Author name used in this publication: C. K. LiVersion of RecordPublishe

Chan, YH

Kwong, HT

Li, CK

Lo, KT

Author name used in this publication: C. K. LiVersion of RecordPublishedVoR allowe

PolyU Institutional Repository

A MULTISCALE ERROR DIFFUSION TECHNIQUE FOR DIGITAL HALFTONING WITH DOT-OVERLAP COMPENSATION Yuk-fIee Chan, H.  T.  Kwong, C.K. Li and K. T.  Lo Departnicnt of Electronic arid Information Engineering The Hong Kong Polyt,cchnic Univcrsity Hung Horn, Kowloon, Hong Kong ABSTRACT In t,his paper, a digital halftoning method is proposed bascd on a rccently-proposed ninlt,iscale error diffusion t,echnique for digit,al halftoning. It can dcfinitely irn- prove the diffusion pcrformance by effcctivcly removing pattcrn noise and eliminating boundary and ‘blackhole’ effects. A dot-overlap cornpcnsation scheme is also pro- posed t,o eliiniiiatc thc bias in t,hc gray scale of the printed images. EDICS: IP 3.2 Qusntizat,ion and Halftoning 1. INTRODUCTION Digital halftoning is a method that nses hilevel pixels (black and white pixels) to simulate a gray-scale image on a hilevel output dcvice. Recently, a mult,iscale level crror diffusion has been proposed[l]. This mcthod is superior to the convcntional error diffusion niethods such as [Z] in a way that no sequential predet,ermined order is requircd for crror diffusion. Accordingly, 11011- cansal filt,crs can be used in diffusing quantization crror to avoid direct,ional hysteresis. In t,his letter, two contributions will hc madc. First,, two modifications will he prcscnted to irnprovc thc mul- tiscalc lcvcl crror diffusion schcme such that a more pleasant output can be provided. Sccond, we shall introduce a compensation schcmc to remove thc dot- overlap dist,ort,ion whcn the algorit,htn is used to gen- cratc printcr output. 2. ALGORITHM Considcr wc want to apply digit,al halftoning to a gray- level input iniagc X whose values arc within [0,1] t,o obtain an output binary imagc B. Wit,hout loss of generality, we assunic tlrcy are of size Z k  x Z k  each, wliere k is a positive integer. Our proposcd algorithm This work fi,xppari.ad by POLYU n7~~.nnn.nn.~zn. is a two-step iterative algorithm. At each iteration, wc first introduce a whitc dot (valuc=l) at  one location of t,he output imagc B. Thc location is chosen in a greedy way based on a corresponding diffiised error image E. Thcn wc diffusc thc crror lo  thc ncighbors of t,liat pixel to iipdatc thc crror imagc E. Thcsc proccdurcs are rc- pcatcd until the sum of all elcmcnts of E is bouiidcd in absolutc valuc by 0.5. Thc crror imagc E is initialized to be X at the beginning. 1. Dctermine the right location of a new dot: The locat,ion where a new whit,e dot shonld bc intro- duced is determined via tlic so-callcd ‘maximum crror intensity guidance’. We start with the error imagc E as our rcgion of interest. Then we divide the region of interest into subrcgions and selcct thc onc wil;h thc largest sum of its all elements to be thc new rcgion of interest. This st,ep is repeat,ed iint,il a particular pixel location is roached. Our approach is different, from Katsavoiinidis’s app- roach[l] in a way that, instcad of partitioning thc region of inkrest, into 4 non-ovcrlapped subregions t o  locat,c the next region of interest in each step, we divide it into 9 overlapped subregions as shown in figurc 1. Flcxibil- ity is introduccd by doing so as more possible paths arc availablc to rcach a particular location. Comparatively, it is potentially more difficult to he trapped in a local optimum and hencc tlic rcgion of thc most significant, error can be taken care in a earlier stage. Besides, it is mom difficult, t,o fall int,o a part,icular dot assignmcnt pattern caused by the limited number of paths, which is helpful to reduce thc pattcrn noise in the out,put. Pi- nally, since we allow subregions t,o overlap each othcr, there will not he any boundary effect;. 