Visual-Based error diffusion for printers

(1)

Rochester Institute of Technology

RIT Scholar Works

Theses Thesis/Dissertation Collections

5-1-1996

Visual-Based error diffusion for printers

Zhenping Bu

Follow this and additional works at:http://scholarworks.rit.edu/theses

This Thesis is brought to you for free and open access by the Thesis/Dissertation Collections at RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please [email protected].

Recommended Citation

(2)

Visual-Based Error Diffusion for Printers

by

ZhenpingBu

B.S. Chongqing University of Architecture and Technology

(1985)

A thesis submitted in partial fulfillment of

the requirements for the degree of Master of Science

in the Chester F. Carlson Center for Imaging Science

College of Science

at the

ROCHESTER INSTITUTE OF TECHNOLOGY

May, 1996

Signature of the Author ~ _

ZhenpingBu

Accepted by Dana G. Marsh

v1~

/b,

/196

(3)

Chester F. Carlson Center for Imaging Science

College of Science

Rochester Institute of Technology

Rochester, New York

CERTIFICATE OF APPROVAL

M.S. DEGREE THESIS

This M. S. Degree Thesis ofZhenping Bu

has been examined and approved by the

thesis committee as satisfactory for the

thesis requirement for the

Master of Science degree

Thesis Advisor: Dr. RogerL. Easton, Jr.

Dr. Jonathan S. Arney

Dr. Mark D. Fairchild

(4)

Chester F. Carlson Center for Imaging Science

College of Science

Rochester Institute of Technology

Rochester, New York

THESIS RELEASE PERMISSION FORM

Title of Thesis:

Visual-based Error Diffusion for Printers

I, Zhenping Bu, hereby grant permission to the Wallace Memorial Library of R.I.T. to

reproduce my thesis inwhole or in part. Any reproduction will not be for commercial use

or profit.

Signature of Author: _

(5)

Visual-based Error Diffusion for Printers

By ZhenpingBu

Submittedtothe

ChesterF. CarlsonCenterfor_Imaging Science

CollegeofScience

inpartial_fulfillment oftherequirements fortheMasterofScience Degree attheRochester Instituteof_Technology

ABSTRACT

Anapproachfor_halftoning ispresented thatincorporates a printer model and also

explicitly uses the human visual model. Conventional methods, such as clustered-dot

screening ordispersed-dot _screening, do not solvethegray-leveldistortionof printers and just _implicitly use the eye as a lowpass filter. Error diffusion accounts for errors when

processing subsequent pixels to minimize the overall mean-square errors. _Recently developed "model-based"

halftoningtechnique eliminates the effect of printer luminance

distortion, but this method does not considerthe _filtering action ofthe _eye, that _is, some artifacts of standard error diffusion still exist when the _printing resolution and view distance change. Another "visual error diffusion" method incorporates the human visual

filter into errordiffusionand resultsin improvednoise characteristics andbetterresolution

for structured image _regions, but gray levels are still distorted. Experiments prove that

humanviewersjudgethe _qualityof a _halftoning image based _mainly onthe region which

exhibits theworst local _error, and _{low-frequency} distortions introduced _by the _halftoning

process are responsible for more _visually _annoying artifacts in the halftone image than high-frequency distortion. Consequently, we adjustthe correction factors ofthe feedback

filter _by local characteristics and adjust the dot patterns for some _gray levels to minimize

the visual blurred local error. Based on the human visual _model, we obtain the

visual-based error diffusion algorithm, and furtherwe will also incorporate the printer model to

correct the _{printing distortion. The} artifacts connected with standard error diffusion are expected to be eliminated or decreased and therefore better print _quality should be achieved. In addition to qualitative _analysis, we also introduce a subjective evaluation of

(6)

ACKNOWLEDGMENTS

Iwishto acknowledgeDr. Roger L. Easton, Jr. for his guidance and advicewhich made

thisworkpossible.

I would like to thank Dr. Dana Marsh for his administrative _help which made life and

studyatCIS easier.

Iwouldliketo thankDr. Jonathan_Arney andDr. Mark Fairchild fortheirparticipation on

mycommitteeandforsuggestionsthat madethis thesisa reality.

Iwould like to thank Mr. Scott_Daly, Kodak _Imaging Corporation for his talking on the

visual model.

Iwouldliketo thankallvisualobservers who_help metofinishthepsychophysicaltests.

Finally, I would like to give _my sincere appreciation to _my _lovely _wife, _Huihui, for her

(7)

Halftoning

Techniques

2.1 Classification of

Halftoning

_Techniques

Digital _halftoning is the process of _transforming a continuous-tone image to a

pattern of black and white pixels which can be printed to produce the illusion of a

continuous-tone_image, dueto the eye'slack of_{high-frequency} resolution. The processis

necessaryto reproduce images_using_hard-copy devicesthat can produce pixelswith _only

two possible brightness values. Table 2-1 shows the classification of conventional and

popular_halftoningtechniques. Thesetechniquesaredescribed below.

HalftoningTechnique Typeof Pattern

Typeof

Operation

Typeof "Dot"

Screening Random-dot aperiodic point dispersed

Clustered-dot periodic point clustered

Dispersed-dot periodic point dispersed

Error Diffusion aperiodic neighborhood dispersed

Stochastic_Screening periodic point dispersed

Table 2-1 Categorizationof_HalftoningTechniques

There is a choice of computational complexity. A point operation _{in image}

processing refers to an algorithm whichproduces output for a given location_based _only

(19)

Pointoperations havetheadvantage of simple computation. _Screeningis anexample ofa

point process. Aneighborhoodoperation calculatesthevaluebased onthe _grayvalues in

a _{neighborhood,} and _generally requires more complicated computation, but produce

higher_qualityresults.

Section 2. 2 to 2. 4 describe the different _halftoning techniques _respectively in

moredetail.

2.2

Screening

In _{screening, the} two-dimensional image is _compared, pixel _by _pixel, with an

image-independent_{threshold matrix; the} result ofthe comparison is a_binary output. The

usual convention is that the maximum value (e.g. _1.0) is white and the minimum value

(e.g. 0.0 ₎ is_black; forpixelswith_grayvalueoftheimage larger thanthe thresholdin the

threshold matrix, the binary output is_white; _{otherwise, the} _binary output is black. There

are _manyways to generate the matrix ofthresholds. The randompattern ofthresholds is

called random screening. Whenthe thresholds are _periodic, the method is called ordered

screening. The threshold matrix is specified _by one period of a grid which is generally

rectangular or hexagonal. Two different types of screens _commonly are used. One is the

clustered-dot screen where the thresholds are arranged so that _they produce clusters of

black dots. The other is dispersed-dot screen where the thresholds are arranged so that

theyproducedispersed blackandwhitedots.

