Andrey Schadenko, Yuri Kuznetsov
North-West Institute of Printing of the St. Petersburg State University of Technology and Design
13, Jambula Lane, Saint Petersburg, Russia, 191180
Fine detail distortion by the halftone dots is investigated with taking into account the quantization errors accompanying the image tone measure spatial dispersion in screening process. The number of these errors correction methods is discussed with illustration of models of test images reproduction.
Halftone, screening, quantization, sampling, error
1. Introduction and background
To make a hardcopy of continuous tone original the image data are, at least, twice subjected to the encoding procedure in modern graphic data processing environment. Each time it involves the operations of an image spatial sampling and of its tone scale quantization. The first of these encodings takes place at the stage of an input image digital file formation. The scanner or camera resolution defines here the image spatial sampling frequency while the “bit depth” of the device being responsible for the “color depth” of an input file. The image code comprising a “byte map” of multilevel tone values is replaced in further halftoning by the another code to produce the bit map as result of once again spatial sampling the image data, for example, at screen ruling frequency, and of anew quantization the tone value by the discrete alphabet of dispersed or clustered halftone dots, each of the latter being formed by the whole number of tiny microdots.
1.1 Quantizing the tone value in halftone printing
Any spatial sampling is accompanied by the low pass filtration resulting in the loss of an image fine detail within the limits defined by the common propositions of the sampling theory. Fine detail destroying by halftone dots comprises the other, specific kind of image deterioration inherent in screening . The interference of the number of sampling frequencies or their interaction with periodic patterns/textures of an image adds to the latter an unwanted data of different kind of moiré and aliasing.
In continuous tone imaging, such as TV, the quantization scale is positioned in the third dimension, which is orthogonal to an image (x, y) plane (Figure 1a). This scale has no direct effect on fine detail accuracy or image structure but mostly defines the tone/color rendition of an image stationary area.
The halftone imaging, to the contrary and according to its earlier suggested  more or less generalized definition, comprises the transformation of an image structure by means of “spatial dispersion of image tone measure among the output pixels to print them bi-level as result of comparison of dispersed value with an input tone value”.
As illustrated by figure 1(b, c), the quantization scale of this measure is located in the same plane where the image is spatially sampled thus involving the eternal conflict of autotypie printing in providing both the desired number of reproduced grey levels and appropriate spatial resolution.
Figure 1. The quantization scale positioned orthogonally to the image plane (a) and variants of its dispersion in the plane of an image (b – e)
Relying on over the hundred years of autotypie practice the ISO 12 647 resolves this trade off on behalf of the first of these requirements by specifying the tone value range of about 4 to 96% for the most kinds of print jobs. With taking into account said priority of an image contrast the screen frequency, which is generally responsible for the image sharpness and definition, comprises just the secondary parameter . Its value depends on the spatial resolution of printing as on an ability of the latter to provide the necessary number of quantization steps within the above mentioned spatially dispersed scale.
1.2 Tone measure spatial dispersion
As shown in table 1, the parameters of dispersion such as margins of its spatial bounds, regularity, linearity, discreteness and direction (geometry) strongly correlate to corresponding properties of a halftone image itself or of its structure.
Bounds of dispersion define the print screen period (ruling) finally affecting an image sharpness and definition. The illustrative examples of figure 1 (b - e) relate to the case of beforehand defining the dispersion by the use of corresponding weight or spot functions. However, in locally adaptive and error diffusion screening techniques, which provide the dispersion “on-fly”, such spatial period does, nevertheless, exist. It’s defined there by the code length of an input pixel. Eight bit input pixel requires, for example, the margins of, at least, 16x16 microdots for adequate presentation of one of its 28 quantization levels on a copy.
The comparison of models of figure 1 (a) and (b) shows that about ten fold excess of the output device resolution over the resolution of an input image file is generally required to provide the corresponding print definition. Moreover, the ability of printer to operate by an ink increments corresponding to the size of a microdot in the idealistic bit-map presentation of raster processor should be also taken into account.
Within said physical margins of dispersion bounds the tone measure distribution can be periodic (Figure 1 b, c) or non-periodic (Figure 1 d) resulting correspondingly in regular (AM) or irregular (FM, stochastic) placement of print elements on the picture.
