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Digital halftoning of images

Dimitris Anastassiou Keith S. Pennington

Digital Halftoningof Images

Most printers and some display devices bilevel (black or white) are and therefore not capable of reproducing continuous tone pictures. Digital halftoning algorithms transform digital gray scale images into bilevel ones which give the appearance of containing various shades of gray. A halftoning algorithm is presented in which novel concepts are combined resulting in an output image in which moirk patterns are suppressed and,at the same time, the edges are enhanced. Various other artifacts associated with the halftoning process, such as contouring due to coarse quantization or to textural changes, are also absent from the output images in the proposed scheme. The algorithm separates the image into many small clusters which are processed independently and, therefore, it is capable of parallel implementation.

1. Introduction Many displays and most printing technologies employ bilevel modulation techniques for image reproduction or recording. Examplesinclude offset lithographyandrelatedgraphics arts recording techniques. These processes employ classical screened halftone dot recording procedures whereby the size and the areal density of recorded dots is variedin direct proportion to the local gray tone values present in the original image. There are, however, many image technologies, such as liquid crystal and gas panel displays, as well as ink jet, wire matrix, and laser scanned electrophotographic printers, which employ bilevel recording techniques in which the recorded dot size is fixed. Thisconstrainthas led to the development of several image processing techniques whose major goal has been to eliminate spurious and distracting artifacts which arise during the scanning and digital halftone reproduction of various image types, e.g., continuous tone, graphics, and pre-halftoned images. Some of the techniques employed for reproduction of various types of images with binary printers are described in [ 1, 21.

[3]. Similarly, the optimization problem is intractable. For these reasons, we have not used such mathematical approaches in this work.
Many digital halftoning algorithms have been developed for use with image presentation on binary printers/displays [ 1 , 2,4-91. The most widely known and used algorithms are usually separated into two classes, (1) “ordered dither” and (2) “error diffusion.” However, in any specific implementation of digitalhalftoningalgorithmsthere is atrade-off between computational complexity and perceived image quality. The use of digital halftoning techniques often leads to a considerable reduction in perceived image quality. Further, measuresthataretakento alleviate one or more image degrading factors often lead to an enhancement of another problem. However, the major image quality trade-off with digital halftoning is between achieving an acceptable reproduction of gray tone image values in large areas (i.e., low spatial frequency rendition) and maintaining edge and similar high resolution information. If, for example, the image raster divided into 3 x 3 pixel is blocks and the dotsinside these blocks are arranged according to the gray tone values, then there are only 10 possible

The central problem associated with the reproduction of gray tone images on a binary printer/display device can be x(i, stated asfollows: Given original intensity values j ) , find a bilevel image y(i, j ) such that d ( x . y )is minimized, where d ( x , yis a predefined distortion measure. The choice of an ) appropriate distortion measure is as yet an unsolved problem

Copyright 1982 by International Business Machines Corporation. Copying in printed form for private use is permitted without payment of royalty provided that (1) each reproduction is done without alteration and (2) the Journal reference and IBM copyright notice are included on the first page. The title and abstract, but other portions, of this paper may be no copied or distributed royalty free without further permission by computer-based and other information-service systems. Permission to republish any other portion of this paper must be obtained from the Editor.



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are met, one can employ digital halftoning algorithms which interpolate between the neighboring low resolution continuous tone image pixels. In this paper we introduce a digital halftoning algorithm based upon the use of a nonlinear edge enhancement operator, loosely referred to as a nonlinear Laplacian, NL. This operator is combined with an 18-pixel digital halftone block size and a five-level print prioritizationmethod which is derived from an understanding of the mechanisms for, and appearance of, noise in digital halftone reproductions. This algorithm has successfully reproduced general images with good visual quality, in most cases devoid of themajor distracting artifacts that have been associated with previous digitalhalftoningalgorithms.Ourimagequalitycriteria have been based on subjective evaluations of such factors as edge sharpness and the absenceof various artifacts, such as moiri: patterns and artificial contours, as explained in detail in Section 2. We intentionally avoided applying a preprocessing recognition scheme that would first separate the image intoits variousregions (e.g., continuous tone, line copy, halftone) prior toapplying specialpurposethresholdinghalftoning techniques in each region of theimage. Our algorithm is inherently capable of efficient parallel implementation, since it separates the image into small areas each of which is processed independently of other areas. Unlike other algorithms with this property, however, it has features which suppress annoying "digital halftone" patterns in continuous tone areas while at the same time retaining good resolution and quality in fine text areas.
A brief description of image quality problems that arise when using bilevel output printers/displays is given in Section 2. In Section 3 we give a brief survey of themore familiar digital halftoning algorithms, while Sections 4-6 describe the novel features associated with our digital halftoningalgorithm;the final section containsexperimental results and conclusions.