Screening is a simple but effective technique _{for reproducing} the illusion of

(20)

techniques isattributedto their_simplicityand ease ofimplementation. Inthe_following, we

usethepractical examplestodescribethedifferent_screeningmethods.

2.2.1 Random _Screening

In the random _screening, the thresholds are _randomly generated. Because all

frequencies are_present, _{low-frequency}_{artifacts are visible and}_the

resultingimages appear

noisy. Figure 2-1 showstwo images halftonedwith the random screening. _{The quality} of

outputfromthismethod makesitoflittlepracticalvalue.

Lena Hats

Figure 2-1 Images HalftonedwithRandom-dotScreen_(300dpi)

2.2.2 Clustered-dot _Screening

This technique for digital _printing is designed to simulate traditional _analog

halftoningtechniques used for many years in printing. The main advantage of

clustered-dot _screening is that it produces images that are _very robust to _{dot overlap} and other

printer distortions. As will be _{shown, the} higher thresholds are centered in the screen

(21)

consists of a central _{black dot} that increases in size and forms a macro-dot as the _gray

value ofthe neighborhood decreases. Whentheink dots are printedin clusters or

macro-dots, most ofthe _{black dots overlap} other black dots rather than white spaces. Thus

changesin apparent _graylevel due to _{dot overlap} are_minimized, andthe_accuracy ofthe

gray-scalerendition of theprintedimage ismaintainedinsome extent.

The macro-dots are formed _by _choosing the elements ofthe threshold matrix so

that _they increase towards a fixed point. Figure 2-2 illustrates a such screen. In this

threshold _matrix, the thresholds in the upper left and lower right quadrants increase

toward themaximumthreshold0.969andform blackmacro-dots. _{The spacing}ofthe dots

is fixed. Darker regions of an image result in even bigger macro-dots. This is _precisely

howtraditional _analog_halftoningworks.

0.576 0.635 0.608 0.514 0.424 0.365 0.392 0.486

0.847 0.878 0.910 0.698 0.153 0.122 0.090 0.302

0.820 0.969 0.941 0.667 0.180 0.031 0.059 0.333

0.725 0.788 0.757 0.545 0.275 0.212 0.243 0.455

0.424 0.365 0.392 0.486 0.576 0.635 0.608 0.514

0.153 0.122 0.090 0.302 0.847 0.878 0.910 0.698

0.180 0.031 0.059 0.333 0.820 0.969 0.941 0.667

0.275 0.212 0.243 0.455 0.725 0.788 0.757 0.545

Figure 2-2 Clustered-dot Matrix_{(Classic-4) (Dong, 1992)}

Figure 2-3 illustratesthe robustness of clustered-dottechniques. It showstwo test

(22)

printer with afairamount ofdotoverlap. Theclustered-dot screens are_generallypreferred

for printing inthepresence ofdotoverlap.

IIP

vg&Sm

mm

V

fm8S&tm&&M&hsssm

Lena Hats

Figure 2-3 Images Halftonedwiththe"Classic-4" Screen_(300dpi)

Althoughtherendition of_graylevels_maybe_reasonablymaintainedinthe clustered

dot _{approach, the} methodhas serious drawbacks. Theimages inFigure 2-3 appear alittle

blurry in the edges such as in the hat bands in Lena and the letters on the largest hat in

Hats, and the details such as the hair in Lena. _Also, the macro-dots ofthe clustered-dot

techniqueare more visibleand unpleasanttotheeye. We_usuallyreferto suchpatterns as

low-frequencyperiodic artifacts. Astheperiod ofthescreenincreasessothat morebitonal

dots are available, the number of _gray levels that can be generated _increases, but the

perceived spatial resolution decreasesbecausethe macro-dotsbecome more visible. Thus

thereisatradeoffbetweenthegray-scale resolution andthe _severityforthe _{low-frequency}

periodicartifacts.

Finally, even though the clustered-dot approach minimizes the effects of dot

(23)

halftoned _Ramp images. _Practically, the original _Ramp image is also halftoned. The

original _Ramp _{is halftoned} with a clustered-dot screen and printed at a resolution of

600dpi. _But, thehalftoned processforthis originalimage _{may include} edge enhancement

andtonalcalibration. It seemsthat thenumber of gray-levels inthe_Ramphalftonedwith

the "Classic-4" screen is reduced becausethe tonal _stepping is visiblein Figure 2-4. The

halftoned_Rampdoes not _accurately reflectthe original_gray levels. The effects ofprinter

distortion_may stillbe _apparent,though it_typicallyis_relativelysmall and canbe corrected

usingdirectmeasurement of printedimage(Lin and_{Wiseman, 1993; Rosenberg,} ₁₉₉₃₎ or

a printer model(Pappas and_Neuhoff, 1991 and 1995).

original

Halftonedwiththe"Classic-4" Screen_(300dpi)

Figure 2-4 OriginalandHalftoned (Clustered-dotScreen) Ramp

2.2.3Dispersed-dot_Screening

In dispersed-dot screening, the threshold matrix is designed to maximize the

(24)

higherthresholdvalues are scatteredthroughout_{the pattern,} _causing small dispersed dots

toincreaseinnumber asthesignal decreases.Figure 2-6 showstwoimageshalftonedwith

thisdispersed-dotscreen.

0.513 0.272 0.724 0.483 0.543 0.302 0.694 0.453 0.151 0.755 0.091 0.966 0.181 0.785 0.121 0.936 0.634 0.392 0.574 0.667 0.180 0.423 0.604 0.362

0.060 0.875 0.211 0815 0.030 0.906 0.241 0.845

0.543 0.694 0.694 0.453 0.513 0.272 0.724 0.483

0.181 0.785 0.121 0.936 0.151 0.755 0.091 0.966 0.664 0.423 0.604 0.362 0.634 0.392 0.574 0.332

0.030 0.906 0.241 0.845 0.060 0.875 0.211 0.815

Figure 2-5 Dispersed-dot Matrix_{(Bayer-5) (Dong,} ₁₉₉₂₎

Lena Hats

Figure 2-6 Images Halftonedwiththe

"Bayer-5"

Screen_(300dpi)

The method increases the apparent spatial resolution ofthe printed images and

minimizes the _{low-frequency}periodic artifacts. The comparisonbetween Figure 2-6 with

Figure 2-3 shows that the technique suffers major degradation in _{gray-scale rendition.}

(25)

objectionable _{low-frequency} periodic artifacts than the

"Classic-4"

screen (Dong, 1992).

