olorant-based drect bnary search» halftonng Journal of Electronc Iagng, vol., no. 4, Oct. 22 Je-Ho Lee and Jan P. Allebach School of Electrcal Engneerng & oputer Scence Kyungpook Natonal Unversty
Abstract Presentng a new colorant-based color halftonng technque Proposng color desgn crtera for unfor color textures ontrollng the qualty of each colorant texture Settng the dots optally wthout alterng the total arrangeent orrespondng to constraned optzaton proble Solvng ths proble va the swap-only drect bnary search Eployng a lunance huan vsual syste odel Enforcng excluson of vsually non-hoogeneous pattern
. Introducton Three groups of dgtal color halftonng Accordng to the coputatonal coplexty Screenng ausng artfacts such as ore patterns Error dffuson Scalar error dffuson and vector error dffuson ausng artfacts by error accuulaton Iteratve processes Least squares and DBS Takng a DBS-based color halftonng n ths paper
2. olorant based DBS Algorth rtera for Unfor olor Texture If we consder the dots of each prary color (, M, or Y) ndvdually, we would lke these dots to be arranged as unfor as possble We also would lke the overall coposte texture that conssts of all these prary colorant dots to be as unfor as possble We wsh to nze dot-on-dot prntng as uch as possble
Dscussng to b-level three-colorant MY prnters n ths paper. But can be appled to b-level four-colorant MYK prnters hoosng jontly halftone only the and M planes, do the Y plane ndependently, and fnally cobne ther halftones To avod dot-on-dot prntng as uch as possble, are gven by f ', M', and B ' = M M' = B = M ()
(a) (b) Fg. Two halftone patterns llustratng (a) dot-on-dot and (b) dotoff-dot prntng for a 7% gray level prnted at dp
(a) M: ndependently processed (b) Y: ndependently processed (c) MY: ndependently processed Fg. 2 oparson between ndependent and jont processng of colorant halftones for colorant aount of =M=Y=2%: (a)-(c) halftones obtaned by separately halftonng each of the color planes (contnue)
(d) M: jontly processed (e) Y: jontly processed (f) MY: jontly processed oparson between ndependent and jont processng of colorant halftones for colorant aount of =M=Y=2%: (d)-(e) halftones obtaned by jontly halftonng the color planes
(a) (b) Fg. 3 oparson between (a) restrctng Y to go nto spaces between colorant dots of jontly desgned and M halftones, and (b) desgn of the Y halftones copletely ndependently of the and M halftones for =M=Y=2%
(a) yan (b) Magenta (c) yan Magenta Fg. 4 Vsualzaton of relatons gven n Eq. () to nze dot-on-dot prntng
(a) (c) (b) (d) Fg. 5 Steps of color halftonng algorth for the case where =8%, M=5%, and Y=%: (a) set overall dot arrangeent, (b) color the dots the randoly, (c) refne the halftones for and M, and (d) fll holes wth B
Extenson to General Iages f f f M f[ ], ' = fm, [ fm, ' ] = f[ ], M [ ' M ' ] = f f, and f Where = [ = and contnuous spatal coordnates to represent dscrete Where f '[ ] and f M ' are, respectvely, the aount of cyan and agenta coponents whch do not contrbute to blue = or and g f f f f otherwse Applyng the onochroe DBS halftong algorth to M t t, n] and (x) ( x, y) f : R otherwse f 2 M f M R. =,M,Yand f. (2) (3) (4) f M []
s M W, f gm = and f B, f gm = and f =, f gm = and f ' M, otherwse f ' f ' < Let s [ ]: R 2 M {W,, M,B} be the functon that represents the colorng of g M [] r s a rando varable whch s unforly dstrbuted n the nterval (,) Seekng an optal color pattern for s M [] by swappng and M pxels to reduce an error etrc teratvely Extng teraton after the algorth has converged f f M M M > r (5)
g g M, f sm = or B =, otherwse, f sm = M or B =, otherwse g [] and g M [] are obtaned fro s M [] (6)
Fg. 6 Block dagra of the flow the halftonng algorth proposed
Error Metrcs g g ' M ' =, =, f f s s M M = = M g [ ] and g M ' denote the halftone age for f ' and ' (7) f M ' g ( x) = g[ ] p( x X), = ', M ' The halftone age rendered by the prnter (8) p(x) s the spot functon of the prnter and X s the perodcty atrx whose coluns coprse the bass for the lattce of prnter addressable dots
e ( x) = h( x) [ g ( x) f ( x)], = ', M ' (9) Defnton of the perceved error age h(x) s the pont spread functon of the HVS (x) s contnuous-tone orgnal age e f ( x) = e p( x X), = ', M' Where e = g f, ', M ' = () ()
ε 2 = e ( x) dx, = ', M ' Measure of error s based on the total squared value of Eq. () (2) nze ε (3a) subject to g ' g M '[ ] = g M (3b) Where ε = αε ' βεm ' s dual error easure whch penalzes the use of both and M halftone textures that lead to a vsually unpleasng appearance.
Error Mnzaton c ( x) = p( y) p( x p p y) dy Defnton of autocorrelaton functon Dscrete for of Eq. (2) ε e [ = = n ] e c [ n], ', M ' p p (4) orrelaton functon c = c ( X) p p p p g = a δ[ ] aδ[ ], = ', M ' (5) onsderng a tral swap between pxels and Descrbng the change n g ' and g '
g = a δ[ ] aδ [ ], = ', M ' onsderng a tral swap between pxels and Descrbng the change n g ' and g ' (5) Where a and a, = ',M' are gven by a j =, f g[ j ] s changed fro to, f g [ ] s changed fro to j j =, (6) The par ( g '[ ], g' [ ]), ( gm '[ ], gm '[ ]) ( g' [ ], gm '[ ]), g [ ], g [ ]) ust all have dfferent bnary states, we have followng relatonshps aong a and a, = ',M' : ( ' M ' a ' = a M ' = a ' = a M ' (7)
Where s the cross correlaton between and Dual etrc ] [ ) 2( ]) [ ] [ ( 2 ] [ ] [ 2 [] ) 2( ' ' ' ' ' ' c c c a c c a c p p M pe p e M pe pe p p = β α β α β α β α ε ' ', ], [ 2 ] [ 2 ] [ 2 [] ] ) ( ) [( 2 2 M c a a c a c a c a a p p pe pe p p = = ε ' ', ], [ ] [ ] [ M n c n e c p p n pe = = ] [ c e p ] [ c p p e [] (8) (9) (2)
Experental Results oparng color halftones Proposed colorant based DBS algorth Plane-ndependent DBS The HP 97 x nkjet prnter drver hoosng two halftones age Rap and dnng table
(a) (b) (c) Fg. 7 Halftones for the Rap age generated by (a) plane-ndependent DBS, (b) the HP 97 x nkjet prnter drver, and (c) colorantbased DBS. Note that ages are prnted at 5 dp. Ths s uch lower resoluton than would norally be used wth the HP 97 x prnter. Therefore (b) s not representatve of the qualty of the real output of the HP 97 x prnter.
(a) (b) (c) Fg. 8 Halftones for the dnng table age generated by (a) planendependent DBS, (b) the HP 97 x nkjet prnter drver, and (c) colorantbased DBS. Note that ages are prnted at 5 dp.
Suary and oncluson Ths algorth can be effcently pleented by recursvely evaluatng the effect of tral changes olorant-based DBS s stll teratve and slower than non-teratve algorth Future work Extenson of proposed algorth to general case