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Figure 1 Original test image.

gray tones in the output image. Increasing the size of the blocks allows more tone gray values to reproduced. be However, as larger digital halftoneblocks are used, arranging the dots on the basis of local gray tone values alone reduces image resolution. Theresultantimage,therefore, appears more defocused. The decrease in resolution is linearly related to the increase block size unless measures in are taken to fill the halftone blocks on the basis of factors other than local gray tonevalues alone. The most significant problems associated with digital halftoning of images fall into two major categories. First, there is a loss of resolution, which manifestsitself as an inability to reproduce sharp and continuous edges, such as occur in line copy andgraphics images. Second,digital halftoning techniques often result in "pattern noise" in the reproduced image.Thesepatterns mostoften arisefrom either ( 1 ) aliasingerrors, which occurduringtheimage scanning and thresholding procedures (moiri: patterns), or (2) digital halftone patterns, which result from the applicahalftoning algorithm (e.g., ordered tion of a particular dither). Throughout this paper assume, without loss of generalwe ity, that the resolution of an original gray tone image and its bilevel reproduction are identical. However, resolution of a bilevel rendition of an image mustbe much higher than that of the original continuous tone image it is to have the same if visual effect. When such "high resolution" printing criteria

All examples shown in this paperhave beenprinted using a high quality photocomposer (APS5), which is installed in the IBM Thomas J. WatsonResearchCenter.Theprinting resolution is 200 dots/inch. Figure 1 shows the portion of the IEEE facsimile test chart which was used for the experiments described in this paper. It was intentionally chosen since it contained separate fine text, continuous tone, and halftone image regions. Although the imagewas scanned a t 200 pixels/inch, due to scannerimperfections the quality of the input data that we used is lower thanother existing scanned versions at the same resolution.

2. Quality problems in digital halftoning As mentioned above, halftoning techniques in general, and
digital halftoning techniques in particular, sacrifice resolu-



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tion in order to have a limited gray tonerendition capability. However, the problem associated with arriving at a suitable “designpoint”for thenumber of discernablegray tones versus resolvable detail in theimage is only one of the problems. Other major factors associated with bilevel recording techniques, which require attention if severe degradation of the reproduced images is to be avoided, can be summarized as follows:
Edge enhancement Techniques that employ edge enhancement are particularly desirable for improving imagequality in areas of high resolution, such as sharp continuous edges (e.g.,text characters). In such regions it would be advantageous if the bilevel printing algorithm were not solely dependent upon methods for reproducing adequate graytones but could also produce a compact setof printed pixels distributed along the edges and boundaries in the image. This need is particularly pronounced in cases where the scanned image contains very thin text or graphics on a very light background.Under such circumstances the recorded gray level values may not be enough for the printing algorithm to justify a solid set of black dots. Of course, this would tend to result in illegible characters and poorly defined graphics. In these cases it is desirable to enhance edges the image despite the gray in low level values. This results in overall increased legibility and enhanced image quality. Coarse quantization contouring This problem arises as a result of the constraints applied in using a halftoning algorithm. In general the digital halftoning algorithms which are used in image reproduction separatetheimageintosmall N-pixel blocks. Thisapproach allows only a limited number ( N + 1) of gray levels to be reproduced.Underthesecircumstancesfalseimage contours, due to coarse quantization, can ensue number N if the is not large enough to adequately represent the tonal range of the image. False contours, due to the small value of N, are very visible in Fig. 2, which shows the reproduction of a low resolution image with N = 8-pixel blocks. In this image the %pixel blocks are arranged diagonally, and the black dots are clustered in the middle of each block. It should be noted that this artifact does not always appear together with the contouring described more general problem of textural below.

cases, a slight variation of the gray level in smooth areas often results in the formation of an artificial contour, simply because the dot pattern (texture) has been changed locally. Textural contouring be can observed in Figs. 3 and 4. Experience would lead us to conclude that, among all possible digital halftoning textures that can generated, the one be that most closely resembles analog halftoning (variable size dotsarranged in a diagonalgrid) is probably the least annoying.