2. Updat,e error image E: Aftcr locating tlic right pixcl position, a whit,e dot, is assigncd to it. Without loss of generality, we as- sunic wc assign the whitc dot to  the pixcl at location 323 0-7803-5167-2/99/ $10.00 (0 1999 IEEE Authorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on July 26, 2009 at 21:47 from IEEE Xplore.  Restrictions apply. (ni,n) hy making b,,,=l and a noncausal diffusion fil- t,er with a support window 12 {(z,y)l 0 5 I z /Jy  5 half T I J ~ ~ O W  size} is used. Let ei, j  and bi,j bc respec- tively thc values of the pixcls of E and B at location ( i j )  aft,er the dot assignment but before the crror dif- fusion. Then, after thc error diffusion, the new value of c i , j ,  say is assigncd to be Input pattern $* { x x l x x a j  {OOO1X)or{X1OnO} {XlOlXj { 1001X}ur{X1001} { 10000)or{O0001} { 10001) {00000} whcrc ujtc,,,’s are the filter weiglits, bi, j  = 1 - D i j ,  and a(1,O) 0 a-Y a - 27 a - P - 7  a - P  a - 2p a Notc this assignment causcs no error leakage in thc error diffusion and the algorithm works with any choice of filter, producing different, results. In the casc when s=O, we cxploit a filter with larger support window to  make s # 0 and Icccp tlic algorithm work. In Ihtsavounidis’s approach[l], quantization error at (m,n) will he diffused to its ncighbors even though thcy are already assigncd to  be white dots. t,his amount of error will then be storcd in these locations forever and will not conlribut,c t,o thc following quantization and diffusion stages. For thc sake of reference, we call t,Iiis effect as ‘blackhole’ effect as energy is absorbcd to  t,liese locations. This cffcct rcsults in an uneven error image E at the end and makes tlic whitc dots not propcrly distributed in a local rcgion. Our proposed approach can obviously solvc this problem. 3. DOT-OVERLAP COMPENSATION Ali.hough error diffusion schcmcs including t,he mul- tiscalc level error diffusion schcrnc can generate very plcasant texturcs, it  suffers from the dot-overlap cffcct introduced in lascr printcrs, and leads to a bias in gray scale. In ordcr t o  compensate for this effect, we suggest, carrying out a compensation step between procedures 1 and 2 in cach iteration. Lct’s assume that an ideal pixcl occupies an unity square. Whcn a circular dot, is put, on pixel pnL,n, some area of pn,*’s neighbors will also be covered by thc dot as shown in figure 2. Accordingly, we should compen- sat,c for t,his effect by adjusting E wit,h e”m+lr,n+v = e,,+,,,,+, - a(u,v) beforc carrying out procedure 2, whcrc e”m+zL,n.l.u is the compcnsatcd valuc, a(u,v) is t,be arca covered in pixel (m+u,n+v) due to the dot assignment and ( T A , ~ )  E {(z,y)lz,p E { - 1 , O , l } } \ { ( O , O ) } .  For iti- stance, in thc case shown in Fig.2, we havc a(O,-l)=a(- l,O)=a, a(-l,1)=~~(-l,-l)=a(l,-1)=fl, a(O,l)=a(l,O)= a- y and a ( l , l ) = O ,  wlierc a ,  f l  and y are respectively tlic Input pattern i** {OOO) {XXXj \ {OOOI area of the shaded arcas shown in Fig.2. The values of a(u,v)’s can be precalculated and stored in a tablc such that a(u,v)’s can be determined easily with a table lookup proccss. Table 1 can be used for such a purposc. Parameters a ,  f l  and y are respectivcly the area of the shaded areas shown in figurc 2. The input pattern $ is madc up with t,he bi,j’s in thc corresponding positions of thc most updatcd image B. Tablc 1 shows thc cams for getting a(1,O) and a(-1,1). Due to tlic geometrical symmctry, onc can make usc of the same table to get a(u,v)’s of other p,,,’s neighbors by providing propcr i ’ s  aft.er rotating the images. For instance, in t,he case as shown in figure 2, we let $ be {OOOlO} and t,hen aftcr a table lookup wc have a(O,l)=a - y. Unlike those compensation algorithms such as [3], [4] and [5] for typical error diffusion schemes, the com- pensat,ion in this scheme is not biased to the diffusion direction, and, dircctly tales effect on pm,n’s neighbors whcrc t,he area is actually covered instead ofp,,,, itself. Note here wc assume a white ink dot is printed on a black paper. If it is the opposite, one can invert X before carrying out the proposed algorithm and com- plemcnt the output at the end. a(-L1) P 0 4. SIMULATION RESULTS Simulat,ious have bccn carried out to  evaluate the per- formance of thc proposed algorithm. Figurc 3a shows a 324 Authorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on July 26, 2009 at 21:47 from IEEE Xplore.  