From Figure _2-6, the false textural _contouring seems to be apparent in the _sky in Hats.

Textural _{contouring is} the phenomenon in which a slight variation ofthe _{gray level} in

smooth areas often resultsintheformationof an artificial _contour, _{simply because}the dot

pattern _(texture)has been changedlocally. Thereason is apparentfrom Figure 2-7 which

includestheoriginal_Ramp and halftoned_Ramp imageswiththe clustered-dot screen and

the dispersed-dot screen. In the halftoned _Ramp with dispersed-dot screen, the textural

patterns for some close _gray levels are _{visibly different. Textural contouring} is a _very

serious problemforthedispersed-dottechnique.

original

Halftonedwiththe"Classic-4" Screen_(300dpi)

Halftonedwiththe"Bayer-5" Screen_(300dpi)

(26)

2.3 Error Diffusion

In error _diffusion, theimage pixels are also comparedwithathreshold. _However,

inthis_case, the thresholdis fixedandthe_grayvalue of eachimagepixelismodifiedbefore

thresholdingbasedonthepreviousimagepixels.

The_screeningtechniquesjust considered illustrate"point operations"; that is , the

binary output depends _only on the _gray value ofthe specific input pixel. Error-diffused

halftoning, first introduced_byFloydand _{Steinberg (1976),} isanadaptive processbasedon

a neighborhood of pixels. In _{this operation, the threshold} is fixed. Error between the

corrected gray-level input and its _binary output is passed through a spatial filter to

produce a correction factorwhich is added to the subsequentinput value. It is clear that

theresult ofthe operationdependsonthepixel values inthe neighborhood andtheerrors

arediffusedovertheentireimage. Aschematicfortheprocessis shownin Figure 2-8.

y[y] _+^-, u[U] Threshold

t

b[ij]

Lowpass ^_

Filterw

e[i,j]

(27)

We assumethat the image is scanned from left toright and_topto bottom. In this

figure, y[ij] representsthe _[ij] pixel ofthe continuoustone gray-scaleimage. The binary

output_b[Lj] produced_byerrordiffusion isobtained_bythe_following set ofequations.

u[i,j]=y[i,j]-w[i,j]*e[Lj] (2-1)

fLO, if u[i,j] > _t

b[i,j]H (2"2>

[0.0, otherwise

e[i,j]=_b[i ,j]

-u[i,j] (2-3)

where _u[i,j] is the corrected value ofthe gray-scale image. The error _e[i,j] at a specific

pixel _[ij]is definedasthedifference betweenthe corrected gray-scaleinputandthe_binary

output. The previous errors are lowpass filtered with and subtracted from the current

image value _y[ij] before _thresholding to obtain the _binary value _b[ij], where w is the

impulseresponseofthelowpass filter._Thus, errors are

"diffused"

overtheimage.

Thethresholdt_typicallyis fixed atthemidpoint ofthe gray-scale _range, e.g. 0.5.

The lowpass filter w has non-symmetric half-plane _support, so that _only the _already

computed errors are filtered. This is the two-dimensional equivalent of_"causality", and

enables the algorithmtomake instantaneousdecisionsat each point. _Thus, error diffusion

requires_onlyone passthroughthedata. Thefiltercoefficientsare positive and theirsumis

equalto onetoensurethat themean_grayvalueispreserved.

Various error diffusion filters have been suggested in the literature _(Ulichney,

1987). In our experiments we will use the filters proposed _by Floyd and _{Steinberg (FL)}

(1976), Jarvis, Judice andNinke (JA) (1976). The impulse response are shownin Figure

(28)

, , .

, _

pixel_bemgprocessed -*

1 5

16 16

16 3

16

Figure 2-9 Floydand_SteinbergError Filter(FL)

Lena Hats

Figure 2-10 Images HalftonedwithFL_(300dpi)

Figure 2-1 1_RampHalftonedwithFL(300dpi)

pixel_beingprocessed

1_

5_

48 48

J_

JL

1-48 48 48 48 48

J_

_3_

J_

48 48 48 48 48

(29)

Lena Hats

Figure2-13 _{Images Halftoned}withJA_(300dpi)

Figure 2-14 _RampHalftonedwithJA_(300dpi)

From Figures_{2-10, 2-11,} 2-13 and _2-14, the effects ofthe errorfilters are visible.

Images are sharpened such as the hair details in Lena and _especially the letters on the

largest hat in Hats. _{Several gray} levels are represented _by a _pleasingly _isotropic

structureless distribution. Thetextural _contouring connectedwith dispersed-dot _screening

is _greatly reduced. _However, some disadvantages also are _apparent; such as correlated

artifacts in many of the gray-level patterns and directional overshoot in highlight and

shadow areas. One more conspicuous artifact for printed images with FL is that the

regions in the _midgray suffer from the most serious gray-scale distortion. _Actually, the

(30)

without "dot-overlap". It is this _shortcoming that producesworm-like artifacts in images

such asthefaceonLenain Figure2-10.

The _halftoning process with the error filter shown in Figure 2-8 is called the

"Minimum AverageError"

algorithm. The larger filterreduces some ofthe artifacts seen

with the four-element filter shown in Figure _2-9, but directional overshoot in highlight

and shadow regions increases and black pixels are clustered together in the _midgray

regions. _{Of course,} theerrordiffusionwithJAalso sharpensthe picture more. For digital

printing with device _having a fair amount of _dot-overlap, the error diffusion with JA

rendersbetter halftoned imagesthantheerrorfilterofFloydandSteinberg.

The above discussion demonstratesthat error diffusion is _very sensitiveto printer

distortions such as dot overlap. Inthe presence ofdot _overlap, error diffusion produces

verydark imagesshowninthesefigures. Thishas limited itsapplicationtocaseswhere no

dot_overlap _occurs, suchasCRTdisplays.