Moirt patterns This image degrading process is observed when the “high” spatial frequencyat which the imageis sampled anda strong spatial frequency component of the original image differ by a relatively small value. Under these circumstances very distracting low frequency beats, or rnoirC patterns, occur in the output image asa result of the “beating” between these two A theoretical treatment of high frequency components. moirC patterns is presented in [ 101. Thesepatternsare typically present, and particularly annoying, when the original scanned image contains areas which are already halftoned. In this case theoriginal halftoning frequency provides Textural contouring the high frequency component which “beats” with the samThis particular bilevel image reproductionproblem manipling frequency. (Figures 3, 6, 8, and 11 show examples of fests itself in theform of relatively regularpatterns of this moirC phenomenon.) halftone dots distributed throughout the image. The form the patternstake is inherent in the halftone processingalgo3. Brief survey of existing approaches rithm; however, they areparticularlyannoying when the Among the various digital halftoningtechniques, that known algorithm forces thedotstobedistributed inaperiodic as “ordered dither” is one of the simplest. In this technique pattern in areas of the image which are smooth. In such



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Testimageprocessed by errordiffusion.


the scanned image is thresholded with a set of periodically changing thresholds [ l , 2, 4, 51. The spatial configuration of these thresholds can be chosen so that the resulting digital halftone approximates the diagonal dot pattern of analog halftone recording, which has been found to be most pleasing to the eye. However, this approach often leads to a loss in resolution or detail in the reproduced image. Alternatively, the threshold configuration can be chosen to maximize the high spatial frequency content of the output image [4]; this approach, however, canenhancethetexturaland moirC pattern defects in the reproduced image. In Fig. 3 we show the bilevel output of our test image using the ordered dither threshold configuration proposed by Bayer [4]. A significant advantage of theordereddithertechniques is thatthe thresholding can be done in parallelsincethe threshold values are all preassigned. Another frequently used approach to digital halftoning is known as “error diffusion,” originally described in [6]. Reference [8] presents a combination of error diffusion with a correction algorithm for circular dot overlap. The output quality achieved with this approachis higher than that the of ordered dither technique. The underlying principle of error diffusion is to diffuse the errors that occur when thresholding any given image pixel among closely neighboring pixels. A “corrected” intensity value is calculated for any pixel as it is to be processed by adding to its actual intensity value a weighted average of the errors that occurred aas result of the

bilevel printing of several of its neighboring pixels. This error-corrected value is compared to a constant threshold to yield a black/white decision, and the error resulting from this latterthresholding operation is then alsodiffused among the neighboring pixels which are subsequently printed.
Error diffusion results in the dots being more randomly and evenly distributed. As a result of this randomization, the reproduced images are substantially pattern-free. Figure 4 shows the output of the test image using error diffusion with a neighborhood of six pixels; we see that, despite its many advantages, there are distracting artifacts associated with error diffusion. For instance, unless the errorneighborhood is sufficiently large, thebilevel image tends to have a “wormy” appearance in smooth areas, and there is also considerable difficulty in the rendition of sharp edges and fine text.

One of the potential disadvantages of using theerror diffusion approach is that it requires a serial implementation (ix., the image pixels are processed in sequence), and the thresholding of each pixel requires significant computation. Various halftoning schemes [ 1 , 21 similarto butnot identical with ordereddither have featuresthat improve overall performance. Among these techniques is a particularly interesting one reported by J. White [7]. This method separates the image into 8-pixel blocks arranged diagonally so that the number (from 0 to 8) of black dots inside each




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block is determined by the gray tone of the original image. These dots are arranged in clustering order to imitate the effect of analog halftoning. The resulting image is a “defocused,” or low resolution, image in the sense that high spatial frequency information is lost. Some dither can be added to the 8-pixel blocks in order to increase the apparent capability of the technique for reproducing gray tone values from 9 to 33 levels. The high frequency detail in this defocused image can beimproved, as shown in [ 7 ] , by further processing of the image asfollows:
A Laplacian operator is applied to the image, and the resultant image is then separated into three pixel classes, namely, those with high, those with intermediate, and those with low values of the Laplacian. This tri-level Laplacian operation is basically an edge extraction process, and the resultant image contains most of the high frequency details of the original image. Thehigh (low) valuesof this Laplacian focused imagearethen used to override, or force, the thresholding decisions in the defocused image so as to print white (black) pixels. The outputof the algorithmis basically the superposition of two images, namely, a focused and a defocused image, in the sense that thepixels with high (low) values of the Laplacian have their gray scale or defocused thresholding decisions overridden in favor of white (black).

