Cluster Dot Screen Design for Direct Binary Search Multitoning

S.D.Kumari Mrs.A.Rajalakshmi
Electronics and Communication Assistant Professor, Electronics and Communicaion
Adhiparasakthi Engg College Adhiparasakthi Engg College
Melmaruvathur, Chennai,India Melmaruvathur,Chennai,India
kumarimugi@gmail.com hereraji@gmail.com

Abstract— Digital multitoning is an advanced levcl of (PWM). PWM allows the laser printer to modulate the time
halftoning more than two tones at each pixel for higher duration of the laser beam to provide sub pixel addressability
image quality. We propose a methodology for multilevel in laser scan direction, which means that the time of laser bean
screen design using direct binary search (DBS). We refer turned on or off can be modulated within a fraction to the
to one period of the screen as a multitone cell. In the length of one pixel. This mechanism basically supports multi
multitoning, which for each absorptance level specifies the tone outputs by increasing the addressability in the scan
fraction of each native tone used in the multitone cell. direction.
Traditional multitoning uses only one native tone in For an Inkjet printer, multi tone writing capability
smooth areas corresponding to absorptance values near can be achieved by thermal head, dye diffusion, and multi-
the native tones, an approach that introduces contouring drop mechanism. Multi-drop mechanism generates different
artifacts. To reduce contouring, we employ schedules that number of drops at each addressable pixel to accomplish
use more than one native tone at each absorptance level. multilevel rendering. In this paper, we focus on making Inkjet
On the basis of the multitone schedule, multitone patterns printer multilevel outputs by varying the number of drops
are designed level by level by adding native tones under from the combination of two pens with different levels of ink
the stacking constraint. At each level the spatial concentration
arrangement of the native tones is determined by a Most of the traditional half toning technologies fall
modified DBS search. As demonstrated in the into three categories: point operations (screening),
experimental results, both of the high homogenous neighborhood processes (error diffusion), and the iterative
multitone texture and less noisy perception at all algorithms (Direct Binary Search (DBS)) [Chandu et al
absorptance levels are offered in contrast to the former (2014)]. The quality of half toned image increases in this
results. order. However the computational complexity also grows in
Keywords—Direct Binary Search, Multitoning, Digital the same order. Screening requires a pixel-by-pixel
Printing. comparison between the continuous tone image and the
I. INTRODUCTION threshold matrix, so it is least computational. Error diffusion
Half toning is a technology that renders a continuous traverses the entire image and the output is determined by the
image with limited number of tone levels. Traditionally, the thresholding, while the quantization error is diffused to its
number of the tone levels is two, which means that the dot on next neighboring pixels. Both screening and error diffusion
the paper is either printed or not printed. Therefore, such can be operated online and be implemented in the printing
conventional half toning technology can also be called bi-level devices.
half toning. Bi-level half toning can produce perceived similar DBS finds the halftone image which is perceived
images compared with other continuous tone images, because most closely compared with the continuous image. Although
the printer usually has very high printing addressability or DBS can produce best image quality, it usually requires
resolution. Due to the low-pass nature of human visual system, several iterations and thus, very computational. It is
the much higher-frequency content cannot be perceived by commonly not directly used in the printing devices, but DBS
human eyes. Thus, the high-resolution bi-level half toned provides important off-line design and supports other half
image is perceived as a continuous image by appropriate half toning technology, like Tone Dependent Error Diffusion,
toning algorithms [Faheem et al (2001)]. which offers good image quality and can be operated in real
The quality of the halftone image can be improved time.
not only by increasing the printing resolution, but also by The other two important catalogues for half toning
raising the number of tone levels printers could render. I call are based on the texture of half toned image: 1) if the texture is
the tone levels can be printed as native tone, since it is the dispersed or clustered 2) if the texture is periodic or aperiodic.
inner property of the device. If the printer produces the All four combinations (2×2) are possible. Clustered half
number of the native tones which is greater than two, the half toning is always used in the electro-photographic printers,
toning technology for such printer is referred to multi toning. because the clustered-dot can provide more stable print and
Multi tone printing can be achieved by different less dot-gain effect. The printing devices which can generate
mechanism in different types of printers. Most of the printers more stable pixels usually employ dispersed half toning.