2.4 Stochastic_Screening

In stochastic _{screening, the} two-dimensional image is _compared, pixel _by _pixel,

with an image-independent threshold matrix; the result ofthe comparison is a _binary

output. Thoughthe halftoneddotpatterns with either stochasticscreening(Ulichney, 1987

and _1993; Yao and _Parker, ₁₉₉₄₎ or random _screening all appear to be _random, the dot

patterns _resulting from random _{screening have} the characteristics of white noise and the

patterns with stochastic screening have the characteristics of blue _noise, which is more

(31)

frequencies; the power spectrum of blue noise shows that most of its power is

concentrated in the high frequencies. Figure 2-15 illustrates the difference between the

spectraof white noise andblue noiseinthe _frequencydomain. The plot was produced in

the_followingway: a 256 x 256 pixel patchwitha constant _graylevel of0.97 (white=1.0

and _black=0.0) was halftoned_respectivelywith a random screen and a stochastic _screen,

and the power spectra of the two halftoned patterns on a radial line were computed.

Because ofits characteristics in _frequency _domain, stochastic _screening is often called

blue-noisemasking.

1.0

-

0.9-'-. /\ /. I

., ., .... f\

0.8-E = 0.7-Bluenoise OJ S 0.5-o Q. VOA TS

S0.3-

l

Whitenoise

0.2-/>

v ^N

-vy w

0.1-

/

0.0- 1 1 1 1 I 1 1 1 1 1 1

RadialFrequency(1/mm)

Figure 2-15 Power SpectrumofBlue NoiseandWhite Noise

The higher thresholds in the stochastic screen also are scattered throughout the

screen, causing small dispersed dots to increase in number as the signal decreases. This

technique can eliminate the periodic structure often presented in _{halftoned images}

(32)

intensive, but the subsequent _halftoningprocess is as _easyto perform asthe conventional

screening methods. _Therefore, stochastic _screening has the advantages of simple

halftoning computation and a _{visually pleasing} pattern. Figures 2-16 and 2-17 show the

images halftonedwiththeblue-noisemask.

These halftoned images show that _they do not suffer from periodic artifacts or

textural _contouring connected with dispersed-dot screening. The halftoned images

producedwith stochastic _screening appear to be somewhat noisier thanthose from error

diffusion. Because _halftoning with a blue-noise mask also produces dispersed _dots, the

images halftonedwith thismask will exhibit the seriousgray-levelartifactswhen printed

withdevices_exhibitingdot overlap.

Lena Hats

Figure 2-16 Images HalftonedwithBlue Noise Mask(300dpi)

(33)

2.5 QualitativeAspects of

Halftoning

Performance

The _halftoning reproduction of a gray-scale image should resemble the original

when viewed under appropriate conditions. _{When choosing} a _halftoning _technique, we

wish maximizethe_{similarity between}thehalftonedimageanditstarget. Twoquestionsto

be answered are: how to evaluate the _quality of halftoned images and compare the

performance of the techniques? Analysis based on traditional root-mean-square error

(Watson, 1993) has been shown to be incapable of _explaining all visible differences

between two images. In this _thesis, we use two methods to evaluate the _quality of

halftoned images. The qualitative measures(Pappasand_Neuhoff, ₁₉₉₅₎ are coveredhere.

Thesecond method uses psychophysicaltests.

2.5.1. RegionofConstant_GrayLevel

The two most important measures of success of a _halftoning method are tone

reproduction,e.g. the _accuracy ofgray-level_rendition, andthe _severityof_{low-frequency}

periodic artifacts. A halftoned image is desired to have the same number of"apparent"

graylevelsas presentedintheoriginal. _{Conventionally,}whenusedin image_halftoning,the

halftoning screen determines how _{many gray} levels can be rendered. Ifthe screen has a

size of Mx_N, this approachallows_onlyalimitednumberof_graylevels (MxN ₊₁₎ to

bereproduced.Underthese cases, ifthenumberofMxNisnot adequateto representthe

gray-level range ofthe image (coarse quantization), a false contour _may be formed. The

most visible example is that of an image after_thresholding _by afixed _gray value (lxl

(34)

(left) andtheimage_alreadyshowninFigure 2-3 (right). Theleft-hand image exhibitsfalse

contoursintheshoulder area andthe area abovethehat becausethe screen usedcan_only

renderthe _{19 gray}_levels; buttheright-hand image doesnot exhibitvisiblefalse contourin

the same areasbecause the "Classic-4" can reproduce more _gray levels(33). _But, for the

conventional_algorithms, more serious_{low-frequency} periodic artifactswillbe introduced

if thesize of a screenis increasedtoobtain more_graylevels. Thecomparisonbetweenthe

two images in Figure 2-18 shows that the right-hand image exhibits more visible

low-frequencyperiodic artifactsbecausethe size ofthe"Classic-4" screenis largerthanthat of

the screen usedforthe left-hand image. _Therefore, for conventional _{algorithms, there} is a

tradeoffbetweengray-scale resolution and_{low-frequency}periodic artifacts. Clustered-dot

screeningproducesthemost serious_{low-frequency}periodic artifacts.

A Screenwith 19_GrayLevels

"Classic-4"

with33 _GrayLevels

Figure 2-18 Images HalftonedwithClustered-dotScreens_(300dpi)

Error diffusion does not produce periodic patterns. In the absence of printer

distortions, the number ofgray-levels it produces is _essentially the same as that in the

(35)

halftone an _image _composed _{of a constant}

gray level, it will render the same _gray level

because ofits

property preserving the mean. Stochastic _screening , the newly developed

method, also introduces no periodic artifacts because it produces the isotropic

structureless patterns.

[image:35.530.197.354.241.425.2]

2.5.2Region of_{Slowly Changing}_Gray_Level

Figure 2-19 Partial MagnificationofLena in Figure2-6 _(150dpi)

When gray level changes _smoothlyover alarge_{region, the}perceived_grayvalue of

the halftoned output should not change abruptly. Ifthis _{happens simultaneously} _along a

contour of constantimage_graylevel, thecontour appears as anedge. As stated in section

2.2.3, the phenomenon is called textural contouring. _Normally, digital _halftoning

algorithms produce varied textures for different rendered _gray _levels. Ifthe patterns for

the similar_gray levels are_visiblydifferent andboth patterns meet in a

(36)

area in an _image, _undesirable

contouring artifacts _may be introduced. Figure 2-19 shows

textural _contouring on the left part offace and hat ofLena. Dispersed-dot _screening

causedthemost serioustexturalcontouring.

