=Paper=
{{Paper
|id=Vol-2533/paper21
|storemode=property
|title=Investigation of Binary Element Reproduction Methods in Elemental Record Processes
|pdfUrl=https://ceur-ws.org/Vol-2533/paper21.pdf
|volume=Vol-2533
|authors=Bohdana Havrysh,Oleksandr Tymchenko,Bohdan Kovalskyi,Myroslava Dubnevych,Orest Khamula,Michal Gregus,Mykola Logoyda
|dblpUrl=https://dblp.org/rec/conf/dcsmart/HavryshTKDKGL19
}}
==Investigation of Binary Element Reproduction Methods in Elemental Record Processes==
https://ceur-ws.org/Vol-2533/paper21.pdf
Investigation of Binary Element Reproduction Methods
in Elemental Record Processes
Bohdana Havrysh1[0000-0003-3213-9747] , Oleksandr Tymchenko 2[0000-0001-6315-9375]
Bohdan Kovalskyi1[0000-0002-5519-0759], Myroslava Dubnevych 1[0000-0001-7089-0190]
Orest Khamula 1 [0000-0003-0926-9156], Michal Gregus 3[0000-0002-8156-8962]
Mykola Logoyda 4[0000-0001-7597-7973]
1 Ukrainian Academy of Printing, Lviv, Ukraine
dana.havrysh@gmail.com, bkovalskyy@ukr.net,
dubnevychmyroslava@gmail.com, khamula@gmail.com
2 University of Warmia and Mazury, Olsztyn, Poland, o_tymch@ukr.net
3 Comenius University in Bratislava, Bratislava, Slovakia, Michal.Gregus@fm.uniba.sk
4 Lviv Polytechnic National University, Lviv, Ukraine, mykola.m.lohoida@lpnu.ua
Abstract. We consider the methods of elemental recording of raster binary
images on photographic or form material for systems of printing reproduction.
In the process of tuning and comparing such processes, it is necessary to evalu-
ate their sensitometric and structural-metric properties, which determine the
quality of reproduction of the minimum image elements - raster points and
strokes on the material carrier. The use of traditional sensitometry and structural
analysis, which are used to calculate photographic processes, does not allow
such a full assessment due to the difference between format and elemental re-
cording methods, semitone and binary images, photographic and form materi-
als. The peculiarities of the methods of reproduction of an image elements with
elemental recording revealed to be expedient to be used at technological ad-
justment of printing reproduction system processes.
Keywords: binary images, optical density, printing forms, sampling, pixel
functions.
1 Introduction and Problem Statement
The basic working properties of the image elements on the material carrier are deter-
mined by the gradation parameter. As a gradation parameter, optical density [1, 10] is
often used to characterize the property of photographic forms to pass or delay radia-
tion in the molding process, or the relative thickness of the printing layer. The register
layer on the printing elements, which characterizes the property of printing forms to
transfer ink in printing process [2]. For binary images, the gradation parameter has
two levels - the upper lu and the lower ll, hich, depending on the polarity of the pro-
Copyright © 2019 for this paper by its authors. Use permitted under Creative Commons License
Attribution 4.0 International (CC BY 4.0)
2019 DCSMart Workshop.
cess, correspond to the active elements, purposefully formed radiation, and passive
formed in the absence of radiation. If the active elements correspond to the lower
level, then the process is positive (Fig. 1a), if to the upper one then the process is
negative (Fig. 1b). The sensitometric curve (Fig. 1) shows the threshold exposure
H thr to which the basic working property of the passive image elements is provided,
and the minimum exposure H min from which the basic working property of the active
elements is provided. If H min H thr we get a threshold or step change in the grada-
tion parameter.
l
1.0
lu
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
ll lgH
0
0.15 0.30 0.45 0.60 0.75 0.90 1.05 1.20
Hthr Hmin
a
l
1.0
lu
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
ll lgH
0
0.15 0.30 0.45 0.60 0.75 0.90 1.05 1.20
Hthr Hmin
b
Fig. 1. Sensitometric curves of the elemental recording process: a - positive process; b - nega-
tive process
Sensitometric process curves will be used to identify the features of methods of re-
producing image elements with elemental recording.
2 Development and Research of the Elemental Record Process
Structure System
The basis of the developed system of structurometry of the elemental recording pro-
cess is based on the normalized functions of distribution of effective energy density:
for the pixel - the function of pixel reproduction (FPR) and for the edges of the energy
plate - the boundary functions in the direction of personnel (BFP) and line scan (BFL)
[3, 11].