Figure 5 Separation of raster into IS-pixel blocks.

the identical area of the original image. Theprinted dots are clustered around the center of each block so that the output takes on an appearance similar to that associated with the electronic screening or analog halftoning technique. In [7], the pixel blocks are arranged so that each block contains 8 pixels. The total number of gray levels in the original image that can be reproduced by this size pixel block level) gray values is therefore 9. Dither added to the (higher of the 8-pixel blocks (with period of 2 in both the horizontal and vertical directions) gives the appearance of a 33-level (Le., 4 x 8 + 1) pseudo-gray tone reproduction. Without adding dither, false contours the image (due to the in limited number of gray tones) are very obvious anddistracting. However, although dither improves the appearance of the outputthroughits tendency to delocalize falsecontours, textural contours areoften visible because of the big difference in the shapes of the 9 possible configurations in each 8-pixel block. Figure 2 shows an example of “defocused” image outputwithout additive dither. It is for theabove reasonsthat we chose to divide the image up into larger pixel blocks, each block containing 18 pixels, of the as shown in Fig. 5 . It is interesting to note that the area image cannot be divided into space-filling pixel blocks arranged in diagonal orderwhich contain from9 to 17pixels, hence our choice of 18 pixels per block. It should be noted also that this statement is not contrary to the work demonstrated in [2, Fig. 181, where 17 pixels in a block are addressed for the purpose of displaying gray tones with a binary printer. In this example the printable pixels in each block do not quite cover all the areaof the image because a single whitedotcannotbe addressed and hencealways remains unprocessed, even for totally black regions in the original image. Employing diagonally ordered 18-pixel blocks results in an ability to reproduce 19 gray tones, and the resulting binary

In order to reduce the possibility of the occurrence or enhancement of moirC patterns, this “focused-defocused” image processing algorithm keeps, wherever possible, the number of black (white) pixels in each block equal to thatin the defocused image. However, this condition may not be satisfied in those circumstances where there is not a sufficient number of black (white) pixels inside an 8-pixel block of the defocused image to both force the high (low) Laplacian pixels andalsomaintainthe local graytone value. Finally,for additional moire pattern suppression, 2 x 2 clusters of exclusively black or white dots arenot allowed to occur. Thebinaryimage processing andhalftoningalgorithm presented in this paper is closely related to the work reported in [7]. However, our algorithm has additional features that result in improved overall image quality. These features are described in the following sections together with a comparison with those existing in [7]. 4. 18-pixel neighborhoods In order thatprocessed binary images be capable yielding of a very good rendition of slowly varying tonal areas in the original image, the image is separated into blocks of pixels which are each processed independently. These pixel blocks are distributed along diagonal lines in the image. The number of dots to be printed black within each of these pixel blocks is dependent upon the graylevel values present within

69 1


The binary printing algorithm specifies that, in smooth areas of the image, in order to arrive at the required gray tone value in the printed image, the pixels in each 18-pixel block are printed in a prespecified order, as given in Fig. 6 . Figure 7 shows our test image separated into 18-pixel blocks and thresholded as explained above in "defocused" form.
Figure 6 Defocusedimageusing18-pixelblocks.


. . . .