2.5.3 Region of _{Rapidly Changing}_Gray_Level

"Classic-4r

FL

Figure2-20 Partial MagnificationofHats in Figure2-3 andFigure2-10 _(100dpi)

The spatial resolution of a halftoned image also is a _primary concern. High

resolutionwhichproduces sharpened continuous edges andfine_details, is_highlydesirable.

Foredgesinahalftoned_image, itwouldbeadvantageous ifthe_halftoningalgorithm could

produce a compact set of printed spotsdistributed_alongthe edges andboundaries. Thisis

particularly important when the halftoned image includes text characters (not white or

[image:36.530.84.428.210.429.2]

(37)

alongeitherthe edge ofhatsortheboundariesofletters becausethedotsaretoolargeand

thespacebetweenthedotsare_fixed;butthedots in right-hand image can. Forthis reason,

the left-hand image exhibits blurred edges and details and the right-hand image has

sharpened edges and clear letters. In the region of _{rapidly changing gray} level, the

perception of blurred and sharpened edges should be evaluated. One of the main

disadvantages of clustered-dot _screening is that it blurs images. _But, dispersed-dot

screening, errordiffusionand stochastic _screeningrendersharperhalftoned images.

2.5.4 Performance WhentheOutput Device Is aPrinter

Normally, both _screening and error diffusion assume that pixels are _identically

shaped dots on positioned rectangular grids. _However, printers produce _{approximately}

circularblack spots on white paper and exhibit dot overlap. Figure 2-21 showsthe

dot-overlapphenomenon.

windowWl windowW2 Actual Dot

(38)

This physical _property causes a black pixel to affect its white neighbor(s), and

distorts the _linearity and even the _monotonicity ofthe perceived _gray scale of output

image. In other _words, the _{gray level is} not proportional to the number of white pixels

over a small area and small areaswiththesame number ofwhitepixels_may have different

average _gray values. Ifthe dot is so smallthat a single pixel can notbe recognized, the

eye perceives an average _gray level over a small area like 3x3 window. _Ideally, the

average_graylevel_gof windowWl andW2 inFigure 2-21 shouldbe

Z

(ona scale white

= ₁

.0 toblack

=

0.0); but_actually, _gisnot equalto

X

. Thoughboth Wl andW2inFigure

2-21 include two black _dots, _they have different _grayvalues because _they have different

white-area (orblack-area) percentages. The phenomenon will be _{discussed quantitatively}

in section 3.2. _Halftoning methods to be used for printing should be re-examined to

determine whether and to what degree _they resist this kind ofdistortion. Clustered-dot

screening can resist the distortion quite well. Figure 2-22 shows simple patterns for

dispersed-dot and clustered-dot patterns. In the clustered-dot _pattern, most black dots

overlap other black dots rather than white _spaces; On the contrary, in the dispersed-dot

pattern, the black dots overlap white spaces rather than other black dots. _Therefore,

dispersed-dot pattern is more sensitive to dot overlap. Dispersed-dot screening, error

diffusion, andstochastic _screening producedispersed-dotpatterns andhence cannot resist

the _dot-overlap distortion of laser or ink-jet printers. This is _why the clustered-dot

(39)

windowWl windowW2 Actual Dot

Dispersed dot Clustered dot

Figure 2-22EffectsofDot_Overlap onClustered-dot andDispersed-dot Patterns

2.6

Summary

In the absence of significant printer distortions ₍ i.e. for _display on most _binary

CRTs), the best ofthe _currently used techniques for digital _halftoning is error diffusion.

Thoughstochastic _screening rendershalftoned imagesof_slightlypoorer_qualitythanerror

diffusion, itcombinestheadvantage of simple computation of conventionaltechniques and

the_visually_pleasing patterns of error diffusion. _Screening is simpler but produces poorer

halftoned imagesthanerror diffusion. _However, whenprinted_by devices withsubstantial

dot _overlap (such as laser _{printers), the} clustered-dot _screening schemes have been the

only available choice. As discussed, the clustered-dot approach is successful in _reducing

the effects of dot _overlap, but sacrifices spatial resolution and generates more

low-frequency periodic artifacts.

Model-based techniques can correct for the effects of dot overlap without

sacrificing spatial resolution or _{increasing low-frequency} periodic artifacts. _Actually,

(40)

resolution. The_keytosuchtechniques isanaccurateprinter_model, whose parameters are

adapted to each individual printer_by calibration. The introduction of an accurate visual

model can eliminate some worm-like and asymmetric artifacts. Before we deal with the

model-based _halftoning and visual error _diffusion, we first discuss the eye model and

(41)

Chapter 3 Eye Model and Printer Model

Two important factors must be consideredwhen _predictingthe _quality of printed

images: the_halftoningtechniqueused andthebehaviorofthe printer. Whenhumans view

an _image, _they_{judge its} quality. Itis clear that the performance of_halftoning algorithms

mustberelatedto theresponse ofthehumanvisualsystem (HVS). _Indeed,theprocess of

halftoning requires that the human eye act as a lowpass filter. In _{this way,} conventional

techniques _implicitly _employ the visual model. In this _thesis, we will _explicitly use this

HVS to avoid some artifacts to which the human eye is _very sensitive. Printed images

exhibit gray-level distortion because ofthe "dot overlap"

and other factors. Traditional

techniques, such as clustered-dot _screening, resist spatial degradation at the expense of

spatial and gray-scale resolution. Themethod wewill discusswill correct printerdistortion

depending on printer _model, and meanwhile maintain both gray-scale and spatial

resolutions.

Before _discussing some _recently developed _algorithms, we will describe the eye

model andtheprinter model inthe _following sections. _{Both play} importantroles in these

algorithmstobe described.