Reproduction functions are functions of a discrete argument. We use the following
notations: P(y, x) – for FPR and E k y – for BFP. The x and y arguments related to
the line and frame scans have a definition area [4]:
1
b : x, y b, b d , ,0, , b, where d – sampling step N, b N .
N
Kernel Energy Density - The fraction of energy density in the center of the image
element from the maximum level of the energy plate obtained while recording pixels
in all positions, and pixel kernel functions - the dependence of the kernel energy den-
sity on the number of pixels forming active and passive elements, hka k and hkp k .
For the purpose of accuracy of estimation, it is advisable to use a balanced raster
structure [5], for which on the matrix of balance points with recorded pixels, active
raster points are formed, and unwritten ones form passive points, with points in light
and dark regions being formed by identical and round shape pixels. For the balance
structure, formulas for calculating the energy density of the kernel for k-pixel image
elements can be written using FPR:
hka 1 P 0,0 , hka 2 2 P 0;0,5 etc.
(1)
hkp k hd yc, yc hka k
where hd yc, yc – the level of the energy plate at a point corresponding to the center
of the image element. Formulas (1) show that the energy density of the nucleus is
completely determined by the central part of the FPR within the sweep step.
3 Binary Images Reproduction Research
Reproducing extended image elements.
Depending on the FPR, a constant unit level or periodic oscillations of the energy
density level in the direction and with the step of the frame scan can be formed on the
energy plate (Fig. 2). In this case, a maximum is formed in integer coordinates
hdmax 1 (rationing to the maximum), and in half offset coordinates, – minium hплmin
(Fig. 2, b). The average level of energy density on the plate is equal to that specified
in the exposure system H w , then, in the transition from relative values to absolute
values for the minimum and maximum, we can write: Rn hdmin and Rn H w , where
2
Rn – is the conversion factor to the average level. In the presence of
1 hdmin
oscillations it is necessary to distinguish two values for the threshold and minimum
exposure - local and average. The first is related to the action of energy density in the
maximum or minimum, the second - with the average value of the energy density on
the plate and the exposure specified in the system.
For offset printing forms, the main working property of the whitespace elements is
provided in the complete absence of the printing layer ll 0 , and printing elements
at full thickness (lu 1) [6]. Then the main working property of passive elements
with exposure increasing begins to break at the maximums in which the energy
loc
density operates at Hthr , with system exposure H thr :
loc
Hthr Rn Hthr (2)
The basic working property of the active elements will finally be reached in the
loc
lows in which the energy density operates at H min , at exposure H min : Rn
R n max
hef, rel. un. hef, rel. un. hds =1
max
hef, rel. un. min
1 hef, rel. un. hds =1
min
1 min
x x
Rmin
n hds
E (y)x Ex (y) R nhhmin
ds
min ds
E (y) E (y) hds
yy y y
a b
Fig. 2. Edge functions in the direction of the frame scan: а – constant level of the plate; b –
plate level fluctuations
Exposure values H thr and H min can be determined experimentally, but values
loc loc
H thr and H min can be calculated by the formulas (2) and (3). With a constant unit
level of the energy plate hdmin Rn 1 the exposure values set in the system are the
same as the local values: Hthr H loc
thr and H min H min
loc
. As the amplitude of the oscilla-
tions increases Rn begins to increase and Rn hdmin decreases, then the threshold expo-
loc
sure of H thr is decreasing in relation to Hthr , and the minimum exposure of H min – is
loc
increasing in relation to the H min .
Starting with H min the basic working properties of the long-lasting elements of the
image will be provided, and this exposure can be considered to be minimally sufficient
to reproduce them.
Reproduction of small image elements.
Image elements in the center of which the basic working property is provided are
considered reproducible and form a pixel reproduction range of k а k p , where k а –
is the number of recorded pixels that form the minimally reproduced active element of
an image, k p – is the number of unwritten pixels that form the minimally reproduced
passive image element. The pixel reproduction range is related to the reproduction
range of tone values [7], which is one of the basic parameters that determine the visual
properties of printed product. The pixel width equals p k а k p 1 , where p – is
the number of pixels in a raster cell, and increases with decrease of k а k p .