Table I: The parameters of tone scale spatial dispersion and
parameters of the screen pattern thereby produced
Halftone image parameter
screen period (definition)
AM, FM (stochastic
tone response curve
number of grey levels
form of print element, screen geometry
The input image file metric relates to visually uniform optical densities or CIE Lab values which are in logarithmic or cubic degree relationship to the absorbance’s (tone values) on a print. So, the dispersed quantization scale should be in the rather strong non-linear connection to that of the input file, requiring, in its turn, the certain excess of dispersion discreteness and, once again, the greater resolution of an output.
At last, the symmetry or direction (geography) of dispersion directly defines the form of print element and screen geometry as demonstrated by quantization scale distribution on figure 1 (e) providing the predominantly triangular shape of a halftone dot.
2. Tone value quantization and spatial phase relationships
The basic error, as the metrological characteristic inherent in any quantization process, doesn’t directly affect the fine detail quality and mostly results in the so called banding which is visible at the vast image areas of continuously varied tone value. It appears for given input value quantized by the whole quantization scale and takes place in the both of the above mentioned quantization processes. The probability of banding is redoubled here by the earlier discussed non-linear connection of the input and output image data metrics. At scanner/camera encoding it is prevented by the excess of binary digits in analog-to-digital converter (ADC) in relation to eight bit of more or less visually uniform output signal sent to computer. The 16 digits or about 64000 quantization levels per channel are, for example, used in ADC to definitely encode the light intensities transmitted by a slide with its maximal optical densities of about 3.5 - 4.0.
The reverse transformation from 256 visually uniform levels to light intensities (halftone values) on a print undermines the use of 256x256 microdot matrix for an each input pixel in the process of screening. However, this formal requirement appears practically easier with taking into account the specific of viewing an image on reflection media, its maximal density lower than 2.0, etc. Nevertheless, from the very beginning of digital electronic screening in 1970ies the spatial margins of tone measure dispersion for high quality halftone printing were bounded in matrixes of up to 30x30 microdots requiring as high imagesetter resolution as 5000 dpi.
As far as the quantization scale of digital screening is dispersed in the same image plane where the image signal is two-dimensionally sampled, this quantization introduces its own specific share of error in the reproduction of an image high frequency data. The area or period of this scale distribution doesn’t, in general, coincide with that of the input pixel for their mutual position depends not only on the kind of screening but also on such obligatory factors as the input/output media resolutions relationship or on the so called screening (sampling) factor – SF. The latter is varied from a unit (coarse scan/fine print mode) up to over 10 (fine scan/fine print mode). This relationship also depends on the ruling of a screen, its geometry, angle, and other factors.
The investigation of such specific errors and the possible ways of their correction with the use of a computer model of spatially dispersed quantization scales comprise the objective of this research.
Firstly the additional errors which are monotonously changed over the spatial interval occupied by the quantization scale were examined. They arise because this scale is complete just in its full two-dimensional spatial interval. So, just the part thereof may cover the given area of an input tone signal and it also may happen that for the certain input pixels combination all their values are lower of spatially corresponding them quantization levels.
Such examples are modeled on figure 2. The test image (Figure 2a) of these models contains two characters, simulating the line work (LW) original, and a couple of CT textures with each their element being comprised of bell-shape grey level distribution shown by the lower columns on figure 2 (c). The average grey level of an each texture element corresponds to 35% tone value on a print. The screen period or the matrix of quantization scale dispersion is comprised of 12x12 printer microdots. Each of these microdots is formed light or dark depending on the multilevel value of the corresponding sample in an input file of test image. So, the SF = 12, i.e. is six times higher of that used in common pre-press practice and corresponds to the above mentioned fine scan/fine print reproduction conditions. The textures 1 and 2 are shifted in relation to each other on a half of said period in vertical and horizontal directions.
Figure 2 (b) shows that the texture 2 isn’t reproduced on a halftone copy because each of its input values happens to be lower than corresponding spatially dispersed quantization levels (Figure 2 c). The texture of intermediate spatial phase will be somehow reproduced but with distortions due to covering the input samples of texture element by just the part of quantization scale. Interaction of this scale with texture of continuously changing phase will provide the aliasing or object moiré on a halftone copy as far as such non-complete, abrupt presentation of tone signal range depends on the relationship of spatial positions of tone signal and interval occupied by the scale.