can be cataloged as Laser electro photographic printer and Clustered periodic half toning commonly provides more
Inkjet printer. For a Laser electro photographic printer, homogeneous structure in mid tone region than the dispersed
multilevel half toning is realized by Pulse Width Modulation
aperiodic half toning, while the stochastic aperiodic half The perceived difference is described by the term,
toning shows more preferred blue-noise texture in highlight. mean square error (MSE) of perceived error between the
Halftoning or analog halftoning is a process that c o n t i n u o u s -tone image and t h e halftone image. Due to the
simulates shades of gray by varying the size of tiny black dots low-pass characteristic of the human v i s i o n , the perceived
arranged in a regular pattern. This technique is used in error is the error between the continuous-tone i m a g e and
printers, as well as the publishing industry. If you inspect a the halftone image filtered by the Human Visual
photograph in a newspaper, you will notice that the picture is System(HVS) which is essentially a low pass filter.
composed of black dots even though it appears to be B. Error diffusion
composed of grays. This is possible because of the spatial Error diffusion works by comparing the actual color of
integration performed by our eyes. Our eyes blend fine details a pixel against its nearest color and taking the difference
and record the overall intensity. between them. This difference is known as the error. Portions of
Digital halftoning is similar to halftoning in which an the error are split between neighbouring pixels causing the error
image is decomposed into a grid of halftone cells. Elements to be diffused hence the name “error diffusion”.
(or dots that halftoning uses in simulates shades of grays) of
an image are simulated by filling the appropriate halftone
cells. The more number of black dots in a halftone cell, the
darker the cell appears. For example, in Fig 1.1, a tiny dot
located at the center is simulated in digital halftoning by
filling the center halftone cell; likewise, a medium size dot
located at the top-left corner is simulated by filling the four
cells at the top-left corner. The large dot covering most of the
area in the third image is simulated by filling all halftone cells.
Fig 2.3 Simple Error Diffusion
With this form of error diffusion half of the error
from the current pixel (represented by the black dot) is
diffused to the pixel on the right and half to the pixel below. In
a color image error diffusion, should be applied to the red,
green and blue channels separately.
An important point to note here is that the total
amount of error diffused should never exceed a value of 1. In
most cases the total amount of error diffused will equal 1
although I am aware of one type of error diffusion where the
total error diffused is less than 1.
Error diffusion was first proposed by Floyd and
Steinberg in 1970s. Error Diffusion is a neighboring process
Fig 1.1 A sample of digital halftoning which has two ways to be viewed. One is to diffuse errors
Three common methods for generating digital immediately after half toning pixel to all pixels in the
halftoning images are neighborhood; the other is to gather errors from neighboring
1. Patterning pixels just prior to half toning. The first way is helpful to
2. Dithering implementation, and the second way is easy to understand its
3. Error diffusio formulas.
II. EXISTING HALF TONING TECHNIQUE
A.Direct Binary Search (DBS)
Direct Binary Search (DBS) is an iterative half toning
algorithm to minimize the perceived difference between the
continuous-tone image and the halftone image. As shown in
Fig. 2.1

Fig 2.3 shows the diagram of a Floyd-Steinberg Error

Diffusion system, pixel value; g[m, n] is the output binary
halftone image which is determined by a threshold value
t[m, n] in a thresholding/quantization process; d[m, n] is
Fig 2.1 Objective of Direct Binary Search the quantized error; w[m, n] is the weight represents the
impact of the pixel on the it neighbor pixels. Where f [m, n] is 3 64 3 0
the input continuous-tone i ma ge ; u [m, n] is the updated.