3.1. Eye Model

3.1.1.ConventionalEye Model

The perception ofimages _by the HVS is difficult to describe. _Many experiments

(42)

The simplestvisual modelincludes justa contrast _sensitivityfunction(CSF)that is related

to thevariationsin visual _sensitivityas afunctionof spatial frequency. The sensitivityS is defined as the inverse ofthe contrast of a square wave _grating required to produce a

thresholdresponse:

S=

(3-1)

wherethecontrastC is definedas

c=Lmax-Lmin

^

max

min

and where _Lmax and _Lmin refer to the maximum and minimum luminance ofthe _grating

intensity, respectively. A complex model _may be composed of two parts: amplitude

nonlinearity and CSF. The amplitude _nonlinearity describes the variations in visual

sensitivity as afunction oflight _level; that _is, the perception ofthe eye to changes in the intensity of illumination is nonlinear. _{This nonlinearity} account for Weber's _law, which says that the smallest noticeable change in _intensity is proportional to the intensity.

Commonly, the _intensity is represented as a logarithm or power law. A more complex model also includes detection mechanism _(Daly, _1992), which describes the variation in visual _sensitivity as a function ofsignal content. It is beyond the scope ofthis paper to

review these results in detail. _Instead, this thesis focuses on the contrast _sensitivity function.

When viewing an _image, the resolution limit of human eye ensures that the

"lightness"

of the printed image is averaged over a small angular extent. That _is, the

(43)

is called the "contrast _sensitivity _function", which is a function ofthe spatial frequency

measuredincyclesper angular degree. _Empiricallymeasured contrast _sensitivityfunctions

vary due to different _viewing conditions. Various approximations have been used in the

literature to representthe CSFthrough an analytic expression. Inthis _thesis, we consider

the_followingtypicalCSFconstructed_byMannos and Sakrison(1974).

H(fr)=_2.6

(0.0192+ 1.1 145 fr) exp(-(1.114

QL1

) (3-3)

where fr istheradial_frequencyincycles per angulardegree.

This curveis shown in Figure 3-1 and peaks at about 8 cycles per _degree; other

empiricalCSFs exhibit maxima atfrequencies intheinterval 2-10 cycles per degree _(Jain,

1992). The peak values_varywithviewers. Equation _(3-3) represents a formofbandpass

filter. The decrease _{in sensitivity} at high frequencies is _generally ascribed to the optical

characteristics oftheeye(Netravali and_Haskell, ₁₉₈₈₎ such astheresolution limitsofthe

optical _{processing in} the lens. It is the attenuation ofthe high frequencies that is most

critical to halftoning. The decrease _{in sensitivity} at low frequencies accounts for the

"illusionof simultaneous

contrast"

where a region offixed_{gray level} appearsdarkerwhen

surroundedbyalighterregionthanwhen surrounded bya darkerregion. The decrease in

sensitivity at low frequencies also accounts for the Mach-band effect where the eye

perceives alighterbandonthelightside ofthe edge and adarkerbandonthe darkside of

(44)

0 24 7 811l3l6l3202i22729 3134363842 454751545B5BeOKa5B7ee

Spatial_Frequency_{(cyde/Uecpee)}

Figure 3-1 Contrast _SensitivityFunction

3.1.2.Modified Eye Models for_HalftoningImages

The conventional contrast _sensitivity function describes the _{detectability} of

sinusoidal signals on a uniform background, and can be used to predict the _visibility of

signal on a near uniform luminous background. _However, for images _containing a lot of

visiblenoise(suprathreshold _{conditions), this} assumption_may notbe _completelyaccurate

(Mitsa, 1992; Mitsa, et al, 1993). In threshold conditions, the contrast is defined as

thresholdresponseforasinusoidal pattern. Inthe suprathreshold _{condition, the}contrastis

defined as _subjectively equal contrast for two stimuli such as two spatial sinusoidal

patterns. In _halftoning applications, the _noisy condition is typical. _Halftoning _may

introduceaunique combinationof_distortions, suchastextural _contouring,resolution_loss,

coarse quantization contouring, and _especially graininess. _Therefore, the CSF must be

modified forthepresent environment. Thehigh-frequency drop off should notbe affected

by suprathreshold conditions, because it is mainly due to resolution limits ofthe optical

(45)

limitsare notaffected_byluminousconditions. Thefall-offatlowspatialfrequenciesis due

to _{lateral inhibition} _in _the_{retina, i.e.} _lateral _{connections made}

byhorizontal and amacrine

cells (a kind of a unipolar nerve _cell) result in a reduction ofthe signal froma cell when

the _neighboring cells are illuminated (Netravali and _Haskell, 1988). Figure 3-2

(Cornsweet, 1970) represents the retinal state when a subjectlooksat a point of light.

Rotation (optical spread)

[image:45.530.145.376.211.450.2]

Retinal location(minutesof_arc)

Figure 3-2 The EffectsofaPointofLightontheVisual System

(TheVisual Point-spread_Function)_{(Cornsweet, 1970)}

The resulting spread of light from aberrations, diffraction, scatter in the _retina, etc. _,

results in a light distribution onthe retina represented _by the curve labeled _{"excitation",}

whilethe_{resulting inhibition (which} depends uponthedistribution of_light) contributes

(46)

Therefore this kind of _decrease _{may be} affected _by _{noisy viewing} conditions. The

increased excitationdue tonoise canleadto a reduction oftheeffect of cell inhibition for

low _frequency _signals, which suggests that the CSF is a lowpass filter rather than a

bandpass one _(Mitsa, etal, 1993). Limb's experiments₍₁₉₇₉₎to evaluateimage_quality

supportthisidea.

Further, wecan also address this issue from another viewpoint. Ifthe HVS has a

bandpass_nature, thevisual model exhibits a reduced response to low spatial frequencies.

As a _{result, the}_{low-frequency}error could bemore_easilyintroducedto _halftoning images

thanwiththemodelderived from lowpass filter. _However,what appears as_{low-frequency}

error at one _viewing distance is _{higher-frequency} error at a larger viewing distance,

possibly occurringwheretheluminanceresponseofthehumanvieweris largest. _Thus, the

use ofthe bandpass model causes _halftoning to be sensitive to _{viewing distance. If}the

nature oftheHVSisconsideredto be_lowpass, thespectral_energyofperceived signal will

tend todecrease_{monotonically}withincreasingfrequency. Therefore, theperceived_quality

of the halftoned image will increase _steadily with increased _viewing distance, which

conformswith practical situations. Hence,thefactthat theeyeisnot sensitiveto_{very low}

frequencies does not have to beused. From this _discussion, we could conclude that it is

thelowpasscharacteristicoftheeyethatallows_halftoningtowork.

