,2s1.,'tl [zzt,o, zss] l24B,2ss,741 [2s0,238,3] [250,6,2s3l Color Bubble (7, o, 252) (o, 7, 2s2) (2s2,0,7) 11,4,252, o) (o,1.4,2s2) (o, 2s2, 14) Hexcone (26, 7, 238) (7, 26, 238) (7, 2s8, 26) (64, 1.8,248) (248,64,18) (rB, 248, 64) Triangle (255,7, 3) (3, 255,7) (3,z, zss) (246,s, 15) (15,246,5) (1,s,s,246) Double Hex. (254,254,O) (o, 254,254) 1254,o,254) [3,0,255) (255,3,0) (0,255,3) Raines (1977) (1.7J,zss, o) (o, 1.23,2ss) (0,2s5, 123) (43, O, 252) (252,43, O) (o,2s2,43) Pratt [19s1) [244,255,2) (2,4,254) [3,2s5, 18) 1234,255,2) (2, 1,O,249) (rr,2ss,7) Niblack (1986) (255,255, 0) lzss, 231,ol lo, z4s,2Bl t1.8,o,2s2l [2ss,25b, o] I2ss,o,7l
PE&RS PEER.REVIEWED ARIICI.E
TneLe4a. AvERAGEMtscLosunts (Sreps 1 rHnoucH 3) AverageError Average Absolute Error
G t,
CIE-L*u*v* - 0.000733 -0.000650 - 0.001032 0.617156 0.4s8570 0.5s7018 - CIE-IHS - 0.000693 - 0.000705 -0.0008s4 0.621808 0.509042 0.696090 -0.000040 Color Bubble 0.001612 -o.00L572 o.413744 0.413804 o.41.3730 Hexcone 0.008087 0.008748 0.0076s3 0.314692 0.314693 0.314692 Triangle 0.000000 0.000000 0.000000 0.463183 0.463183 0.463183 Double Hexcone - 0.246636 - 0.245965 -o.257021 o.472382 o.472247 o.472472 Raines(1977) -o.ooo227 0.000200 0.000021 o.340292 0.3402s3 o.340252 Pratt (1.9911 0.001359 0.001320 0.000038 0.455454 0.358639 0.388680 Niblack (1sB6) 0.001ss4 -0.002113 0,00011s 0.516513 0.516505 0.230915
TneLE4b. AvrnncE lvllscLosuREs(Sreps 1 THRoUGH4)
Average Error AverageAbsolute Error
G G
CIE-L*u*v* 0.000707 - 0.0004s8 - 0.001070 o.570067 0.436569 0.542836 CIE-IHS 0.000603 - 0.0009s1 -0.000645 o.575676 o.452490 o.652524 -0.000264 t,olor IJuDDle 0.001887 -0.001209 o.332004 o.332117 o.331S86 o.239776 Hexcone 0.004853 0.005489 0,004464 o.239"175 o.239774 Triangle - 0.000376 - 0.000376 - 0,000376 0.381392 0.381392 0.381392 Double Hexcone -o.246372 -o.245645 -o.246707 o.426773 0.426606 o.426872 Raines(rgzz) 0.000s66 o.oo1240 o.oo11.27 o.234453 o.234453 o.234453 - - o.288557 Pratt[19s1) 0.001268 0.001063 0.000149 0.365176 o.252219 Niblack (1986) 0.003830 - 0.000176 0.000186 o.439327 0.43S316 o.o87788
TABLE4c. AVERAGEMtscLosuRES (STEPS 1 rHRouGH 5) AverageError Average Absolute Error r G
CIE-L*u*v* 0.000688 0.001052 0.000743 0.567461 o.434788 o.5404L4 CIE-IHS 0.000665 0.0002s0 0.o01038 o.572914 0.45056S 0.649373 - Color Bubble 0.001861 - 0.001210 0.000251 0.330582 o.330720 0.330576 o.375523 r r rorIElrs 0.001493 0.0014s3 0.001493 o,379523 o.379523 Raines(1977) 0.000983 0.001256 0.001146 o.233487 0.233489 0.233486 -0.000164 Pratt (1s91) - 0.001182 0.001019 0.363613 o.251."171. o.287354 Niblack (19861 0.003842 - 0.000126 0.000180 0.437160 o.437171 0.087395
as HSV; The singular condition is (max : min), that is, all fi : G to convert RGBinto perceptual components, such round the resulting perceptual coordinates : B cases. to scale and to into 255] integers for storage; (5) HSV Model (Raines, 1977) [0, to read in the peiceptual coordinates of an 8-bit unsigned and Raines (1984), R : G : B In the model of Kruse integer and to scale them into the pro-per domain: : makes V, zeto, R G makes V, zero. to c6nvert perceptual coordinates back to ncs and to round (6) IHS Model (Pratt, 1991) ano (a)f =0:^R: G:B:o; -- (b) S : 0; R + G: 28 which causes V, to be zeto,2R G which causes V, to be zero TABLE5a. Roor-Mrn|l-SqunneEnnoRs (STEPS 1 rHnoucH3) There are 45 points in the B-bit integer (fi, G, B) space which satisfy the S : 0 condition. (7) (Niblack, 1986) rHSModel CIE-L*u*v* o.773502 0.626774 o.764209 The situation is the same as the I{SV model of Raines CIE-IHS 0.780609 0.632892 0.88S928 (1.577). Color Bubble o.526557 0.526887 0.526895 Hexcone o.57007r o.570074 0.570069 Reversibility Triangle o.655407 0.655407 0.655407 Double Hexcone 0.696489 0.696253 0.696632 Because all of these color space transformations are non-lin- Raines (1977) 0.45117S 0.451181 0.451180 from RcB, then transforming back with B-bit ear, converting Pratt (1991) 0.605020 0.468074 o.51.6202 unsigned integers fails to assure a full recovery. Niblack (1e86) 0.683059 0.683039 o.2s2574 Examining the procedure, the steps are