4 85 1 1
Tone Dependent Error Diffusion
Tone Dependent Error Diffusion (TDED) is an 5 106 2 1
evolution of Floyd-Steinberg error diffusion. It pre-optimized
the weights matrix and the threshold value dependent on 6 128 3 1
different input continuous-tone. [Allebach et al (2000)]
7 149 1 2
optimized the parameter by the perception from HVS. For
midtone, highlight and shadow regions, they utilized different 8 170 2 2
strategies to do optimization and reduce artifacts. However,
the optimization process is beyond the content of their paper. 9 191 3 2
We only use their parameters in the result of this paper.
10 213 1 3

11 234 2 3

12 255 3 3

E.One-Two-Tone-Mixture Schedule S1−2 Half toning Design

A simple one-two-tone-mixture schedule S1−2 for
multilevel half toning that can be straightforwardly extended
from bi-level half toning. In this method extend the bi-
Fig 2.5 Tone Dependent Error Diffusion levelDBS screen, error diffusion, Tone Dependent Error
C. Hybrid Screen Diffusion, and hybrid screen to the corresponding multilevel
In traditional clustered-dot periodic screen versions. It first describes the modification made on the
design, there is always a tradeoff between the screen traditional half toning methods. After that, experimental
frequency and the number of realizable gray levels. The screen results will be shown respectively. And the experiments from
frequency is related to the detail rendering of the image. The different half toning are compared in the rest of this section.
higher the screen frequency is, the more capable the clustered-
dot periodic screen can represent the details of the image.
However, the increase in the screen frequency leads to the
decrease in the halftone cell size, which directly causes the
drop in the number of realizable gray levels by this halftone
cell. Therefore, the super cell is introduced by using the
concept macro dot growing order.
D.MultiLevel Toning
The ink printer utilizes two different
ink density pens of multi-drop capability to generate
multilevel native tones. The two drop pens are called full drop
pen and light drop pen due to the different density of the pens. Fig 2.6 One-Two-Tone-Mixture Schedule S1−2
The density of the drop pens is subject to changing. In this
Chapter, we modulate t h a t the density of three drops from
the light drop pen are equal to the density of one drop from the Multilevel half toning with DBS screen of four native
full drop pen. According to dot arrangement in the Table 2. 1, tones. Contouring artifacts are observed in the simple one-two
we can achieve at most 13 native tones. In this Chapter, we schedule. However, with the increase of the number of native
refer to the number of native tones (including paper white) as tones to thirteen, which means the sharp
N = 13. decreases of the gray level contrast between the adjacent
Table 2.1 Dot arrangement for two drop pens native tones, we believe that the quality will be greatly
improved [Blum et al (2014)]. We first decide at which multi
GL# Gray level Light Full Drops tone cell, the output should be located. Meanwhile, it
Drops determines which two of the native tone levels will be
0 0 0 0 considered, according to Eq: i = f [m, n]/ (256/ (N − 1))]
Where f [m, n] is the input continuous-tone image.
1 21 1 0 N = 13 is the number of native tones.

2 43 2 0
 native tones throughout the whole ramp. The ideal
checkerboard to achieve during the intermediate step is Table
2.2. In the table, k is the index of native tones and 0 ≤ k ≤ 10.

Α Α α α
k k k+2 k+2
α α
Αk Αk k+2 k+2
Fig. 2.7 Ramp half toned by multilevel DBS α α
screen F. Multilevel Tone Dependent Error Diffusion k+2 k+2 Αk αk Table2.2 Ideal
Tone Dependent Error Diffusion is an
evolutional version of Floyd-Steinberg error diffusion α α Α α checkerboard texture
k+2 k+2 k k to achieve during
proposed by [Allebach et al(2000)]. We can guess the
evolution in Tone dependent Error Diffusion from its name. intermediate steps
The weights and the threshold are all dependent on the input
tones. The weights and threshold are optimized with the First, confirm that you have the correct template for your
assistance of DBS. paper size. This template has been tailored for output on the
A4 paper size. If you are using US letter-sized paper, please
close this file and download the file “MSW_USltr_format”.
