Color and Printer Models for Color Halftoning

Transcription

1 Color and Prnter Models for Color Halftonng Chang-Yeong Km Samsung Advanced Insttute of Technology, Sgnal Processng Laboratory P.O. Box 111, Suwon, Korea 44-6 E-mal: satgw.sat.samsung.co.kr In-So Kweon Korea Advanced Insttute of Scence and Technology, Department of Electrcal and Electronc Engneerng 27-43, CheongRyangRDong, DongDaeMoonGu, Seoul, Korea Yang-Seock Seo Samsung Advanced Insttute of Technology, Sgnal Processng Laboratory P.O. Box 111, Suwon, Korea 44-6 Abstract Two error dffuson algorthms, based on Pappas s prnter model accountng for dot-overlappng and nk dstorton, are presented to acheve good color reproducton. The basc dea s to comblne prnter and color models on the perceptually unform Commsson Intematonale de l Eclarge (CIE) L*a*b* (CIE 1916) color space. The models, derved from the Neugebauer equatons and color matchng theores, are desgned to acheve the mnmzaton of the human vsual color dstortons between the colors of orgnal pxels and those of a halftoned mage. The effectveness of our approaches s shown by comparson and examnaton of two error dffuson algorthms wth prevous methods: the error dffuson based models and the wndow based mnmzaton algorthm. Expermental results of the error clppng technque, focused on the real applcaton of the nonseparable algorthm, and the desred range of error dppng, where an mage produced by the nonseparable algorthm can be stable wthout addtonal color dstorton, are reported. 1 Introducton Color halftonng s a method to smulate a contnuous tone mage wth lmted number of colors. 1,2 One of the man drawbacks of halftonng technques s the poor spatal resoluton, whch s caused from dther matrces. To overcome ths problem, error dffuson methods are wdely used 1,3 and several research results were obtaned that mproved the performance of error dffuson method. 4 1 Currently, color prnters are wdely used and there are efforts to mprove the sgnfcant problem n color prnters of the spreadng of nks, whch generates color dstortons by dot overlap. To consder the problem and mprove the mage qualty, a general framework for the model-based approach n color error dffuson was proposed by Pappas. 5 He also treated the mperfect nk case and showed examples that dot sze s 2 tmes the deal pxel sze. 6 Recently, the model-based approaches usng Pappas s prnter mode1 5,6 have been exploted by several authors. 11,12 As the result of these approaches, t has become clear that the model-based approach can be a powerful tool to mprove the qualty of the mage produced by error dffuson. However, the effectveness of color halftonng technques consderably depends on the color space that s used. Prevous methods have not adequately taken ths characterstc nto account n mplementaton. Some mportant ponts to be consdered n desgnng color error dffuson algorthm are the followng, The frst s to select standard color space lke Commsson Internatonale de l Eclarage (CIE) XYZ, CIE 1976 L*a*b*, and CIE 1976 L*u*v* (Ref. 13) as the quantzaton doman n the error dffuson algorthm. The advantage of adaptng a standard color space s that t s then possble to drectly prnt mage data composed of the standard color space. For example, the CIE 1976 L*a*b*, whch s referred to as LAB n the followng sectons, wll be used as the standard color space for color facsmle n the future, 14 and t must characterze color devces n terms of a standard color space n the color management system. 15,16 The second pont s the selecton of the color space where the quantzaton process occurs, so that the error vector or dstance measurement s perceptually unform over that space. 1 We have shown the algorthm structure and an ntal result that shows mage qualty could be mproved by adoptng the perceptual unform color space LAB n the model-based approach. Based on Ref. 12 and expermental data, we report here the method, expanded and mproved to focus on the applcaton technology n practce. Especally, Chapter IV Halftone Analyss and Modelng 325

2 we gve the optmal range of error clppng to effectvely prevent the dvergence of an mage n the nonseparable algorthm. The effectveness of the error clppng method s proved by applyng t n the mages of dvergence and convergence. In these algorthms, we use the color model from Pappas s prnter model, whch ncludes a color model and a prnter model, 5,6 to analyze color correcton effects n terms of the standard color space LAB. The models are derved from a numercal calculaton based on the Neugebauer equaton when the fractonal area s known, as n Pappas s approach. 5,6 The one dfference between the models descrbed here and Pappas s prnter model s that our model uses the perceptually unform color space CIELAB and s desgned to mnmze the human vsual color dstorton. Hence, the color dstorton caused by nterdot overlappng and mperfect nk 5,6 can be explaned n terms of the standard color space LAB n ths paper. The model-based error dffuson algorthm wth the nonseparable prnter model s sometmes unstable and dverges for some mages. 6 In the case of selectng the LAB color space as a quantzaton doman, the algorthm s also nonseparable and becomes unstable, especally t dverges when the outsde colors of the prnter gamut range are contnuously nput to the system. To correct ths dvergence problem, the error clppng method s used. dots do not have the shape of the deal pxel. The real features of the prnted dots are more closely round than square and the dameter of the dots produced by the color prnter must be at least 2I, a mnmum dot sze. Hence the smallest dot dameter of the prnter must be desgned as 2I. The recprocal of I s the resoluton of the prnter n dots per nch (dp). The HP PantJet XL3 and PantJet XL18 and the IBM Color Jet prnter PS 479, wth 36 dp color nk-jet prnters wth four color (cyan, magenta, yellow and black) nozzles are used as test vehcles. A specfc color prnter model, wth regons, whch are shown as the sold lnes n Fgure 2, s developed. In ths model, the area of each regon becomes the same as that of the deal pxel. We also assume that the dameter of the dots produced by prnter D satsfes 5 2I D 2I. (1) It s found that the dot dameter of the 3 dp HP prnter s D = 2.2I, and those of the IBM prnter and the 18 dp HP prnter are D = 1.7I. Fgure 3 shows eght dfferent colored segments, C to C 7 n the regon T p (Ref. 5). Each segment s color s determned from the colors of neghborng pxels P 1 to P 4 and the current pxel P. In Fgure 3, a, b, c and d are, respectvely, fractonal areas of segments and P 1, P 2, P 3 and P 4 are neghborng pxels that have an effect on the color of the current pxel P. Here C to C 7 represent the color of each segment and C P to C P4 represent the colors of the current pxel P and neghborng pxels P 1 to P 4, whch have the shape of deal pxel. The fractonal areas of segments, a, b, c and d, are calculated by the geometrcal nterpretaton of the regon as 5 a = 1 2b 4c d, (2) Fgure 1. Ideal pxels of the prnter model. For the experments we use a color scanner (CLC5 by Canon) and three nk jet prnters (3 dp PantJet XL3, 18 dp PantJet XL18 by HP, and 36 dp IBM 479) each of whch has dfferent physcal dot characterstcs. A spectrophotometer s used to measure the color values of nks of the three prnters, and a hgh scope system s used to measure the dameter of the physcal prnted dot of the color prnters. 2 Prnter Model A prnter model s ndependent of the color characterstcs of a prnter. Modelng prnters can begn wth the assumpton of a raster prntng model, from left to rght and top to bottom, and the produced colored dots on a meda (typcally paper) make a Cartesan grd wth a horzontal and vertcal spacng of I nches. The term deal pxel such as P to P 4 n Fgure 1 s defned as the square dot of I nches. Usually, the features of prnted 1 b = 2 ΠD 4I I D I 4I 6D I cos D, 2 1 ( ) ( ) / 2 1 c = 2 3ΠD 12I 6I D I 12I 8D I cos D, 2 1 ( ) / / I d = I = D I D I + D I Π 4 ( ) 4 cos 2 D. Fgure 2. Target regon of prnter model. (3) (4) (5) 326 Recent Progress n Dgtal Halftonng II