Based onthis_discussion, equation_(3-3)_maybemodified asthefollowing:

J2.6(0.0192+1.145_fr)exp( -( 1.114fr)1]), fr2>f

^

(47)

where_f^isthe_frequencythatcorrespondsthemaximum value ofH(Q.

\

E

<05- 1"-e

OS

03-\.

e.*79 111316tt20222527293l3<362e4245474S5<55S5B6063E66rEB

SpatialFrequency(cydeMegree)

Fig3-3 Modified Contrast_SensitivityFunction

Another important fact is that the human eye is more sensitive to horizontal or

vertical sinusoidal patterns than to diagonal ones. _{Specifically,} it is least sensitive to

sinusoids oriented at _45, with the _{difference in sensitivity} _being about 0.6 dB at 10

cycles/degree and about3 dB at30cycles/degree. Itisclearthat the two-dimensional CSF

is a function ofthe _viewing angle. _{By Daly (Sullivan,} et_al, _1993), the radial _frequency

willbenormalizedbyanangulardependentfunction, _s(9[Lj]) , suchthat

fliJ]=

^T^

(3"5)

s(Q[i,jD

where: s(0[i,jTj=

ii^cos(40[i,j])

+

^^-

_(3-6)

e[i,j]=arctan(

-) (3-7)

(48)

3.1.3. Extraction ofDiscrete Visual Blur Filter

In practical digital _modeling _{applications,} a finite impulse response (FIR) visual

filter is employed. In_fact, the response ofhumaneyeto one image_may connectwith the

perception to the former images. _But, FIR is _inherently stable; in addition, the finite

wordlength ofinfinite impulseresponse_(IIR) is complicated. The finitewordlength refers

to thefiniterepresentationofthecoefficients and componentsforaIIR. Forthe_halftoning

techniques discussedin thelater chapters, a discrete-spacemodel ofthe _folowingform is

required:

p[i,j]=WIN(d[k,l]) (3-8)

where_d[k,l] are samples oftheinput_image, the_p[i,j] isthe set ofvisualfilter _outputs, and

WIN(.) is some sliding-windowfunctionk= _i

-m, ..., i + m and1 =

j

-m, ...,j+m (m is a

non-negative integer). Fromequation(3-8),we_have,

p[ij] =

vis[i,j]*d[i,j] (3-9)

where _vis[i,j] is an eye filter in spatial domain and * denotes convolution. _Clearly, our

purpose is to obtain an expression for the impulse filter ofhuman eye which has finite

support.

The CSF can be represented inthe space domainby a linear shift-invariant filter.

(49)

kindof error excitesthisfilter. TheCSFitselfspecifies _onlytheamplitude spectrumofthe

filter; to _uniquely determine the filter we assume that it introduces no spatial phase

variation. _{The spacing between}_the _adjacent_discrete _frequencycomponents is determined

by the _sampling _frequency in the spatial domain. _{The sampling} in the spatial domain is

already determinedby the _printingresolution R _(dpi) (not the printer _resolution) and the

viewdistance. Figure3-4 shows the _geometry for _converting _frequencyunits. Assume

Figure 3-4 The_Geometryfor_Converting_FrequencyUnit from

cycles/inchestocycles/degree(Lin, ₁₉₉₃₎

that thesamplenumberisN, andthat the_frequencyinterval space ofCSFis Af = _R/N.

Whenthe_viewing distanceis dmm, ,thespatialfrequency f[i,j] incycles/mmisrelatedto

theangularfrequency fr[i,j] incycles/degree:

fr[i,j] =

2dtan(0.5)fli,j] (3-10)

The_frequencyintheverticaldirectionis

fr[i,j] =_k_Af

x 2d_tan(0.5)=₂_k_d_R/N

(50)

The_frequencyinthehorizontal direction is

fr[i,j] =_{1 Af}

x2d_tan(0.5)=₂

1 dR/N_tan(0.5) _(3-12)

where k and1referto the[k,l]-thcomponentinthe_frequencydomain.

From the transformed human visual model in the spatial _domain, we can extract

the desired filter. Fora practical_calculation, weconstruct afilterof size of5 x 5 or 7 x 7 that will capture the central character ofthe CSF filter in spatial domain. Figure 3-5 is typicalimpulseresponse ofthe CSF of

Mannos'

model(Mannos and _Sakrison, ₁₉₇₄₎for the_printingresolution of300dpi.

* 1

<L1

f* _o

VerticalDistance (1/18 mm)

Horizontal_{Distance (1/18 mm)}

(51)

The CSF filter can be applied to the error diffusioncalculation to minimize some

artifacts. Two such methods are the visual error diffusion _(Sullivan, et _al, ₁₉₉₃₎ and

visual-basederror diffusion developed inthis thesis. Thesealgorithms are discussedinthe

laterchapters.

3.2. Printer Model

Printers have _manyeffects on the_resultingimages. Themost visibleeffect _maybe

the distortion ofthe output _gray levels. The purpose of a printer model is to predict the

gray levels (luminance) produced _by a printerto compensatefor suchdistortion. Agood

printer model requires that some important factors _affectingthe behavior of printers be

understood.

The function of a printeris to _lay down black ink dots at designated locations on

paper; the locations usually are specified _by a Cartesian grid. There exist two types of

printers: write-black and write-_white. _This _thesis deals

only withthe write-black printer.

Thereare_manyreasons connectedwiththedistortionof_gray_levels, suchasthe_spreading

ofthelaser_beam, interaction ofthe laserandthe charge applied to the _drum, thetype of

toner particlesused, andthe heat finishing. Some otherfactors that affect a printed image

arethe_qualityandthe typeof paperused, theinteraction between inkand paper etc. The

discussionaboutthesefactors isbeyondthe scopeofthethesis.