PROPOSED CLUSTERED DOT MULTI TONING
A. Maintaining the Integrity of the Specifications
The template is used to format your paper and style the
text. All margins, column widths, line spaces, and text fonts
are prescribed; please do not alter them. You may note
peculiarities. For example, the head margin in this template
measures proportionately more than is customary. This
measurement and others are deliberate, using specifications
that anticipate your paper as one part of the entire proceedings,
and not as an independent document. Please do not revise any
of the current designations.
III. PROPOSED CLUSTERED DOT MULTI
TONING A. Introduction
Multi toning is used to render continuous-
tone i ma ges with output devices that are capable of
directly printing or displaying only two or a small number
G. Summary and Comparison for Four Multilevel Half toning of different gray levels. For example, Inkjet systems may
Generally speaking, we can say that, from the ramps have light and dark pens for a given color and/or they
half toned by the four-multilevel half toning, the DBS and may be capable of placing 0, 1, or 2 drops at a given
hybrid screen surmount error diffusion or Tone Dependent addressable pixel location. The various combinations of
Error Diffusion, while hybrid screen even shows more drop density and number of drops yield what we refer to
homogeneous texture in the mid tone area than DBS does. On as a set of native tones. Multi toning succeeds by
the other hand, although it is not obvious, all the four generating a high spatial frequency pattern of alternating
multilevel half toning technologies show the contouring native tone values that i s not well resolved by the human
artifacts in the area where there is no texture. We hope to observer at normal viewing distances. Instead, a local
eliminate such contouring by keeping the texture all along in spatial average of the texture i s perceived.
the ramp. The three most widely used categories of half
H. Two-Four-Tone-Mixture Schedule S2−4 Half toning toning methods are pixel method, neighboring method,
Design and iterative me t ho d . Usually the halftone output quality
Observing the contouring artifacts caused by the no texture and computation timing both i n c r e a s e in the order of
area in one-two tone-mixture schedule, we wish to use a pixel, neighboring and iterative. The p i x e l method i s
schedule that contains texture in the entire ramp. As the first known as screening, o r dither. For e xa mp le , L i c h e n
step, we generate a 4 × 4 screen, before we go further. There pro- posed a dither method to generate the blue-noise
are thirteen native tones for choice, so the contrast graylevel or which is visually pleasant halftone pattern [Lichen et al
density between two adjacent native tones is very small. Our (2008)]. Pixel method compares or computes on the pixel of
objective is to keep texture of a contrast of two intervals of the screen and corresponding pixel on the image only,
so it is usually computational-efficient. Another pixel method dispersed aperiodic multi toning, while the stochastic
is look-up-table half toning. aperiodic multi toning shows more preferred blue-noise
Li and Allebach (2000) invented a look-up-table texture in highlight. The other multi toning algorithm may
half toning using the correlation information between apply hybrid texture, like hybrid screen, which has the blue-
different gray levels in order to minimize noise dispersed dot in highlight and shadow region, also
enjoys the homogenous clustered periodic texture i n the mid
the artifact n o i s e . The neighboring method is well-known tone.
as the Floyd- Steinberg error diffusion. It diffuses the error In multi toning, three categories: pixel,
between the halftone output image and the continuous-tone i neighboring and iterative m e t h o d s can all be adapted
n p u t image to the afterward pixels in the raster order. It is f o r multilevel output devices. For example, [Sarailidis et
essentially serial algorithm, s o error diffusion is more al (2012)] describe an error-diffusion-like approach that i s
computational inefficient than pixel method. Lots of work has based on the correlation between adjacent pixels. Ideally,
been done to improve the error diffusion algorithm the multilevel multi toning has much better p r i n t i n g
[Goldschneider et al(1997)]. q u a l i t y t h a n b i -level halftoning. However, multi toning
Tone Dependent Error Diffusion was invented by h a s its own trouble a s well. When the desired tone-value
Li and Allebach, which largely eliminated t h e artifacts c a u s is near a native tone, traditional multi toning approaches
e d by the conventional e r r o r diffusion. The most visually use the native tone of the output device directly. In these
pleasant halftone pattern can be generated b y the iterative m e areas of the output image, there will be no halftone
t h o d , l i k e Direct Bi- nary Search (DBS). DBS is texture. Consequently, as the gray value of the continuous-
computational inefficient, but it is widely used combined with tone image to be rendered changes smoothly, the output
other halftoning algorithms. Lin and Allebach invented the image transitions between regions with halftone texture
FM screen by DBS with the stacking constraint. a n d regions with no halftone texture. This may cause an
objectionable c o n t o u r i n g a r t i f a c t . To overcome this
Hybrid screen also use DBS to generate the blue- problem, i n t r o d u ce over modulation i mp le me nted via a
noise texture in the highlight and shadow regions. Tone lookup-table-based approach.