It should be noted that this process of finding the average gray level inside each 18-pixel block, andthen filling the block in aprespecified order until the correct gray tone value is achieved, is not equivalent to using an image processing technique in which 18 different threshold valuesare assigned to each pixel inside the block. The latter technique [2], a form of ordered dither, oftenresults in areproduction of some of the frequency high information in the image, because local intensity variations inside an 18-pixel block can be detected. For example, a thin dark character stroke has if very low intensity values, chances are that itwill be thresholded black for most (but not all) pixels, while if the background is very light itwill be thresholded white for most of the corresponding pixels. However, this approach results in imperfect rendition of the high resolution detail in the image, and we found it preferable to use more sophisticated techniques in order to reproduce the high resolution detail in the image. These techniques are explained in the following sections. 5. Nonlinear edge enhancement As is understood from the above, one of the most important requirements forhigh a qualitygeneral purpose digital halftoning algorithm is its ability to reproduce sharp, solid, and smooth edges. This must hold true for both well-defined objects and for the text areas of images. A powerful way of achieving this objective, which is at the same time pleasing to the eye, to printa stripe of black dots along the edgesof the is darker object together a neighboring stripe of white dots with around the lighter objects. For thispurpose, it is necessary to use some operator that detects edges so that they can be processed independently. One of the most widely used image processing techniques for edgelocation and enhancementis to operateon the image with the Laplacian operator. For each pixel of a sampled image, application of the Laplacian creates the difference between the intensityvalue at that pixel and an average intensity a in neighborhood surrounding the pixel. The Laplacian, a form of high pass filtering, is a linear operator. Adding the values of the Laplacian to the original image yields an image with enhanced high frequency components. This means, of course, that not only are the edges in the original image enhanced but any high frequency patterns, including noise and texture, are also enhanced. Itshould also be noted that although moire patterns are essentially low

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Figure 7 Order of printing black dots inside a block.

images exhibit very acceptable quality. The advantage of using large pixel blocks is the elimination of false contours. Neighboring gray tone values are sufficiently close to each otherthatthedigitization process doesnot result in the generation of false contours. Adding dither to the 18-pixel blocks further delocalizes and completely eliminates false contours from the reproduced image. At resolutions of 400 pixels/inch the above approach results in excellent renditions of the smooth areas of images. (This is shown in Fig. 13, towhich we refer later.) However, a t a printing resolution of 200 pixels/inch the 18-pixel blocks are very visible but they have a pleasing appearance. The reason that large pixel blocks are notused in the schemes reported in the literatureis the unacceptableloss of resolution that they produce in the "defocused image." In ourapproach, however, this problem is solved by using nonlinear edge enhancement (explained in Section 5).




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frequency entities, they are also enhanced the application by of the Laplacian, as shown in the left columnof Fig. 8. The produces reason for this result is that the Laplacian operator high valuesor enhanced edges at thepositions of the halftone dots in the original image. Thisis equivalent to an increase of theamplitude of the high frequencycomponents in the halftone information. Since the sampling frequency of the image remains the same, this results in an increase in the amplitude or intensity of the detected moirC beat. In the remainder of this section we describe a nonlinear edge enhancement technique which avoids many of these problems. In order to obtain relatively high quality reproduction of a the image with a binary printingprocess it is necessaryto add the high resolution detail in the original image to thebilevel gray tone outputdescribed above. A very convenient way to do this is to partially override thegray level ordering technique, for printing the black dots inside each 18-pixel block, in such a manner that we retain information about image detail within each block. In [7] the operator used to achieve this function is the linear Laplacian. The pixels are separatedintothree priority classes each of which can partially override the preassigned order. This approach has proven to be an excellent way to achieve edge emphasis, but, as explained above, moir6 patterns arealso enhanced by this technique. In order to achieve edge enhancementwhile at the same time suppressing moir6 patterns, we have found it advantageous toapply a new nonlinear operator, NL, to theimage. The operatorIVL is derived by considering the pixel values in a 3 x 3 window centered around each pixel (see Fig. 9) as follows. Using thenotation of Fig. 9 we firstdefine the quantities
1 A=x--(a+c+f+h),

Figure 8 Demonstration of edge enhancement and moire pattern suppression using "nonlinear Laplacian" operator.



Figure 9 Pixel notation for a 3 x 3 window.