3 yellow. Hence, we try to modfy the color space of Pappas s model from devce color space 5,6 to standard color space. If the fractonal area of each prmary color s determned, the Neugebauer equatons specfy the averaged color of the halftone screen. 19 Therefore, n the model-based approach, once the trstmulus values and fractonal area of eght segments of the regon are determned, the trstmulus values of the regon can be calculated. 5,6 Let us revew the prnter model 5 and estmate the color values of a regon n terms of LAB. Fgure 3. Colors and fractonal area of the regon. 3 Color Model A prnter model usng devce colors R (red), G (green), B (blue), C (cyan), M (magenta), and Y (yellow) was proposed by Pappas, 5 whose prnter model ncludes both a color model and a prnter model. The color model descrbed here s based on t. The man dfferences between Pappas s model and our model descrbed here are n the choce of the regon and the use of the perceptually unform color space LAB as the quantzaton doman. If we defne the regon T p, as shown n Fgure 2, under the condton of Eq. (1), the area of the regon s the same as that of the deal pxel I 2 and the number of neghborng pxels that affect the color of regon reduces from eght to four. Also, we do not need to consder other neghborng pxels, except the four neghborng pxels P 1 to P 4 n the quantzaton step. If we consder the regon composed of eght dfferent colored segments and the current pxel P and four neghborng pxels P 1 to P 4, the number of avalable colors of the regon s 8 5 (Ref. 17). In ths paper, the concept of devce-ndependent color 15,16 s also appled n the model-based error dffuson algorthm. The concept of devce-ndependent color, whch s ntroduced by Schreber, 18 s more suted to horzontally dstrbuted systems enabled by networks than a stand-alone system. For example, for an nk-jet prnter networked by other devces such as other prnters, dsplay devces, computers, and facsmle, the devce ndependent color concept s mportant. One thng n partcular dstngushed n the devce ndependent color s that standard color values are converted to the nk values of cyan, magenta, and 3.1 Revew of Color Estmaton Model Bnary color prnters usually use cyan (C), magenta (M), yellow (Y), and black (B) nks to produce color dots. But f we consder that the dfferent nks of C, M, Y are prnted on top of each other to produce red (R), green (G), blue (B), and whte (W), the prmary colors of a color prnter are defned by eght colors. Fgure 3 shows eght segment colors C to C 7, and each color of effectve pxels C to C 4, whch affects the color values of the regon. Snce the color of each effectve pxel s specfed as one of eght prmary colors, the color of each segment can be rep resented by Eqs. (6) to (13). Methods to decde the segment s color are classfed nto four categores by the number of effectve pxels. A segment s color C s determned only by one effectve pxel C P. Some segments colors, such as C 1 and C 6 are determned by two effectve pxels, C P and C Pl and C P and C P2, respectvely, by Eqs. (7) and (12). A thrd class of segment colors (C 2, C 3, C 4, C 5 ) s specfed by three effectve pxels by Eqs. (8), (9), and (1), and (11). The last class s determned by four effectve pxels, as shown n Eq. (13). C = f(c P ), (6) C 1 = f(c P,C P1 ), (7) C 2 = f(c P,C P1,C P4 ), (8) C 3 = f(c P,C P1,C P3 ), (9) C 4 = f(c P,C P2,C P3 ), (1) C 5 = f(c P,C P1,C P2 ), (11) C 6 = f(c P,C P2 ), (12) C 7 = f(c P,C P1,C P2,C P3 ), (13) where f( ) s some functon thereof. If all segment colors C to C 7 are specfed by Eqs. (6) to (13), the color of the regon C, s determned by C = f(c,c 1,C 2,C 3,C 4,C 5,C 6,C 7 ). (14) To evaluate segments colors C to C 7, the remanng task s to fnd the relatonshp between the effectve pxels colors C P to C P4 and the segments colors. To establsh the color estmaton model of each segment we assume that the segment color s ndependent of the prnt- Chapter IV Halftone Analyss and Modelng 327