PE&RS PEER.REVIEWED ARIICTE
Tnere5b. Roor-Mrnru-SqunREERnoRs (SrEps 1 rHnoucH4) TaeLe6. FREeuErucvoF OccuRRENcES(TRrntcle vooel, Srrp 4)
G B O osH<2d3 -5 o 0 0 -4 651 651 0 Tnarr5c. Roor-Menru-SqunRrEnRons (SrEps 1 rHnoucH5) _J 12255 12259 0 G -z 1571.89 15951 1 0 _I \202547 r224042 63750 CIE-L*u*v* 0.822900 0.682018 0.810803 0 282846"1 2816112 5467349 CIE-IHS 0.828930 0.690840 0.931380 1 1.220059 1210898 67227 Color Bubble o.587852 o.587857 o.587751 z 159578 1.57271 0 Triangle 0.686820 0.686820 0.686820 1L1.46 1.1.1.46 0 Raines(1977) 0.488092 0.488094 0.488090 A 430 430 0 Pratt{19911 0.645138' o.508427 o,553797 0 o o Niblack (1s86) o.725375 o,725274 o.295627 2n/33H<4n/3 *5 0 _A 0 ocl crcl -J 0 12259 72259 (5) to fit into the range [0, 25S]by setting negativevalues to 0 0 15718S 159511 and values larger than 255 to 255. -"1 63048 1.201.845 7277740 0 JAJO IbJ 2797277 2757343 Clearly, steps (1J and (3) are B-bit unsigned integer-to-real 1 60467 1,21.5305 7203929 computations, whereas steps (2), (+), and (5) are real-to-B-bit z 0 159578 75727\ integer computations. The major rounding effect is expected 3 0 1.11.46 71746 to occur in step [2). Because the transformation from RGB to 4 0 430 430 tr the perceptual space transformation is not linear, the magni- 0 o0 tude of the influence is not constant for all Rcn coordinaie 4n/3 L230 PE&RS PEER.REVIEWED ARIICTE TneLe7. Srnrrsrrcsor MrscrosuneOccURRENcE (Srrps l- rHnoucn5) All Different At Least One CIE-L*u*v* 1.594-124 14269186 8602044 7039857 8089868 CIE-IHS 2266029 14321,981 8673515 73354L4 9201630 Color Bubble / / +JJZ lllb5/ lJ 5420507 5423949 5420980 Hexcone 0 9775963 3258659 3258650 3258654 Triangle 2897"1 12621165 5644918 5644S18 5644918 Double Hex. 0 L326044 6243L2B 6241.543 6244004 Raines[1977] 276690 7029387 3877440 3877472 3877423 Pratt(1991) 734224 8228563 5660608 4L52546 465A790 Niblack (1986) 4371.94 8474632 6602490 6602275 1466250 TeaLe8. MMIMUN4EUcLTDEAN Drsrlnce ANDITS LocATtoN Gloss, G., 1-984. Lecture Notes for Cartography I, Department of Sur- veying Engineering, University of New Brunswick, N.I]., Canada. Maximum Dist Location Gonzalez, R.C., and R.E. Woods, 1.992. Digital Image Prccessing, Ad.- CIE-L*u*v* 4.35889S (222,226,2s5) dison-Wesley Publishing Co. CIE-IHS 5.099020 (230,10, 15s) Grasso, D.N., 1993. Applications of the IHS Color Transformation for Color Bubble 3.000000 (o,7, zso) 1:24,000-Scale Geologic Mapping: A Low Cost SPOT Alternative, Hexcone 3.000000 (0,3,234) Photogrammetric Engineering & Remote Sensing, 59(1):73-80. Triangle 5.000000 (o,3,2o2) Green, W.B., 7989. Digital Image Processing, A Systems Approach, Double Hex. 4.1.23106 (0,87,25s) Second Edition, Van Nostrand Reinhold. Raines(1977) 2.828427 [0,4,250) Pmtt (1es1) 3.741657 (1,2ss, s) Harris, f,R., and R. Murray, 1Ss0. IHS Transform for the Integration Niblack (1s86) 4.242614 (o,6, 247) of Radar Imagery with other Remotely Sensed Dala, Photogram- metric Engineering & Remote Sensing, 56(12) :163 1-1641. foblove, G.H., and D. Greenberg, 1978. Color Spaces for Computer Graphics, Proceedings of SIGGRAPH'79 