Restrictions apply. 256 x 256 point light, source patt,ern. Figures 3b and 3c show t,hc results obtaincd with Katsavounidis’s and our algorit,hms. The 3x3  non-causal diffusion filtcr used in [I] was used to realize both algorithms. Howcver, the sizc of the fiker uscd was adjusted when s=O happcncd in realizing our algorithm. Wc dcliherately print,ed thc figures using a 6DOdpi lascr printer so that thc individ- ual dots can he clcarly printcd and the effect, of dot overlapping is not dominant. Onc can clcarly see the pattern noise in Fig.3b especially in the uppcr right, quadrant, while hardly find any in Fig.3~.  Figures 4a-c show another simulation rcsult on a ramp image of size 256 x 256. No coinpcnsat,ion was done to get, F i g . 3 ~  and Fig.4~.  Figures 3d and 3e show the effect of dot-ovcrlap compensation. A printer model of x = 1.1, which is defined as the ratio of the actual dot, radius t,o thc idcal dot radius T/&, was used for cornpcnsation and gen- crating the printed outputs. The connection among x, 0, b, and y is given in [3]. A darlccr output is obtaincd without, compensat,ion as shown in Fig.3d. 5. CONCLUSION In this letter, we proposcd a new digital halftoning al- gorithm based on multiscale error diffusion. Comparc with [l], it is more faithful to  the “maximum crror in- tensity guidance” principle. Thc proposcd algorithm can definitcly reduce pattern noise and eliminatc the boundary effect and the ‘blaclchole’ effect. Finally, a compensation scheme for this algorithm is proposed to compensate for thc dotbovcrlap effect introduccd by printers. 6. REFERENCES [l] I. Katsavounidis and C.C. J. Kuo, “A multiscalc error diffusion techniquc for digital halftoning,” IEEE trans. on imagc processing, Vo1.6, No., Mar 1997, pp.483-490. [2] R. W. Floyd and L. Steinherg, “An Adaptive Al- gorithm for Spatial Gray Scale,” Proc. SID Inter- naiional Symposium Digest of Technical Papcrs, Society for Information Displays, 1975, pp.36-37. [3] Y .  Lin and T.C. KO, “A modified model-based error diffusion,” IEEE Signal Processing Lettcrs, Vol. 4, No.2, Fch 1997, pp.36-38. [4] T. N. Pappas and D. L. Neuhoff, “Printer niodcls and error diffusion,” IEEE trans. on Imagc Pro- cessing, Vol.4, No.1, Jan 1995, pp.6G-79. [5] Y.H.Chan, H.T.Kwong, K.T.Lo and C K L i ,  “An crror diffusion t,eclinique with reduccd directional Size of a region =dud 4-----d- Size of a subregion t 1 dQ + dQ + Possible anchor locations of the centroid of a subregion : 0 proposed approach A Katsavounidis’s approach Figurc 1: Suhrcgions of a region of intcrefit,. Figure 2: Circular dot-ovcrlap model hysteresis,” Proccedings, IEEE ISCAS’99, May 30 - June 2, 1999, Orlando, Florida, USA. Vol. IV, pp.263-266. 325 Authorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on July 26, 2009 at 21:47 from IEEE Xplore.  Restrictions apply. Figuri of the result (d) (e) 3 3: (a): Original t,est, pattern; (b): Diffusion result of Katsavounidis’s algorithm [I]; (c): Diffusion proposed algorithm; (d): Actual printed output of Fig.3b; (e): Actual printed output of the compc of the proposed algorithm. result, :nsatcd 326 Authorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on July 26, 2009 at 21:47 from IEEE Xplore.  Restrictions apply. Figure 4: (a): Original ramp image; (b): Diffusion result of Katsavounidis’s algorithm [l]; ( c ) :  Diffusion result of the proposed algorithm. 327 Authorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on July 26, 2009 at 21:47 from IEEE Xplore.  Restrictions apply. 

A multiscale error diffusion technique for digital halftoning with dot-overlap compensation

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