4 ng order. To approxmate the segment color wth varous color combnatons, the followng color combnaton rules are used. 1. The order of color: zeroth order: whte (W) frst order: yellow (Y), magenta (M), cyan (C) second order: red (R), green (G), blue (B) thrd order: varatons of black (K). 2. If a color s added to the same color, the resultng color s not changed. 3. A color added to the zeroth order makes the same color. 4. The frst order color added to the second order except for complementary color makes the second order. 5. A combnaton of the second order colors, or the second order color and complementary color, makes the thrd order. 6. The thrd order color added to any color makes an another thrd order. As a result of the applcaton of these rules, the color of each segment s computed n terms of the eght prmary colors and one of the thrd order colors that have a dfferent color. 3.2 Estmaton of Color Values, LAB, of Target Regon In the followng colormetrc computaton, the CIE standard llumnant D 65 and the color matchng functons of the CIE 1931 standard observer have been adapted. Sxteen dfferent colors are used for the estmaton of each segment s color, but nne of these colors are varatons of black. To obtan the XYZ values of the 16 dfferent colors, a sold color chart has been desgned and the prnted samples produced by nk-jet prnter (PantJet XL 3) are measured wth a spectrophotometer (CM22- Mnolta) n terms of XYZ, whch refers to CIE XYZ (1931) n the followng sectons. We can observe from Table 1 that the color nks of PantJet XL 3 are mperfect. For example, the Y component of R patch has the 5% value of the X component of R patch, and the C patch also has a nonneglgble X component, and so on. The modelbased error dffuson algorthm wth a nonseparable prnter model s sometmes unstable and dverges for some mages. 6 In the case of adaptng the standard color space as a quantzaton doman, the error dffuson algorthm s also nonseparable; moreover, the degree of mperfecton can not be neglgble. Once we know the segments XYZ values and the fractonal area of eght segments from Eqs. (2) to (5) as Pappas treated the mperfect prnter mode1, 5,6 the XYZ values of the regon can be specfed by: X Y 7 = = 7 = = Z 7 = = X f, (15) Y f, (16) Z f, (17) where f s fractonal area, and X, Y, and Z are the CIE XYZ values (1931) of each segment from Table 1, and X, Y and Z are the CIE XYZ values (1931) of the regon, respectvely. The XYZ values of the regon can be transformed nto LAB color doman: L a b Y * = , Y n 1/ 3 1/ 3 / Y Y * =, X 1 3 n 5 Y n 1/ 3 / Y Z * =, Y 1 3 n 2 Z n (18) (19) (2) where X n, Y n, and Z n are the XYZ values of the standard llumnant, CIE D 65 and L*,a*, and b* represent LAB values of the regon. Table 1. The XYZ Values of Possble Segment Colors under CIE D, Standard Illumnant No. Color Patches XValues YValues ZValues 1 R G B C M Y K W CMY RB RC BY RGB RG OB GM Model Based Halftonng In ths secton, we consder two algorthms, the modelbased error dffuson and the wndow-based error mnmzaton algorthm: Two algorthms are based on the model-based approach 5 and the concept of devce-ndependent color. 15,16 In Secton 4.1, a model-based error dffuson on LAB color space s descrbed and expermental data of the error clppng technque, focused on the real applcaton, are reported. We can obtan the desred range of error clppng where an mage produced by the nonseparable algorthm, can be stable wthout addtonal color dstorton. In Secton 4.2, a wndowbased mnmzaton algorthm that uses the wndow prmary colors and pxel reallocaton technque s ntroduced. We use I j to denote a color mage, where and j denote the locaton of a pxel at th column and jth raw n the Cartesan grd. Typcal color mage has three channels n whch each channel has 256 gray levels. We 328 Recent Progress n Dgtal Halftonng II

5 consder LAB mage wth 256 gray levels for each channel. The choce of gamut range s as follows: L* = [,1], a* = [ 125,125], b* = [ 125,125]. 4.1 Error Dffuson Based on Models (EDBM) Error dffuson s superor n spatal resoluton and contnuous tone reproducblty to any other halftonng technques. 2,21 The color error dffuson algorthm s usually appled to each R, G, and B component ndependently, then t has a smple structure and the mert of a low computatonal cost. However, when the error dffuson algorthm s appled to a prntng system, the mage becomes dark and dsplays color dstorton due to dot overlap. In addton, the nks used by most color prnters are mperfect and present sgnfcant unwanted absorpton. Moreover, the amount of nk absorpton s varable and depends on colorants. To overcome these problems, a model-based approach to color error dffuson was proposed by Pappas. 5,6 Another approach to make color correcton and solve ths problem s to generate the prnter and color models usng a standard color space such as XYZ or LAB. Moreover, the color space chosen for the error dffuson makes a sgnfcant dfference n the color reproducton accuracy. Hence, the mportant desgn consderaton for error dffuson s to select the color space, n whch the quantzaton occurs, so that the error vector can be estmated n perceptually unform color space. Unform color spaces 13 are desgned wth the objectve of provdng a color coordnate system n whch the length of the color dfference vector corresponds to a dfference that s just notceable and s the same throughout the color space regardless of locaton and angular orentaton. The error dffuson algorthm on unform color space mnmzes the human vsual color dfference between the modfed color mage C j and the reproduced color mage at the locaton (,j). The block dagram of the EDBM s shown n Fgure 4, where I j represents the color of a pxel and s gven as three values correspondng to the color components of perceptually unform color space LAB: * * * I = ( L a, b ), 1 N, 1 j N, (21) j j j j w H Fgure 4. Block dagram of the proposed regular algorthm of color error dffuson on a unform color space (CIE L*a*b* 1976). where N W and N H represent the horzontal and vertcal ranges of the prnter, respectvely. The regular algorthm of the EDBM conssts of three steps: Frst s the estmaton of the modfed nput vector C j from the nput color I j and an error vector that s dffused from neghborng pxels: 1 7,22 Cj = Ij ( P m, j n C m, j n ) hm, n = I E h j mn mn m, n, (22) where h m,n s a transfer functon of a low-pass flter, proposed by Jarvs et al. 3 Second s fndng the closest prmary color of the current pxel P, to modfed nput color C j, by mnmzng the norm of the error vector between the modfed nput color C j and color M j : k Pj = ( Mj ) M k C, ( k =, 1,..., 7 ). (23) mn j Thrd s estmaton of the error vector: j E j = P j C j. (24) Fgure 5. Block dagram of the proposed smple algorthm of color error dffuson on an unform color space (CIE L*a*b* 1976). The error E j accounts for prnter dstortons as well as the quantzaton effect. 5,6 The algorthm descrbed here mnmzes the squared color dfference n the unform LAB doman between the modfed nput and the color produced by the prnter. But t requres an expensve computaton cost to fnd the closest prmary color of the current pxel wth models. Ths problem s solved by another approach, as shown n Fgure 5, where P s assumed to be one of eght prmary colors and has the closest prmary color value to the modfed nput color C j, n unform space (CIE L*a*b* 1976), whch s performed wthout models. Here P j s estmated wth the models, the nformaton of the neghbors, and the selected prmary. In the next step, the error vector E j s the color dfference between the modfed nput C j and the color of the regon P j, whch s also estmated 5,6 by Eqs. (15) to (2). Whle the smple verson has a sgnfcant computatonal smplcty, the mages obtaned from the smple algorthm stll show a qualty approxmately equvalent to those produced by the precedng error df- Chapter IV Halftone Analyss and Modelng 329