Dependent Error Diffusion trained the coefficients and Lin and Allebach ( 2 0 0 2 ) use a schedule-
thresholds by the blue-noise DBS pattern in Fourier domain. based framework to control the number of native tones
With the assistance of off-line design by DBS, screen or error used to render any specific gray level. Bacca Rodriguez
diffusion can significantly improve the halftone quality and (2008) implement stochastic, dispersed-dot m u l t i toning
remain the same computational complexity. by applying error diffusion to separate channels of the
image that has been decomposed according to the range
On the o t h e r h a n d , according the halftone of gray levels.
texture, we can also separate the multi toning a l g o r i t h m All theseapproaches use stochastic,
as AM, which is also called clustered-dot, and FM, which dispersed-dot halftone textures. They all do eliminate
is also called dispersed-dot. Using the modulation contouring, but at the expense of an increase in graininess
concepts in communication t h e o r y . We define the relative to traditional multi toning. In addition, the
multi characteristics of the halftone texture changes continually
toning as AM, when the pattern forms the clustered dots, as a function of gray level, which further increases the
as the absorptance g l o w s , which in Fourier domain visibility of these textures.
produces a donut-like band-pass green- noise filter [Allebach B.CLUSTERED DOT HYBRID SCREEN GEOMETRIC
et al (1996)]. However, FM halftone pattern generates the PARAMETERS
high-frequency blue noise in Fourier domain. Usually, Ink- In periodic screen multi toning, w e use a
jet can produce much more robust single dots, so it uses pair of linearly independent screen tile vectors z = [z1, z2
dispersed-dot multi toning more often. However, due to the
] and w = [w1, w2 ] to represent the parallelogram multi
instability of the single dots produced by electro- tone screen. The parallelogram multi tone screen limited by
photographical printers, t h e y use clustered-dot m u l t i those vectors can be called continuous- parameter multi
t o n i n g more often. Another classification of multi toning tone cell (CPMC). By repeatedly t i l i n g the CPMC, we
according to the texture is periodic or aperiodic. Screen is can cover the whole multi tone i ma g e by it. In digital
a periodic multi toning, while error diffusion and DBS are m u l t i t o n i n g , w e assume a printing d o t as a square
aperiodic. dot.
All four combinations ( AM/FM,
C.Microcell and Super cell
periodic/aperiodic, 2 × 2) are possible. Multi toning is Each microcell can represent |Ω| + 1
always used in the electro-photographic printers, b e ca u se gray levels 0, 1/|Ω|, 2/|Ω|, ..., (|Ω| − 1)/|Ω|, 1, by setting 0, 1,
the clustered- dot can provide more stable print and less dot- 2, ..., |Ω| − 1, |Ω|, pixels equal to 1, respectively. As the
gain effect. The printing devices which can generate more example mentioned a b o v e , only |Ω| = det|M| = |3 × (−3) −
stable pixels usually employ dispersed multi toning. Clustered
1 × 1| = 10 pixels are in that microcell. Then the output
periodic multi toning commonly provides more homogeneous
gray levels that c a n be rendered by that h a l f t o n e cell
structure in mid tone region than the
are limited by 10 + 1 = 11. We hope that t h e possible
+ −
tone texture i s shown as having levels α and α . For
gray levels can reach 256 or even larger, like 1024. a binary half toning p ro cess , these two levels would be
However, as |Ω| increases for an output device with fixed
spatial
resolution, the number of realizable gray levels α+ = 1 and α− = 0. Note that o u r choice of
prototype b i n a r y texture corresponds to a gray level of
increases; but the halftone texture becomes increasingly +
visible. 0.4 in absorptance units and the region with level α is a
Super cell techniques a l l o w one to achieve a 2 × 2 square. How- ever, our choice of the region with
greater number of output levels, while toning
still keeping |Ω| level α+ is not restricted t o square. It can be
relatively small. All the half methods to be rectangular as well, which as if it complies with the two
described in this paper will use the super cell method; In criteria as close as possible.