The nonlinear Laplacian that we apply to the image is then

NL = O

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= m i n ( ~ Ai~ , ~> O a n d B > O , fA B~) if AB < 0, Therefore, all pixels having a high value of NL will also have a high value of L. The inverse is not true, however. It should be noted that if the value of the central pixel x is approximately equal to the average of its four neighbors in the horizontal, the vertical, or the diagonal direction, then the resultant magnitude NL will be small,even though the of magnitude of L may be high. This operator is found to be very helpful in reducing (but not totally eliminating) moirC patterns when thesampling frequency andthe original halftone frequency are very close to other. each The reason

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priority classes, into which all pixels are divided in a manner similar to that described in 171. The priority class to which to each pixel is assigned is used partially override the printing order assigned on the basis of gray level alone. The priority classes are assigned as follows: Class I contains pixels in which NL < - T, where T is a constant threshold; class I1 contains pixels which satisfy the condition that - T I NL 5 T, and class 111 contains those pixels for which NL > T. There are two ways in which the priority classes can be used todeterminetheorder in which the pixels in the 18-pixel blocks are printed: In the first approach the pixels are printed first by priority classes I to 111, and in each priority class the pixels are printed according to the relative order assigned by the “gray tone” algorithm. In Fig. 10(a) we show an example of this approach to improving image resolution in which the number of pixels inside the 18-pixel block that fall into each priority class is assumed to be 5 , 10, and 3 pixels, respectively. Application of the above criteria then results in the orderin which the pixels are printedbeing modified from that derived from the graylevel values alone, as shown in Fig. 7, to that shown in Fig. 10(b). If the gray level data require that three pixels be printedinside the 18-pixel block, then the configuration of the printed pixels will be asshown in Fig. 1O(c). In the second approach to using the priority classification to determine the order printing for the 18 pixels in a block, of all pixels in class I are printed black and all pixels in class 111 are printed white, regardless of the numberof black or white pixels that are required the 18-pixel block in in order toyield the gray tone values measured in the original image. after If employingthis black/white override featureto pixels in classes I and I11 there is still a need to print more pixels in order to reach the required gray tone value, then pixels in class I1 are printed according to their relative order in the gray tone algorithm. An example approachis shown in of this Fig. 10(d). The formermethod has the disadvantage that it eliminates or degrades fine lines in text whenever the average gray level in an area is so low that it results in the printing of too few black dots to a solid appearance to the text. give This problem is solved if one follows the second approach. Underthesecircumstances, however, moir& patternsare enhanced,as shown in Fig.11, which shows the type of results that accrue from using the features of our algorithm described up tothis point. For reasons these we have developed an additional improvement to the algorithm, as explained in the following section.



Figure 10 Example of pixel order modification due to the priority classes.

for this property is that, in regions such as halftoned areas which are highly susceptible to the generation moirCbeats, of thecheckerboard configuration of light anddark pixels results in avalue of NL which iszero due to the large directional dependence of the values of A and B. The nonlinear Laplacian, therefore, tends not to enhance moirt beats in these areas. However, the value NL approximates that of the linear Laplacianin other regions of the image. It should, however, be noted thatthevalue of thelinear Laplacian, L, will not tend to be zero in halftoned regions of the image. In Fig. 8, we demonstrate the moirt suppression that can result from using the nonlinear Laplacian N L as the edge enhancement algorithm instead of the Laplacian L. The left four image segments are enlarged versions of the L function thresholded with four different thresholds, while the right four image segments are the corresponding images using the NL function. The image segment chosen is an original analog halftone. The annoying moirt patterns present in the left column of imagesare suppressed those in in theright column. Of course, our definition of NL above is not unique, and according to the spatial frequencies of both the halftone and image sampling frequencies, one might obtain better results for moirt suppression by defining NL to be the minimum of more terms. For instance, NL could also take into account a larger numberof pixels situated at greater distances from the central pixel. In all circumstances the use of NL tends to reduce moirC beats while also resultingin edge enhancement in non-halftoned regions of the image. Following the application of our nonlinear operator, NL, the values of the nonlinear operatorare used to define three