Conference, Atlanta, 1992; Khoros, 19s1), and for computer graphic applications Georgia, 23-25 August, 3[ACM):10-25. (Claris, 1991; Joblove and Greenberg, 1978; Schneier, 1993; The Khoros Group, University of New Tajima, 1983; Torel and Smith, 1990). Among all these mod- Khoros, 1,991.Khoros Manual, Mexico. els, the sSV model derived by Raines (r9ZZl provides the least error in the forward and backward transformations for Kruse, F.A., and G.L. Raines, 1984. A Technique for Enharrcing Digi- in Munsell Color Space, B-bit depth image representation. The reversibility error is in- tal Color Images by Contrast Stretching Proceedings of the lnternational Symposium on Remote Sensing significant for human visual interpretation. However, it may of Environment Third Themotic Conference: "Remote Sensing be worth considering when an analytic operation, such as for Exploration Geology," 16-19 April, Colorado Springs, Colo- classification, follows the color space transformation. rado, ERIM, pp. 755-760. Levkowitz, H., and G.T. Herman, 1993. GLHS: A Generalized Light- Acknowledgment ness, Hue, and Saturation Color Model, CVGIP: Graphics Models The author wishes to exDress his sincere thanks to the anon- and Image Processing, 55(4):271,-285. ymous reviewer, whose tonstructive suggestions have greatly Munechika, C.K., J.S.Warnick, C. Salvaggio,and J.R. Schott, 1993. enhanced the completeness of this article, and to the Na- Resolution Enhancement of Multispectral Image Data to Improve tional Science Council of the Republic of China for financial Classification Accuracy, Photogrammetric Engineering & Remote support through the NSC 82-0410-E-009-160research grant. Sensing, 59(1):67-72. PCI, 1s87. IHS-RGB Conversion, Manual for PACE Image Analysis Kernel Package, PCI. References Pratt, W.K., 1997. Digital Image Processing, Second Edition, John Wiley & Sons, Inc. "1981. Billmeyer, F.W., and M. Saltxman, Principles of Color Tech- Raines, G.L., 1,s77. Digital Color Analysis of Color Ratio Composite nology, SecondEdition, John Wiley & Sons. Landsat Scenes, Proceedings of 11th International Syntposium Carper,W. J.,T.M. Lillesand, and R.W. Kiefer, 1990.The Use of In- on Remote Sensing of Environment, University of Michigan, tensity-Hue-SaturationTransformations for Merging SPOT Pan- Ann Arbor, pp. 1463-1472. chromatic Muitispectral Image and DaIa,Photogrammetilc Schneier, 8., 1993. Color Models, Dr. Dobb's lournal, 1993(July):38- Engineering & Remote Sensing, 56(4):459467. 43. Chavez,P.S., S.C. Sides, and Anderson,1991. Comparison of J.A. Schwarz, M.W., W.B. Cowan, and J.C. Beatty, 1987. An Experimental Three Different Methods to Merge Multiresolution and Multis- Comparison of RGB, YIQ, LAB, HSV, and Opponent Color Mod- pectral Data:Landsat TM and SPOT Panchromalic,Photogram- els, ACM Transactions on Graphics, 6[2) :12 3-158. metric Engineering& RemoteSensing, 57(3):295-303, Shettigara, V.K,, 1s92. A Generalized Component Substitution Tech- Claris, 1991.MacDraw Pro Color Gujde,Claris Corporation. nique for Spatial Enhancement of Multispectral Images Using a ERM, 19S3.ER Mapper Reference,Earth ResourceMapping, Austra- Higher Resolution Data SeI, Photogrammetric Engineering & Re- mote Sensing, 58t5):561-567. Foley,f.D., A. van Dam, S.K.Feiner, and J.F.Hughes, 1990. Com- Smith, A.R., 1978. Color Gamut Transform Pairs, Proceedings of SIG- puter Graphics,Principles and Practice,Second Edition, Addi- GRAPH'78 Conference, Atlanta, Georgia, 23-25 August, 3(ACM): son-WesleyPublishing Company. L2-L9. PE&RS PEER.REVIEWED ARIICTE Smith, Harry J., 1993.Putting Colors in Order, Dr. Dobb'sloutnal, f- Tian-Yuan Shih tssslluiy):+0. 