Figure 2. The texture distortion of the continuous tone (CT) original because of the phase shift between the spatially dispersed quantization scale and input image signal in fine scan/fine print mode:
a) test with the textures (1 and 2) both orthogonally shifted on half period at the CT original and corresponding to 35% tone value of halftone copy;
b) halftone copy at SF = 12;
c) the relationship of spatially dispersed quantization levels and input signal values for texture 2;
d) the same 36 times downsampled test (screening factor SF =2);
e) halftone copy produced at SF = 2.
One of the possible ways to guarantee the both of these textures reproduction and eliminate the aliasing is, for example, to down sample the input data by 36 times, i.e. to use the SF of 2 instead of 12. The model of such way down sampled test and its halftone copy are illustrated on figures 2 (d) and 2 (e). The both of textures are reproduced with still recognizable characters. These examples vividly show the certain disadvantage of an input data extra redundancy in the commonly used periodic halftoning.
There is the theoretically possible other way to somehow improve the situation, i.e. to make some use of the excess of an input data. It comprises the low pass filtration the input image file with providing the greater, than at SF = 2, number of samples. The geometry of these samples should match such a part of dispersed scale which, in spite of being coarser because of containing the fewer number of quantization levels, is still complete in its range. The example of such spatial filter configuration comprised of the sectors, where input samples values are averaged, is illustrated on figure 3 (a). The sectors are indicated there by color on the background of resulting values of these new samples for one of the texture elements.
Figure 3. Screening with the use of optimal filtration of high resolution input data: (a) - geometry of spatial filter and segmentation of the whole period of dispersed quantization scale on the background of sampling values of the texture element after filtration; (b) - the signal of the test image sampled this way; (c) - the halftone copy
The number of samples within the screen (dispersion) period on figure 3a is 10. So, SF comprises here about 3.3 and the input data is reduced by just the 14.4 times. This way sampled test image and its halftone copy are illustrated by Figure 3 (b) and 3 (c). The result of screening shows in this case more faithful rendition, especially for characters of a test, as compared to examples on figures 2 (b, e).
3. Locally adaptive halftoning
There is locally adaptive quantization scale dispersion can be used to improve the fine detail reproduction quality.
The ready made set (alphabet) of about 32 various geometry scale distributions providing 36 grey levels within the 6x6 microdot matrix is used in the High Definition Halftone Printing – HDHP technology. Having four times shorter length, as compared to the basic scale of 12x12 matrix, these distributions are intended for approximate matching the contour geometry. The basic scale of full length is, in its turn, intended for the stationary image area. This technology provides the twice higher halftone print definition and facsimile thin line rendition at the commonly used SF = 2 without applying any additional requirements to physical properties of printing channel in relation of substrates, inks, plates or their interaction .
The greater use of higher SF values or input data redundancy (fine scan/fine print) is theoretically possible in error diffusion screening. However, for over 30 years of its exploring this approach couldn’t find wide practical implementation because of providing the non-periodic screen pattern for the stationary image area and thus ignoring physical specific of printing channel .
This specific is taken into account by preserving the regular and, so, printable halftone structure for such an area in one of the other of our screening approaches . The method is also intended for the fine scan/fine print reproduction. However, it uses the quantization scale dispersion which is adaptive or variable not to the tone value itself, as it takes place in error diffusion screening, but, as in HDHP technique, just to the tone value gradient. At the same time, it uses, to the contrary to HDHP, the dispersion which is adaptive to the arbitrary contour of an image and allows for the complete use of an excessive input resolution in the process of printing as illustrated by the models on figure 4.
The input test comprises here the dark grey character and its lighter background the both to be screened to provide a halftone copy. The 3D presentation of multilevel, for example, 8 bit tone value of this test is given on figure 4 (a), while the figure 4 (c) shows its halftone copy produced with the commonly used periodically dispersed scale of figure 4 (b).
Figure 4. Screening with scale dispersion adaptively to arbitrary image contour.
Variants of: traditional (b) and adaptive (f, g, h) scale distributions; halftone copies (c, k, i); multilevel signals of test (a, l). The bi-level contour trace signal - (d). Positioning of contour trace signal 1 and bounds 2 of scale dispersion - (e).