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6. Priority assignments In order to further suppress moirC patterns, while at the same time retaininga good solid rendition of fine text and superior rendition of smooth areas, we haveapplied the following algorithmic technique: Some of the pixels, which according tothe above classification fall intoeitherthe highest or lowest priority classification, have their priority black/white print override classification reduced according to a strategy described later in this section. The basic result of this additionalstrategy is toincreasethenumber of priority classes which ensue from theuse of the nonlinear Laplacian operator from three to five. In this new priority classification approach, the intermediate priority class 111 plays the same role as class 11 in the earlier method described above. The decisions as to how to print each pixel in the 18-pixel blocks are then made using the following logic:
The highest (class I) and lowest (class V) priority pixels are always printed with blackandwhitedots, respectively, even if this overrides the computed total number of black dots necessary to accurately print the measured gray tonevalue. The remaining three priority classes modify the original gray tone prespecified printing order for the 18 pixels so that every pixel in a higher priority class is considered for printing before any consideration is given to pixels of lower priority classes. The process of printing black dots is continued until the correct number black dotsrequired of to attain the measured gray tone is reached. value The reduction of the priority class of certain pixels is directly aimed at suppressing moirtbeats in the printed image. Those pixels whose priority is reduced from class I to class 11 or from class V to class IV are those thatare arranged in spatial configurations which are most often associated with the appearanceof moirt beats in the image. These are the high-NL pixels which are clusteredin blocks of dimension either 2 x 2 or 2 x 1. The reason that clusters of pixels with high valued Laplaciansaremore likely to occur in regionsassociatedwith moirC patternsthan in regionsassociated with real edge information is that real edges have alinear spatialconfiguration (along the edge),while aliasing tendsto create dispersed or clusteredhigh Laplacian pixels. Therefore, sharp elongated edges in the image create a strip of high Laplacian values with a width of one or two pixels and a relatively large length. However, moirt beats, between an original halftone frequency and a sampling frequency, which have been enhanced with a Laplacian operator,usually result in a set of small clusters. It should be noted thatthe correspondingmethodfor suppressing moirt beats, as described in [7], is based upon

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completely disregarding either high or low Laplacian values when they are associated with pixel clusters which entirely cover a 2 x 2 block of pixels. This method is based upon the spatial configuration of pixels and the values of their Laplacians rather than their"nonlinear Laplacians," as described above. Ifall pixels in a 2 x 2 block have high Laplacian values, then they will be treated as if they did not have high Laplacian values. This techniquedefinitely tends tosuppress moirt beats in the printed output; however, there is a high risk that in totally removing priority assignment realedge the information will be lost and result in an otherwise unacceptable reduction in the qualityof the image. The in quality loss is particularly detrimental in those cases where the pixels actually belong to thereal edges of a text character. The novelty of the binary printing algorithm described in this paperis that instead of disregarding high or low "nonlinearLaplacian" values if theyare associated with pixel clusters, we simply reduce the priority of these pixels and in doing so we retain some of the necessary edge information. Pixels inside high NL value clusters will not have a forced black/white override but will simply have a priority higher than pixels with a low magnitude of the nonlinear Laplacian, NL. As described earlier, the use of the nonlinear Laplacian alone tends to deemphasize the appearance of moirt patterns. However, this final step of reducing the priority associated with pixels in high NL clusters has the significant effect that it almost entirely suppresses the appearance of



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moir6 patterns while minimizing image quality degradation in the neighborhood of edges and general text. In Fig. 12 we show the final output imageprocessed by our scheme using all five priority classes.
7. Results and conclusions Optimum selection of a general purpose digital halftoning algorithm is often difficult. Severalalgorithms have been described in the literaturewhich perform satisfactorily under particular well-defined conditions. For example, errordiffusion-like schemes have an excellent capability of suppressing moirC patterns and are therefore very appropriate for use when processing original halftoned images. However, the use of these algorithms is inappropriate if the original image consists primarily of text and linecopy images.

ted these image-degrading factors and presented an imageprocessing algorithm which contains many features that are required in a robust, high quality digital halftoning algorithm. If a high implementation complexity is unacceptable in a particular application, it is possible to use just one or more of the featuresof this algorithmin order toimprove the output quality and still retain the capability for a parallel hardware implementation. The algorithm we have presented is also suitable for use in situations where the resolution of the printer is higher than that of the scanned image. As might be expected the image quality in such cases is improved even further and in many cases can be rated as excellent. Figure 13 shows the output obtained using our printing algorithmwith a printing resolution twice that of the original scanned image. For the determination of thisexampleeach pixel of the original scanned image was replaced by a 2 x 2 block of pixels with all the same gray tonevalues. This example is indicative of the quality that can be obtained using our entiredigital halftoning algorithm which, of course, includesbasic a 18-pixel digital halftone block. However, if the image had been calculated and printed with an algorithm which used 8-pixel digital halftone blocks, the image would have contained distinct false contours. In conclusion we have described a digital halftoning algorithm which is amenabletoparallelimplementation