1ff$\ fi"tt-you.r Shih is AssociateProfessor of Civil Taiima,J., 1983. Uniform Color Scale Applications to Computer $ffif Engineeringat NationalChiao-Tung University, Graphics,Computer Vision, Graphics,and Image Processing,2L: W Taiwan, Republic of China. He received his 'W\- 305-325' B.Sc.E. andM.Sc.E. degrees from National rhorell, L.G., and w.]. smith, 1ee0. using computer co)or Effec- aKI 3h"""d-tftT''l].rirrursity, Taiwan, and the Ph.D. tively, An lllustrated Reference,Prentice Hall. deqree from the University of New Brunswick, Fredericton, Welch, R., and M. Ehlers, 1987.Merging Multiresolution SPOT HRV N.E., Canada. His current research interests include digital and Landsat TM Data, Photogrammetric Engineering & Remote photogrammetry, knowledge-based image analysis, and the Sensing,s3(3):301-303 ilata fision in a CfS environment. (Received4 January1994; accepted 2o lune 19941 I 0 n IH C0 rtrI ll G AnIr c LEs The following list includes only thosearticles scheduled for Ieffrcy S. Peake,Remote Measurement of Algal Chloro- publication in PE6frS through March 1996. phyll in Surface Waters: The Case for the First Deri- vative of Reflectancenear 690 NM. R. M. Batson and E M. Eliason, Digital Maps of Mars. Sorcn Ryherdand Curtis Woodcock,Combining Spoctral and Michael F. Baumgatuter and Nbfi Rango,A Microcomputer- Texture Data in the Segmentationof RemotelySensed BasedAlpine Snow Cover Analysis System(ASCAS). Images. Michal Boulianna, Rock Santenv, Paul-Andr6 Gagnon, and Eric M. Sanden, Carlton M. Brittan, and lames H. Everitt, Cl6ment Nolefte,Floating Lines and Cones for Use as a Total Ground-CoverEstimates from Corrected Scene GPSMission Planning Aid. BrightnessMeasurements. Grcgory l. Carbone, Sunr,l Norumo/anr, and Michelle Kng' Howard Schulb' ShapeReconstruction from Multiple Imagesof Application of RemoteSensing and GIS Technologies the OceanSurface. with PhysiologicalCrop Models. Tian-Yuan Sfirrt, A Photogrammehic Simulator for Close- NIen E. Coo,kand John E. Pinder III Relative Accuracy of RangeApplications. RectificationsUsing CoordinatesDetermined from Maps Mohammed E. Shokr, lnutence l, Wilson, and Dwayne L' and Global Positioning Systems. Sutdu-Miller, Effect of Radar Parameters on Sea Ice Christopher Deckeft and Poul V. Bolstad, Forest Canopy, Tonal and Textural SigrraturesUsing Multi-Frequency Terrain, and Distance Effects on Global Positioning Polarimetric SAR Data. SystemPoint Accuracy. Daniel R. Steinwand, John A Hutchinson, and lohn P. Snydea Bon A. Dewitt, Initial Approximations for the Three- Map hojections for Global and ContinentalData Setsand Dimensional Conformal Coordinate Transformation. an Analysis of Pixel Distortion Causedby Reprojection. Sam E&sfrun4 Landsat TM-Based Forest Damage Assess- Antonio M. G. Tommaselli and Cl6sio LuisTozzi, A Recursive ment: Correction for Topographic Effects. Approach to SpaceResection Using Straight Lines. YosserEl-Manadili and Kurt Novak, Precision Rectification Gary M. Wohl, Aperational Sea Ice Classification from of SPOT Imagery Using the Direct Linear Transfor- Synthetic Aperture Radar Imagery. mation Model. . November Special Issue on Iaila M.G. Fonseca and B.S. Maniunath, Registration Tech- Geographic Information Systems niques for Multisensor RemotelySonsed Imagery. David l. Cowen, lohn R. lensen, Patrick l. Bresnahan, Maurice S. Gyea Methods for Computing Photogrammetric Re' GeoffrcyB. Ehlea Denick Grcves,Xueqiao Huang, Chris fraction Corrections for Vertical and Oblique Photographs. Wisner, and Hol/ L232