We will investigate the factors that affect this amount and width of the range. In the
center of the k-pixel active image element the energy density acts like this:
hkа k Rn H w , which for its reproduction should be not less then H min
loc
, then, consider-
ing (3) we can write the reproduction condition:
loc
H min hmin H min
hkа k hmin where hmin d (4)
Rn H w Hw
In the center of k-pixel of the passive element, the image gives energy density
h k Rn H w , which should be smaller then Hthr
k
p loc
to recreate it, and considering (1) we
can record the reproduction condition:
hkp k hthr (5)
loc
H thr H
where hthr thr
Rn H w H w
Analysis (4) and (5) shows that starting with H min active and passive elements are
reproduced, H w H min – is the condition of the best reproduction of the passive ele-
ments and the worst active, and the increase of H w comparatively to H min improves
the reproduction of the active and the reproduction of the passive elements.
hk ,rel. un.
a
hk(k)
k =1
hmin
h
hthr p
k =2 p
hk(k)
k
Fig. 3. Graphs of pixel functions
Let's consider the graphs of pixel functions for active hkа k and passive elements
hkp k , which are piecewise linear, in one coordinate system (Fig. 3). The line hmin at
the intersection with the curve hkа k will give us the point whose abscissa, when
rounded, is greater than the number of pixels k а , that form the minimally reproduced
active element. Similarly, the line hthr at the intersection with the curve hkp k gives
us the point whose abscissa, when rounded to a greater number of pixels k p , that
form the minimally reproduced passive element.
Researching the influence of the values hthr and hmin , де hthr , hmin 0,1 and
hthr hmin , the sum of k а k p allows us to draw the following conclusions.
The value of k а k p depends on the width of the interval h hmin hthr
and its position along the y-axis.
The smaller the interval h , the smaller the sum of k а k p and the wider
the pixel recreation range.
At a fixed value of the interval h , the minimum k а k p corresponds ap-
proximately to its central position on the segment of the y-axis, i.e.
hmin hthr 1 or H w Hthr hdmin H min . In this case, we obtain a symmetric
pixel range with equal boundary values k а k p . Some incertitude in the
width of the range is introduced by the piecewise-linear nature of the func-
tions, the angular coefficients of the linear sections of which depend on
the FPR and the positions of the pixel recording.
The maximum possible pixel reproducing range can be obtained when
hmin hthr 0,5 , which corresponds to the threshold sensitometric curve
H min Hthr . The maximum possible range for a given raster structure is
completely determined by the central part of the FPR.
1
Judging by (4) and (5) h ~ , the interval narrows with increasing ex-
Hw
posure in the system. However, as the exposure increases, the interval
from the central position down the ordinate is shifted and k а k p increas-
es. As a result of these factors, in this case, the maximum range is asym-
metrical with a smaller value of k а .
The piecewise linear nature of the pixel functions and the rounding of the
pixels to integers results in the uncertainty of the bandwidth of up to two
pixels. Also, the bandwidth is affected by the lower durability of the small
printing elements not taken into account.
Let's investigate the effect of the nature of the FPR distribution on the reproduction
of small image elements. In the analytical method of calculating FPR as a factor con-
trolling the distribution proposed analytical method of calculating FPR. As a factor
controlling the distribution of the energy density of the FPR, we take r0 – the laser
beam radius in the area of constriction at the level e 2 at constant scattering parame-
ters, selected to approximate the experimental data obtained for offset heat-sensitive
plates [8].
As r0 , decreases , the energy density fraction in the central part of the FPR increas-
es, the values of the pixel function hkа k increase accordingly, and the values hkp k
decrease (table 1), increasing the pixel range to full k а k p 1 . The energy density
values in the center of the 1-pixel active and passive elements are calculated by (1),
and by (4) and (5), we calculate the conditions for their reproduction and calculate the
exposures from which these conditions are satisfied:
H loc loc
H min
hkа 1 min H w1а (6)
Rn H w Rn L 0,0
loc loc
H thr H thr
hkp 1 H w1п (7)
Rn H w Rn 1 L 0,0
However, as r0 decreases, the amplitude of the oscillation level of the energy plate
increases (columns hdmin and Rn of table 1), which can lead to the inadmissible parti-
tioning of image elements into parts. The energy density at each point is formed by
pixels that fall into the FPR definition area, and the minimals are formed in the coor-
dinates of the frame sweep offset by half a step from the line item positions. Then the
smallest value of the energy density is formed in the center of the 2-pixel element
with the frame placement of pixels, for the calculation of which in formula (1) for the
2-pixel element with a row arrangement of pixels it is necessary to replace the argu-
а
ments of FPR: hmin 2 2L 0,5; 0 . Starting with r0 0,8 the energy density at the
center of such an element begins to fall (Table 1). From (4) we can calculate the con-
dition of the integrity of the elements of the image and calculate the exposure at
which this condition is satisfied:
H loc loc
H min
а
hmin 2 min H wint (8)
Rn H w 2 Rn L 0,5; 0
Table 1. Influence of laser beam radius on image element reproduction.