Likewise, ordered dither, using either Bayer's or the "supercircle" threshold selection techniques, provides a very simple method of digital halftoningwhich is also suitable for use with certain kinds of pictures. While these techniques were also seen to have disadvantages, itshould be noted that at sufficiently high printing resolution adequate results can often be obtained with this method. For general purpose high quality digital halftoning, however, each of the available algorithmic approaches has been demonstrated to possess drawbacks. This paper has delinea-




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while a t thesametime minimizing virtuallyall of the image-degrading artifacts which have been shown to occur with the use of otherstate of theartdigitalhalftoning algorithms. Acknowledgments Appreciation is expressed to J. White for providing image data as well as for many helpful discussions. Also, we thank the anonymousreferees for their comments. References
1 . J. F. Jarvis, C. N. Judice, and W. H. Ninke,

Received March 25, 1982; revised June16, 1982

2. 3. 4. 5. 6. 7.



“A Survey of Techniques for the Display of Continuous Tone Pictures on Bilevel Displays,” Computer Graph.& Image Process. 5,13-40 (1976). J. C. Stoffel and J. F. Moreland,“A Survey of Electronic Techniques for Pictorial Image Reproduction,” IEEE Trans. Commun. COM-29, 1898-1924 (December 1981). J. Mannos and D. J. Sakrison, “TheEffects of a Visual Fidelity Criterion on the Encoding of Images,” IEEE Trans. Info. Theory IT-ZO,525-536 (July 1974). B. E. Bayer, “An Optimum Method for Two-Level Rendition of Continuous Tone Pictures,” Proceedings ofthe IEEE International Conference on Communications, 1973, pp. 11-15, P. Stucki,“Image Processing for Document Reproduction,” Research Report RZ 983. IBM Research Laboratory, Zurich, Switzerland, 1979. R. Floyd and L. Steinberg, “An Adaptive Algorithm for Spatial Gray Scale, SID Digest 36 (1975). J. M. White, “RecentAdvances in Thresholding Techniques for Facsimile,” J. Appl. Photog. Eng. 6,49-57 (June 1980). P. Stucki, “MECCA-A Multiple-Error Correction Computation Algorithm for Bilevel Image Hardcopy Reproduction,” Research Report RZ 1060, IBM Research Laboratory, Zurich, Switzerland, 1981, K. Wong and P. Stucki, “Adaptive Switching of Dispersed and Clustered Halftone Patterns for Bilevel Image Rendition,” Research Report RJ 2020. IBM Research Laboratory,San Jose, CA, 1977. A. Steinbach and K. Y . Wong, “An Understanding of Moirt Patterns in the Reproduction of Halftone Images,” Research Report RJ 2494, IBM Research Laboratory,San Jose, CA, 1979.

IBM Research Division. P.O. Box 218, Yorktown Heights, New York 10598. Dr. Anastassiou received the Diploma in electrical engineering from the National Technical University of Athens, Greece, in 1974. He then received the M S . and Ph.D. degrees in electrical engineering from the University of California, Berkeley, in 1975 and 1979. Since 1978, he has been working at the Thomas J. Watson Research Center as a research staff member on teleconferencing system development.
Dimitris Anastassiou

IBMResearch Division, P.O. Box 218, Yorktown Heights, New York 10598. Dr. Pennington is the manager of the Image Technologies Department at the Thomas J. Watson Research Center. graduated He with a B.Sc. in physics from Birmingham University, England, in 1957 and a Ph.D. in physics from McMaster University, Canada, in 1961. He started his research career at Bell Telephone Laboratories, Murray Hill, New Jersey, where he developed the first multicolor holograms while doing early work in holographic interferometry and optical information processing. He joined IBM Research in 1967 and subsequently made several leading contributions to the development of improved holographic materials and techniques for three-dimensional scene analysis. He was appointed manager of the exploratory terminal technologies group in 1972 and in this position he has made significant contributions to thedevelopment of new printing technologies. Dr. Pennington was promoted to his present position with the Image Technologies Department in 1979 and has responsibility for several non-coded information-related research projects including projects related to teleconferencing, document scanning, and novel printing processes. Dr. Pennington has received two IBM Outstanding Contribution Awards and one 1BM Outstanding Innovation Award. Dr. Pennington is a member of the Instituteof Electrical and Electronics Engineers and the Optical Society of America.
Keith S. Pennington





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