To improve an image quality the auxiliary one bit signal of a contour trace or path (Figure 4 d) is generated by marking, for example, the peaks of first spatial derivative of an input tone values in their local neighborhood. The quantization scale dispersion is then provided outward this trace 1 within the bounds 2 (Figure 4 e) resulting in locally adaptive dispersed scale illustrated on figure 4 (f). With taking into account the lower ability of human visual system (HVS) to discern grey steps for smaller image details the margins of this dispersion may be much narrower of the period of basic dispersed scale of figure 4 (b) thus providing the coarser quantization. However, such coarser but, nevertheless, complete scale is still necessary because the fine detail of the CT original may have the different contrast and tone value the both of these parameters have to be faithfully reproduced on a halftone copy.
With replacing the corresponding part (Figure 4 g) of initial periodic scale of figure 4 (b) by an adaptive one the final scale is provided as shown on figure 4 (h). This combined scale allows for the input image reproduction (Figure 4 k) which is much more accurate than on figure 4 (c) due to the higher use of printing process resolution.
After the presentation of high spatial frequency image data by trace of a contour the input signal can be down sampled by about 100 times (Figure 4 l), i.e. to the volume which is commonly used in coarse scan/fine print way of reproduction. The screening of such file by the adaptively dispersed scale of figure 4 (h) still provide the good rendering of detail as is shown on figure 4 (i). So, there may be recommended the specific two-component compact file format for pre-press image processing which, at the same time, provides the high definition of a halftone print. This file may comprise the down sampled multi-level input data of a whole image in combination with the previously made bit map of counter trace signal.
4. Topologic approach to tone value transformation in screening
Reproduction in graphic industry results in creating the physical image by placing the ink on printing substrate. All the pre-press operations are guided by this final stage and can be brought to it through the common variable of physical volume V of conditional ink placed on an ideal substrate. For each two-dimensional unit image area Su (Figure 5 a) this volume can be expressed by the ordinate 0 <V <Vmax to consider such presentation as the secondary one which completely matches the original within the limits of its sampling and quantization at the digital encoding stage. According to autotypie principle the same ink volume can be expressed by the area S with a unit ordinate Vmax (Figure 5 b) which comprises the image signal in form of Boolean numbers plurality (0; 1) instead of multilevel sampling values. However, such form of an input signal can’t be directly repeated in real printing process due to the limited resolution of the latter.
Figure 5. The principles of an image data presentation within its halftone symbol by the amount of conditional ink V:
a) - by ordinate 0 <V <Vmax over unit area Su of a symbol;
b) - by area S of a unit ordinate Vmax ;
c) – by grouping the volumes of conditional ink within symbol margins into halftone dot area Shtd
There are two operators used in topologic approach for optimal ink distribution over the halftone symbol area . Both of them operate the form of halftone dot as the dependant variable. However, the first of these operators is based on the principle of a halftone dot perimeter minimization for all values of its area thus taking into account the physical specific of real printing channel and thereby to continuously render the image stationary areas. This is performed in conventional way of applying the threshold screen weighting function of the kind illustrated on figure 1 (b) or figure 2 (b). The second, topologic operator provides the sorting of an input image data within the halftone symbol margins to create the, so called, spot function providing the form of a dot precisely matching the image fine detail geometry within a halftone symbol as is schematically shown on figure 5 (c).
Figure 6. Halftone transformation of test (a) by traditional (b) and topological (c) methods
The models of test image and its reproduction by the traditional way and with the use of topological approach are given on figure 6 while the results of screening the watermark kind of an image are illustrated on figure 7 in comparison also with the halftone produced by the error diffusion method.
Figure 7. The reproduction example of watermark and engraved area (a) of a banknote by topological screening algorithm (d) as compared to traditional (b) and error diffusion (c) halftoning.
As can be seen from figures 6 and 7, this approach provides the greatest accuracy as compared to the other above discussed methods. However, it uses the iterative sorting procedures and that’s why is computationally more busy.
The parameters of spatial dispersion providing the tone measure quantization scale strongly correlate to corresponding properties of a halftone image and its structure.
Along with the basic metrological error inherent in quantization process there are the specific ones lowering the fine detail reproduction accuracy in screening.
At the fine scan/fine print resolutions relationship these errors can be corrected by the reducing of an input image signal redundancy along with this signal optimal filtration.
The complete use of said redundancy and output printer resolution can be provided by the tone measure spatial dispersion adaptive to arbitrary contour of an image.
The greatest effect can be achieved in topologic approach of sorting the amount of ink within the margins of a halftone symbol.
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