6 (a) (b) (c) (d) (e) (f) (g) (h) () Fgure 6. Prnted mage of the Macbeth Color Checker wth an error clppng parameter of (a) no clppng, (b) 2., (c) 1.5, (d) 1., (e).8, (f).6, (g).4, (h).2, and ().. 33 Recent Progress n Dgtal Halftonng II

7 fuson algorthm, as shown n Fgure 4. Therefore, the smple algorthm s used to obtan the expermental results. In a real applcaton of a separable algorthm, the algorthm s stable because the modfed nput of three components (R,G,B) s clpped ndependently wthn the range of avalable prnter nput, to 255. In the case of a nonseparable algorthm, the algorthm s unstable and dverges for some mages, 6 especally when the outsde colors of the prnter gamut are contnuously nput to the system and three components of the error vector have large values. Such characterstcs also appear n EDBM and can be corrected by clppng the modfed nput wthn the 3-D prnter gamut or the error clppng of the quantzaton step. In our experment, the error clppng method and the lghtness clppng of a gamut mappng are exploted to correct ths dvergence problem and focus on a real applcaton. We know that the nonseparable algorthm can be made stable by the error clppng technque, but the mert of error dffuson, whch enables us to represent a contnuous mage by a lmted number of colors, goes down as the amount of error clppng ncreases. If we set error to zero, then usng error dffuson a prnter produces not a contnuous tone mage but an mage quantzed by eght colors. Hence, t s mportant to determne optmal values for error clppng through experments to generate a color mage wthout color dstorton caused by the clppng. In our experment, the gamut range of an nk-jet prnter (PantJet XL3) s selected as the reference values of error clppng: EC L = (L max L mn )/2, EC A = (A max A mn )/2, and EC B = (B max B mn )/2, where EC L, EC A, and EC B represent the reference values of the L, A, and B components for error clppng, respectvely. We experment wth an mage of pxels of the Macbeth Color Checker, whch s scanned by a CLC 5 scanner. The parameters for error clppng are selected as: Fgure 6(a) fve tmes, Fgure 6(b) two tmes, Fgure 6(c) 1.5 tmes, Fgure 6(d) 1. tmes, Fgure 6(e).8, Fgure 6(1).6, and Fgure 6(g). of reference values, respectvely. Fgures 6(a) to 6(h) shows the mages produced by the PantJet XL 3 usng these parameters. The Macbeth Color Checker s composed of 24 dfferent color patches. Let us number them from 1 to 24. In the case of no error clppng [Fgure 6(a)], many patches are dverse; 6th and 17th patches show whte strpes under each patch; and the 7th, 1th, 13th, 15th, 17th, 18th, 19th, and 23rd patches also dverge. Most patches that dverged wthout clppng change to stable ones except for 1th, 13th, and 15th patches, and the whte strpes of the 6th and 17th patches also dsappear after the error clppng parameter s set to 1.5. All patches are not changed for the parameter range from 1.5 to.6. We observe that the error dffusoned mages are not as senstve to the parameter wthn the range of 1.5 to.6. Hence, we can guess that the optmal range of the error clppng parameter s from 1.2 to.8, and the optmal value s 1.. It s mportant to know that the 1th, 13th, and 15th patches dverge for all parameters except for crtcal parameter value.. Ths reveals the lmt of error clppng method appled n the nonseparable algorthm. As mentoned, the modfed nput must stay wthn the 3-D gamut range of a prnter to be stable n the nonseparable algorthm. But the 3-D gamut of the eght color prnter (PantJet XL 3) s unclear and napproprate to treat the modfed nput of contnuous color n the LAB doman, whch becomes an obstacle to a smple algorthm for real applcatons. However, the gray drecton of the LAB space s nearly consstent wth that of the black and whte ponts of a prnter. Hence, the clppng for lghtness value L can be appled n the modfed nput ndependently. The pseudo-algorthm of the lghtness clppng s as followng: f L > Lmax, L = Lmax and ERROR = ; else f L < Lmn, L = Lmn and ERROR = ; else; Fgure 7. Prnted mage of the Macbeth Color Checker wth (a) lghtness clppng, (b) an error clppng parameter of 2. and lghtness dppng, (c) an error clppng parameter of 1.5 and lghtness clppng, and (d) an error clppng parameter of 1. and lghtness clppng. Chapter IV Halftone Analyss and Modelng 331