H thr H min H w1а H wint H w1п
hdmin Rn h 1 h 1 h
r0 a
k k
p а
min 2 H thrloc loc
H min loc
H min loc
H min loc
H thr
1,20 1,00 1,00 0,37 0,63 0,53 1,00 1,00 2,72 1,89 1,58
1,10 0,99 1,00 0,42 0,58 0,57 1,00 1,00 2,36 1,73 1,73
1,00 0,98 1,01 0,49 0,51 0,62 0,99 1,01 2,02 1,60 1,94
0,90 0,94 1,03 0,57 0,43 0,64 0,97 1,03 1,71 1,51 2,25
0,80 0,87 1,07 0,65 0,35 0,64 0,94 1,07 1,43 1,46 2,70
0,70 0,75 1,14 0,74 0,26 0,59 0,87 1,17 1,18 1,48 3,35
0,60 0,57 1,27 0,81 0,19 0,48 0,79 1,37 0,97 1,63 4,20
0,50 0,37 1,46 0,87 0,13 0,32 0,68 1,87 0,78 2,11 5,28
4×4 1,00 1,00 0,97 0,03 0,98 1,00 1,00 1,02 1,03 33,11
It should be added that in the case of 4 × 4, a pixel consisting of 16 subpixels is
used. With decreasing of r0 the exposure of H w1а decreasesfrom which the 1-pixel
active element is reproduced, and the exposure of H w1p , to which the 1-pixel passive
element is reproduced (the table shows the ratio of H w to local values). However,
with r0 0,8 the minimum sufficient process exposure begins to be determined by
the increased exposure of H wint integers required to maintain the integrity of the image
elements (values highlighted in the table in bold). The need to increase exposure con-
tradicts the lack of activity that is characteristic of, for example, the technology of
elemental recording of offset printing forms. When using a pixel consisting of subpix-
els of a larger recording extension [9], a constant single level of the energy plate is
formed, and the full pixel range is reached without increasing the exposure (row 4 × 4
of the table). However, this approach requires specific hardware solutions.
4 Results and discussions
As a result of the researches the following features of reproduction of image elements
in the processes of elemental recording were revealed:
To obtain a larger pixel recreation range, the H thr threshold and the mini-
mum H min exposure should be as close as possible to each other. The
maximum possible range is reached in the case of a threshold sensitomet-
ric curve H min Hthr .
Choosing a working exposure H w in a system close to the minimum H min
results in poor reproduction of the active elements.
The pixel range with equal lower and upper bounds is obtained at
H w Hthr hdmin H min , but it is not maximal. The maximum pixel range is
shifted toward larger exposures, with active elements reproducing better
than passive ones. The result may be due to the lower resistance of small
print elements to processing.
The integrity of the image elements can be controlled in the center of a 2-
pixel pixel element.
Reducing the laser beam radius r0 allows us to obtain the full pixel range
k k 1 , but this increases the oscillation amplitude of the energy
а p
plate and, as a consequence: increases the minimum H min , and decreases
the threshold H thr of the exposure; the integrity of the image elements is
impaired and the condition of its preservation determines the minimum
sufficient exposure in the system. This increases the working exposure in
the system, which may be unacceptable with insufficient activity, which is
characteristic, for example, for the technology of elemental recording of
offset printing forms.
The use of a pixel consisting of sub-pixels of greater recording expansion
allows to obtain the full pixel range at a constant level of the power plate.
It is expedient to use the revealed features of reproduction of image elements when
designing and technological tuning of processes with elemental recording.
5 Conclusion
Methods of elemental recording of bitmap raster images for photographic and form
material for printing systems have been considered. The expediency of maximizing
the minimum and maximum exposures with each other is shown, but the maximum
pixel range is shifted toward larger exposures. To get the full pixel range, it is advisa-
ble to use sub-pixels and reduce the laser pro-radius.
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