"Dot overlap"

is an important cause ofthe distortion _{in gray} levels. Figure 3-6

showsmeasurementsofthedotarea ofprinter output vs. the_printingresolutionfortheTI

(52)

resolution used in image _processing software packages such as Adobe Photoshop. The

target imagesarecheckerboard patternpatches(50% black area and50%white area). The

dot areas of printed patches with different _printing resolution were measured with a

PlateMaster made _by Beta Industries. The PlateMaster is a black and white reflection

densitometerwith uniquecapabilities. Itnot _onlymeasures alltypes oflithographic plates,

with either conventional or stochastic halftone _images, but also measures conventional

photographic and print materials. The simple instrument first measuresthe reflectance of

the printed patches andthen _{automatically} converts itto dot area percentage. This graph

reflects the gray-level distortion exhibited _by printed images. The ideal dot-area

percentage should remainunchanged at 50%. The gray-leveldistortion isthecombination

of dot _overlap, interaction among light, ink, and paper etc. The graph illustrates that

different printers _mayhave different degree of

"dot-overlap"

andthe dot-area percentage

increaseswiththeincreaseofthe_printingresolution.

o

Q

-+ TIMICO 600dpi Printer

HP LJ IV600dpiPrinter

1 50 200

PrintingResolution

(53)

Now, we face the issue of_constructing a proper model ofthe printer. For the

specific _printer,theperfect model should _completelyoffsettheeffect ofprinterdistortion.

However, this result cannot be easily achieved because of various practical limitations.

Generally, two kinds oftechniques are usedto build a printer model. The first one relies

on the mathematical formulation of the physical behavior of printers. The second is

through practical measurement for printed images and construction ofthe _look-up table.

Two methods for_using a printer modelin the halftone process: one approach is the

so-called precompensation method for modifying the input level through _look-up tables

before halftoning. This method is _{computationally} efficient. _However, for different

algorithms, the look-up tables built from the practical measurement are different. For

example, the dispersed-dot _screening and error diffusion exhibit the different degrees of

gray-level distortionandhencerequiredifferent_look-uptables. These_look-up tablesmust

be pre-stored in printers and require a lot of memory. The other is to incorporate the

printermodelintothe available algorithmthatcan be formedanintegrated algorithm. The

method causes the computation tobe more _complicated, but is easier to implementwith

simple printer parameters. In this thesis, we will _employ the first technique to build a

printermodel andthesecondapproachtousethemodel.

3.2.1 Circular_Dot-OverlapModel

This kind of model was developed _by Pappas and Neuhoff(1991), who modeled

(54)

that affect them. In this _model, each ink spot is assumed to be circular with a uniform

distributionof ink.

Inthe_following _description, we introduce some notation. Abinary image b[i,j] is

printed, if_b[i,j]=

0.0 _(black);no spot isprintedif_b[i,j] = _1.0 _{(white). As}

a result ofprinter

distortions, the_{gray level}_p[i,j] produced inthe_vicinity depends insome complicated _way

on_b[i,j] andthe_neighboringpixel values. Theprinter modeltakes theform:

p[i,j]=P(WIN[i,j]) (3-13)

where_WIN[i,j] isthefiniteneighborhood of values of_b[i,j] anditsneighbors(Figure 3-7).

Thisisthemost generalformoftheprintermodel of PappasandNeuhoff.

As illustrated in Figure _3-7, printers produce ink spots on a Cartesian grid with

horizontal and vertical _{spacing T. The} reciprocal of T is referred to as the printer

resolutionand_usuallyis measuredin dotsperinch. Idealrectangulardots produced _by a

printerareT x T. Theradius ofideal circularinkspots produced _byrealistic printers is at

least -j=, so theycover an area ofsize = n r

= _T _{(Figure 3-7).} _The

circular spot of

V2 2

radius with -j= is 57% larger than a T x T square. Neighboring black dots overlap V2

horizontallyand_vertically, butnot _diagonally andwhite dotsare darkened _by_neighboring

black dots. We will use _pto denotethe ratio ofthe actual dot radius to the ideal circular

dot radius -j= _ofthe _printer. The effective_{gray level} of a printed pixel is assumedto be V2

(55)

then theeffective _graylevel of all 2-D patterns canbepredicted_by_calculatingthe area of

each pixelthatiscovered_byink.

ideal dot idealcirculardot actualdot

window_W[i,j] _p[i,j]*_b[ij\(=₁

.0white)

Figure3-7 DotsandTheir Radius

[image:55.530.51.381.117.360.2]

(56)

The amount of _{ink spreading} at each pixel can be expressed in terms of the

parameters_a, _P, and _y, showninFigure 3-8. Theseparameters arethe ratios ofthe areas

oftheshaded regionsto_T2, the area ofthepixel. _Theycan_easilybeexpressedinterms of

theradius ratio_p andtheradius r(Pappasand_Neuhoff, 1991 and 1995):

P[ij]=p(wiN[i,j]

)={1-(p>a+

p>p-P3*)> lfb^J] =

10(whlte)'

[0.0, ifb[i,j] = _0.0

(black);

(3-10)

where r is the radius of an actual circular dot and _pi-p3 are the number ofblack pixels

within a3 x 3 window(Figure_3-7)_bygeometricdistribution. _p[i,j] isthe current pixel, _pi

is the number of _horizontally and _{vertically neighboring} dots that are _black, _p2 is the

number of_diagonally_neighboringdotsthat areblackand not adjacent to _any _horizontally

or_vertically_neighboringblack_dot, and_p3isthenumber of pairs of_neighboringblack dots

inwhich oneis ahorizontal neighborandtheotherisaverticalneighbor. Forthe situation

inFigure_3-7,pi is 1, p2is 1 and_p3is0. Theparameters_a, _P,and_y aredeterminedfrom:

a^V^+

^sin-^-i

_(3-11)

3=^_^sin-i(

1

)-IV27^T+

-(3-12)

8 2

\[2r

^ 4

-2 J2.

(57)

Figure 3-9 shows a specific ideal dot pattern. Figure 3-10 illustrates the practical

gray levelafter we consider_{dot overlap}withthecircular_dot-overlap model.

s

'pixel

Figure 3-9 Ideal Dotwithout_Dot-overlap

Now, the practical _{gray level} of each pixel is no longer _binary, but rather one of

nine values. For a checkerboard _patterns,the _gray valueof each white pixel _actuallyis

(l-(4a-4y)), rather than 0. This

Visual-Based error diffusion for printers

Rochester Institute of Technology

Visual-Based Error Diffusion for Printers

ROCHESTER INSTITUTE OF TECHNOLOGY

CERTIFICATE OF APPROVAL

THESIS RELEASE PERMISSION FORM

ABSTRACT

ACKNOWLEDGMENTS

CONTENTS

Halftoning

Screening

Halftoning

Summary

ii^cos(40[i,j])