8 (a) (b) (c) Fgure 8. Prnted mage of a conventonal mage wth (a) no clppng, (b) lghtness clppng and (c) an error clppng parameter of 1. and lghtness clppng. 332 Recent Progress n Dgtal Halftonng II

9 If the L value goes off the gamut range, the error s meanngless because a prnter cannot reproduce the color. Turnng back the orgnal objectve of the error dffuson technque, to represent the gray scale usng a bnary prnter wthn the prnter gamut range, n any case, the outsde color of the prnter gamut can not be treated and reproduced by a prnter. Fgure 7(a) shows the case of lghtness clppng wthout error clppng. We can observe that some patches also dverge. However, we can observe from Fgures 7(b), 7(c), and 7(d) that the patches rapdly converge and all patches are converged n Fgure 7(d) wth an error clppng parameter 1.. Ths s mportant because t shows that the nstablty problem n the nonseparable algorthm can be effectvely solved by usng error and lghtness clppng smultaneously. Fgures 8(a), 8(b), and 8(c) show the converged case n the nonseparable algorthm for Fgure 8(a) no clppng, Fgure 8(b) lghtness clppng, and Fgure 8(c) an error clppng parameter of 1. and lghtness clppng, respectvely. We cannot fnd any dfference from these mages. In stable crcumstances, we can observe that error clppng and lghtness clppng do not have an effect on an mage. 4.2 Wndow-Based Error Mnmzaton Algorthm (WBMA) In a color error dffuson algorthm for a bnary prnter, the unt of the halftone cell s a pxel, the number of the avalable prmary colors n quantzaton step s eght, and the error ncurred at 1 pxel s propagated to the unprocessed neghborng pxels usng a low-pass flter. Ths adaptve characterstc makes error dffuson superor to other dtherng technques. Nevertheless, n real applcatons, error dffuson can create a large number of nonprntable ndvdual pxels, whch results n a change n the tone reproducton curve (TRC). Fan 23 expermented wth a halftone technque that combnes tradtonal halftonng (ordered dtherng) and the error dffuson algorthm and obtaned an mage that has no coarse quantzaton effect and a well formed dot structure lke error dffuson. Moreover, snce only eght colors are used n quantzaton, the error defned by Eq. (24) often becomes a large value, whch dstorts the colors of the neghborng pxels and makes t dffcult to reproduce an accurate color at a pxel s orgnal locaton. To solve these problems, we use addtonal prmary colors by a wndow composed of more than 2 pxels n error dffuson. For example, f the wndow s composed of 2 1 pxels, the avalable wndow prmary colors for quantzaton become 36 and n the case of 2 2, 33 (Ref. 17). The WBMA has the effect of reducng the amount of error at each wndow locaton. Moreover, the error can be mnmzed and a pxel array has a well formed structure, lke a pxel based error dffuson, by applyng the pxel reallocaton technque. In WBMA, by accommodatng wndow-to-wndow error propagaton wth the pxel reallocaton technque, we can obtan an mage that s fathful to the orgnal color at each wndow locaton and has no artfacts. Fgure 9 shows the block dagram of the WBMA. Let us consder a wndow wth 2 2 pxels and 33 prmary colors. Then, the WBMA wth the pxel reallocaton technque can be descrbed n the followng fve steps: 1. An nput mage I j s transformed nto the unt of a wndow, I kl by Eq. (25). In the case of 2 2 pxels, I kl represents nput color of the unt of wndow. The subscrpts k and l denote the wndow located at (k,l). Hence, the pxel poston of the wndow wll be (2 1) th column and (2j l) th row. I kl 2k 2l = I, /( 2 2), (25) j = 2k 1j= 2l 1 where, 1 N w, 1 j N H, 1 k N w /2, 1 1 N H /2. 2. The estmaton of the modfed nput vector C kl s the same as that of step 1 n EDBM except for the subscrpts. 3. To fnd the closest prmary color wth the modfed nput color and the ndexes of pxels of the wndow, frst, we pck one of wndow prmary colors from the look-up table (LUT) and estmate the norm of the error vector between the modfed nput color C kl and the wndow color M kl. The wndow s color M kl can be calculated from Eqs. (26) to (31). X Y 7 p = = 7 p = = Z 7 p = = N X f, (26) Y f, (27) Z f, (28) p X = X / N, (29) p= N p Y = Y / N, (3) p= N p Z = Z / N, (31) p= where N s the number of pxels that consst of a wndow: X p, Y p, and Z p denote the XYZ values of each pxel; and X, Y, and Z, represent the XYZ values of wndow. The wndow s XYZ values are converted nto LAB values by Eqs. (18) and (2). We pck one of wndow prmary colors from the LUT and estmate the norm t of error vector M kl C kl between the modfed nput color C kl and the wndow color M kl. If we terate ths step untl the last prmary color, then we can fnd P Wtmp, whch has a mnmum error among the wndow prmary colors by Pwtmp = ( Mkl ) M t C, (32) mn where t ndcates the number of prmares. But ths algorthm has the dsadvantage of reducng a reso- kl kl Chapter IV Halftone Analyss and Modelng 333

10 luton, whle the error defned by Eq. (24) s reduced, whch supports the am to reproduce accurate color at the pxel s orgnal locaton. The pxel reallocaton technque s appled n ths algorthm to mnmze an error agan and prevent the resoluton from decreasng. 4. Reallocate the pxels of the wndows to fnd an array structure wth the mnmum error and that satsfes a constrant that prevents the resoluton from decreasng. In step 3, the selected wndow conssts of N pxels. The number of avalable colors becomes N! by changng the poston of each pxel n a wndow. Moreover, to reduce coarse quantzaton effect n an mage and to have a well formed dot structure lke the one dot based error dffuson algorthm, the constrant that the pxels of the same colors should not be neghbors n a wndow s used. The coarse quantzaton effect and decreases of resoluton are reduced dramatcally n an mage by applyng ths poston constrant. The avalable colors decrease to a value smaller than N!. Each wndow s color values are estmated by Eqs. (26) to (31) and we can select the array structure and color values from Eq. (32) and the constrant. In ths step, we can mnmze the error between the modfed nput of the wndow and the color of the reallocated wndow n the perceptually unform color space. For example, assume that the neghborng pxels of a wndow are already assgned by M, M, C, and C, as n Fgure 1(a) and the ndces of the wndow prmary color selected from the LUT are composed of Y, C, M, and R. Snce the colors of neghborng pxels n the upper row are assumed to be M and M, any pxel n the frst row n the wndow should not have color M. In a smlar way, the frst column of the wndow cannot have color C. Hence, when we consder the colors of neghborng pxels n Fgure 1(a), the possble pxel postons of each C, M, Y, and R pxel n the wndow wll be as shown n Fgure 1(b). The number of avalable colors of the wndow reduce from 4! to 6, as shown n Fgure 1(c). Next, we can select an array structure, whch has mnmum error among the sx structures n Fgure 1(c). Ths approach causes WBMA to have an adaptve characterstc by consderng the colors of neghborng pxels. We can determne the optmzed pxel array that satsfes both havng mnmum error and preservng resoluton. As a result of ths step, a loss n resoluton due to a pxel groupng (2 2) s corrected. Fgure 9. Block dagram of the proposed WBMA for the color error dffuson algorthm on unform color space (CIE L*a*b* 1976). (a) Fgure 1 (a) Example of the wndow and neghborng pxels n WBMA, (b) possble pxel postons of C, M, Y, and R n the wndow of (a), and (c) possble pxel array structures of C, M, Y, end R n wndow consderng the colors of neghborng pxels n (a). P j m = ( P ) m, ( m = 1, 2,..., N). (33) j (b) (c) Pj Pj mn 5. Estmaton of the error vector s the same as that of step 3 n EDBM. The error vector s dffused to neghborng wndows. The WBMA has an advantage that the quantzaton error s reduced and the error E j can be mnmzed agan by the pxel real 334 Recent Progress n Dgtal Halftonng II

11 locaton technque. The algorthm mnmzes the squared color dfference n LAB between the modfed nput and the prnter output at the wndow of the current locaton. 5 Expermental Results and Dscussons 5.1 Color Chart Experment The smple verson of EDBM s tested on several mages and the color precson are estmated n terms of LAB. For the experments, we used a color scanner (CLC5 by Canon), and three knds of nk-jet prnters (a 18 dp Pant-Jet XL18 and a 3 dp PantJet XL3 by HP and a 36 dp IBM 479) whch have dfferent physcal dot characterstcs. The H-Scope system (KH22 by HRox) s used to measure the actual dameters of the physcal dots. We a spectrophotometer (CM22 by Mnolta) to measure the color values of the prntng output. Frst, a color chart for estmatng the feasblty of the models s desgned. The color chart has 33 dfferent color chps. Snce each color chp has a number of halftone cells wth 2 2 pxel arrays, the total number of colors of the color prnter wth a four color prntng system becomes 33 (Ref. 21). The LAB values of the prnted color chart, measured by the spectrophotometer, are compared wth those estmated by Eqs. (18) to (2). Fgure 11(a) shows the relatonshp between the pxel dameters of the model and the color dfferences between the estmated and measured values of the 2 2 pxel array composed of a sngle color component for PantJet XL18: cyan represents the average color dfference of 2 2 pxel array composed of only cyan pxels. We can observe from Fgure 11(a) that the mnmum color dfference E ab of the cyan array s 5.3 at d =.2395 mm, the magenta array s 4.9 at d =.2435 mm, and the yellow array s 5.53 at d =.235 mm. Ths also shows that the estmated dameters wth a mnmum color dfference for three color components have close agreement wth the value d =.245 mm measured by H-Scope system. Fgure 11(b) llustrates the pxel dameter versus E (LAB unt) plots n the PantJet XL18 for 33 color chps. We classfed the 33 color chps nto three categores: the CMY class composed of only cyan, magenta, yellow, and whte pxels; the RGMCMY class composed of cyan, magenta, yellow, red, green, blue, and whte pxels; and the Others class composed of one black pxel and three pxels of R, G, B, C, M, Y, R, G, or W. In the case of PantJet XL 18, the CMY class has mnmum error, and the next s the Others class, the last s the RGBCMY class, and the dameters wth mnmum error for each class are consstent wth the measured values. Hence we are able to see that the color (a) (b) (c) (d) Fgure 11. Pxel dameters of the model versus the color dfferences (a) of cyan, magenta, and yellow for the HP PantJet XL 18, (b) for 33 colors reproduced by the PantJet XL 18, (c) for the HP PantJet XL 3, and (d) for the IBM 479. Chapter IV Halftone Analyss and Modelng 335

12 dstorton s due to the msregstraton of color pxels and the approxmated color model. As ponted out n the prnter model secton, the measured dameters of the 3 dp HP prnter and IBM prnter are D ave = 2.2I(.19 mm) and D ave = 1.7I(.12mm), respectvely. Unfortunately, the measured dameter (D = 2.2I) of the 3 dp HP prnter s out of the range of the our model [Eq. (1)]. Hence, three classes of Fgure 11(c) show monotonc decreasng characterstcs untl D = 2.I. In Fgures 11(c) and 11(d), however, t can stll be observed that the calculated dameters of the two prnters are 2.I (.17 mm) and 1.7I (.13 mm), whch show a close agreement. We argue that the average color dfference ( E = 1.5) for the desgned 33 color chps s due to such characterstcs of the prnter as msregstraton and the varaton of produced dot sze and the approxmated color model. 5.2 Real Image Experment To demonstrate the effectveness of our methods, we tested several algorthms: the conventonal error dffuson algorthm on LAB doman, EDBM, wndow-based error dffuson wthout the prnter model, WBMA, and WBMA wth the pxel reallocaton technque, for a number of mages. A PantJet XL3 (HP, 3 dp) s used as an mage test vehcle. Fgure 12(a) (see Color Plate) shows the photographc mage of the color test chart (The Insttute of Image Electroncs Engneer of Japan, 11). Fgure 12(b) shows the mage of the conventonal error dffuson wthout models and Fgure 12(c) shows the mage wth the smple algorthm wth an error clppng value of 1. and lghtness clppng. Fgure 12(d) s an example of the mage quantzed by 3 colors on the LAB doman, Fgure 12(e) shows the mage of the wndow-based error dffuson wthout the prnter model, Fgure 12(f) shows that of the WBMA, and Fgure 12(g) s that of the WBMA wth pxel reallocaton. Fgure 12(b) shows color dstorton clearly due to the dot overlappng and Fgures 12(c), 12(f), and 12(g) show the effectveness of our approaches n color error dffuson. We can observe that the mage s corrected sgnfcantly by the model based technques. Vsual comparsons of Fgures 12(b), 12(c), 12(f), and 12(g) ndcate that Fgures 12(c), 12(f), and 12(g) exhbt a brght and acceptable color, whle Fgure 12(b) shows a dark and dstorted color mage. It s easy to observe that Fgures 12(c), 12(f), and 12(g) show more fathful reproducton for hue and saturaton than the mage of Fgure 12(b). The yellowsh cloth n Fgures 12(f) and 12(g) has more accurate color than the color produced by EDBM. By comparng Fgure 12(c) wth Fgure 12(f), t s also perceved that the colors of apple, grape, cloth, rose, etc. shown n Fgure 12(f) dsplay more smlarty to the orgnal colors, n Fgure 12(a), than those of Fgure 12(c). Fgures 12(b) and 12(e) represent the same case wthout the prnter model. One dfference between them s that Fgure 12(b) s a one dot based error dffuson, whle Fgure 12(e) s the case of a 2 2 wndow. We can see from Fgures 12(b) and 12(e) that the error of the wndow-based algorthm s smaller than that of the one dot case, as explaned earler. Hence, t also proves the effectveness of usng addtonal prmary colors n a wndow. Fgure 12(d) s an mage quantzed by 33 colors on the LAB doman and shows very poor color reproducton wth contourng and rough mage qualty. It s dramatcally corrected by applyng error dffuson based on a 2 2 wndow n Fgure 12(e). In the case of large wndow sze, wndowbased error dffuson wthout the prnter model reproduces more accurate color than small wndow sze. In the 2 2 wndow, color dstorton due to dot overlappng s stll observed and some color dstortons n Fgure 12(e) are corrected n Fgure 12(f). Fgure 12(g) s the case of WBMA wth pxel reallocaton technque, whch has the objectve of reducng the coarseness n wndow-based error dffuson by fndng the optmal structure of pxels n a wndow. The pxel reallocaton technque wth the poston constrant prevents the coarse quantzaton effect due to decreased spatal resoluton and a changed ntal structure of the LUT nto fne structure n a wndow. As shown n Fgure 12(f), there are some defects such as decreased resoluton and the coarse quantzaton effect from the mage produced by the wndow-based mnmzaton algorthm. However, we can see from Fgures 12(f) and 12(g) that the coarse quantzaton effect due to the decreased mage resoluton s consderably corrected by applyng WBMA wth the pxel reallocaton technque. Whle the pctures produced by WBMA n Fgures 12(f) and 12(g) have the mert of reproducng accurate color at the orgnal locaton, these unfortunately dd not show better mage qualty than that of EDBM n our experment. We beleve the mage qualty of WBMA s related to the characterstcs of the nk-jet prnter, such as resoluton, the number of physcal colors produced by a wndow, the sze of a prnted dot, and the colorant. In the case of WBMA, the resoluton s decreased to half of that n EDBM n our experments; however, the avalable number of prmary wndow colors dd not actually ncrease to 33 colors, n whch there are so many patches we can not dscrmnate the colors. The mage qualty n WBMA s the trade-off of the number of avalable colors and mage resoluton. WBMA wll be more useful and gve more fathful mage qualty than that of EDBM or the current status of WBMA under the condton that the actual number of prmary wndow colors s nearly same as that of the predesgned ones, n our case 33 colors. The mnmum wndow resoluton for acceptable mage qualty s determned by human vsual characterstc and the number of physcal prmary wndow colors, whch are beyond the scope of ths paper. In the case of a prnter wth low resoluton, t s not so free to desgn the prmary wndow colors, whch strongly depend on the prnter characterstcs, as n our experment, whle we can desgn prmary wndow colors by examnng varous dther matrces n a prnter wth hgh resoluton. However, the number of physcal prmary wndow color can be ncreased by the pxel reallocaton technque, whch makes varous prmary wndow prmary colors usng 4 pxels, moreover, t consders the colors of neghborng pxels. We can nterpret the EDBM as a specal case of WBMA wth a one dot wndow, n other word, WBMA s the expanded verson of EDBM n the spatal doman. 336 Recent Progress n Dgtal Halftonng II

13 (a) (b) (c) (d) (e) (f) Fgure 12. (a) Photography of the orgnal mage, (b) prnted mage wth the correcton of the conventonal error dffuson algorthm on the LAB doman (c) prnted-mage wth the correcton of the proposed smple algorthm wth an error clppng of 1. and lghtness clppng, (d) example of mage quantzed by 3 colors on the LAB doman, (e) prnted mage wth the correcton of the wndow-based error dffuson wthout the prnter model, (f) prnted mage wth the correcton of the proposed WBMA, and (g) prnted mage wth the correcton of the proposed wth WBMA wth pxel reallocaton. Chapter IV Halftone Analyss and Modelng 337

14 6 Conclusons We have examned an approach to reproduce a hgh qualty mage by usng the prnter model based on the measurements of a small number of patches and color model on the unform color space (CIE L*a*b* 1976). The algorthms are desgned to mnmze the color dstorton between the contnuous tone mage and ts low-pass fltered halftone mage at each pxel locaton (or wndow locaton), and the error has been analyzed n unform human vsual doman. In EDBM, we have performed an experment focused on real applcatons and have shown that the mage produced by the nonseparable algorthm also could be made stable by applyng the error clppng and lghtness clppng methods. Especally, the optmal range of error clppng to effectvely prevent the dvergence of an mage n the nonseparable algorthm s gven as from.8 to 1.2 tmes the lmtng values of the nk-jet prnter gamut. The effectveness of the error clppng method has been proved by applyng t n dverged and converged mages respectvely. By the algorthms, the color dstortons caused by dot overlap and mperfect nk could be sgnfcantly corrected. To prevent decreased spatal resoluton n WBMA, the pxel reallocaton technque has been examned. Snce the two algorthms descrbed n ths paper are performed n standard color space, t s easy to apply them to color prntng devces drectly, whch requre devce ndependent color processng technques, wthout extra color correcton of a prnter. The next step of our research s to nvestgate hardware mplement acton for hgh speed applcatons. References 1. R. Ulchney, Dgtal Halftonng, The MIT Press, (1987). 2. B. E. Payer, An optmum method for two-level rendton of contnuous tone pctures, n Proc. IEEE Int. Conf. on Comm., pp (1973). 3. J. F. Jarvs, C. N. Judce, and W. H. Nnke, A survey of technques for the dsplay of contnuous tone pctures on blevel dsplay. Comput. Graph. Image Process. 5, 13 4 (1976). 4. D. A. Carrara, M. Analou, and J. P. Allebach, Recent progress a dgtal halftonng, n Proc. IS&T s 8th Int. Congr. on Advances n Non-Impact Prntng Technologes, pp. 25 3, Wllamsburg VA (1992). 5. T. N. Pappas, Model based halftonng of color mages, n Proc. IS&T s 8th Int. Congr. on Advances n Non-mpact Prntng Technologes, pp , Wllamsburg VA (1992). 6. T. N. Pappas, Prnter models and color halftonng, n Proc. IEEE ICASSP-93, Vol. 5, pp , Mnneapols, MN (1993). 7. T. N. Pappas and D. L. Neuhoff, Model-based halftonng, n Human Vson, Vsual Proc, and Dgtal Dsplay II, Proc. SPIE 1453, (1991). 8. T. N. Pappas and D. L. Neuhoff, Least-squares modelbased halftonng, Human Vson, Vsual Proc., and Dgtal Dsplay III, Proc. SPIE 1666, (1992). 9. D. L. Neuhoff, T. N. Pappas, and N. Seshadr, One-dmensonal least-squares model-based halftonng, n Proc. IEEE ICASSP-92, San Francsco, CA (1992). 1. C. J. Rosenberg, Measurement based verfcaton of an electrophotographc prnter dot model for halftone algorthm tone correcton, n Proc. IS&T s 8th Int., Cong. on Adv. Non-mpact Prntng Technologes, pp Wllamsburg, VA (1992). 11. Y. S. Rm and S. K. Rm, Adaptve color error dffuson for natural color prntng n bnary color prnter, n Proc. IS&T s 9th Int. Cong. on Adv. Non-mpact prntng Technologes, Japan Hardcopy 93, pp , Yokohama, Japan (1993). 12. C. Y. Rm, S. G. Km, Y. S. See, and I. S. Kweon, Model based color halftonng technques on perceptually unform color space, n Proc. IS&T s 47th Annual Conference/CPS 1994, pp , Rochester (1994). 13. G. Wyszeck and W. S. Stles, Color Scence, 2nd ed., Wley, New York (1982). 14. Commsson Internatonale de l Eclarage (CIE), Colormetry, Publcaton CIE No. 15.2, Venna (1986). 15. R. Buckley, A short hstory of devce-ndependent color, n Proc. 1 st IS&T/SID Color Imagng Conference, pp (1993). 16. G. Murch, Color management system, n Proc. 1st IS&T/ SID Color Imagng Conference, pp (1993). 17. P. G. Engeldrum, Four color reproducton theory for dot formed magng systems, J. Imagng Technol. 12(126), (1986). 18. W. F. Schreber, A color prepress system usng appearance varables, J. Imagng Technol. 12, (1986). 19. G. G. Feld Color scannng and magng System, GATF. 2. R. W. Floyd and L. Stenberg, An adaptve algorthm for spatal grey scale, Proc. SID 17(2), (1976). 21. O. Bryngdahl, Halftone mages: spatal resoluton and tone reproducton, J. Opt. Soc. Am. 68, (1978). 22. J. C. Stoffel and J. F. Moreland, A survey of electronc technques for pctoral mage representaton, IEEE Trans. Comm 29, (1981). 23. Z. Fan, Halftonng by combnng ordered dtherng and error dffuson, n Proc. IS&T s 8th Int. Cong. on Adv. Non-mpact prntng Technologes, Japan Hardcopy 92, pp , Wllamsburg, VA (1992). 24. A. H. Mutz and D. T. Lee, An nternatonal standard for color facsmle, n Proc. 2nd IS&T/SID Color Imagng Conference, pp (1994). Prevously publshed n the Journal of Electronc Imagng, 6(2) pp , Recent Progress n Dgtal Halftonng II