particular, we will use a variant of the super cell method,
known as the hybrid screen that generates high quality
stochastic,aperiodic, dispersed-dot textures in the
highlights and shadows that transition to periodic,
clustered-dot textures in the mid tones. There are two sets
of orders in the half toning s c r e e n . One is still the order
of the microcell. Another is the macro dot order which
represents the order among the microcell in one super
cell. Although most of the microcell or the tiling of
microcells, super cell, are not square or rectangular, we still
hope to represent a periodic screen as a rectangular, because it Fig 3.1 Prototype microcell p0 [m, n; a] and
would be more convenient to store or process in prototype m u l t i t o n e texture p [m, n; a].
the computer. G.Optimizing the Dot Profile Transition Order
D.DOT PROFILE FUNCTION In the previous section, we described a process
We will describe our half toning processes whereby the native tone values are alternately
in terms of the dot profile function p[m, n; a], which is the + −
halftone pattern used to represent each level of constant tone 0 incremented w i t h i n the regions Ω and Ω to maintain
≤ a ≤ 1, where level 0 denotes the absorptance of paper only t h e form of the prototype h a l f t o n e texture, as
with no colorant; and level 1 denotes the absorptance of the specified for example, by the index matrix illustrated in
Fig. 3.2. This determines t h e division of the indices 1, 2,
paper printed with the maximum amount of colorant. In the + −
subsection above, we let Ω denote a single period or unit cell ..., |Ω| between the two regions Ω and Ω . indices
of this pattern. We refer to Ω as a microcell as well. Each within these two regions. We also discussed, in general
microcell contains |Ω| = det(M) pixels. terms, the tradeoff between maintaining constancy of the
+ −
texture Specifically, {2, 4, 7, 9} ∈ Ω ; and {1, 3, 5, 6, 8, 10} ∈ Ω , as shown in Fig. 3.
E.Dot Hybrid Screen H.INTER-ITERATIVE CLU-DMS
Hybrid screen uses DBS to generate the CLU-DBS generated halftone clusters for a green-noise
property with the use of two-component cost function, which was majorly
blue-noise highlight gray levels and uses the periodic formulated by both initial filter ci p˜ p˜ [m, n] and update filter cu p˜ p˜ [m, n]. Its
clustered-dot screen to generate the homogenous mid tone purpose is to minimize the perceived errors between the continuous tone image f
[m, n] ∈ [0, 1] and the multi tone image g [m, n] ∈ {αi|0 ≤ αi ≤ 1}S i=1. There are
regions. Therefore, it is called ‟hybrid‟ screen. The most two main stages, trial and update, involved in the iterative process for each pixel of
significant concepts in the hybrid screen are super cell and an image. Prior to these stages, an initialization stage is required to form an initial
ci p˜e˜0 [m, n] with ci p˜ p˜ [m, n] for simulating the perceived error as ci p˜e˜0 [m,
core. We focus on the advantage o f using core. Because n] = e0 [m, n] ∗ ci p˜ p˜[m, n], where e0 [m, n] = g0 [m, n] − f [m, n], where the
the Bayer screen induces maze-like artifacts i n the operator „∗‟ denotes convolution, and g0 [m, n] denotes the initial multi tone
pattern for being optimized. Subsequently, the trial and update stages are performed
highlight region, the natural re- placement to it is the with a different filter cu p˜ p˜ [m, n] in opposed to the use of ci p˜ p˜ [m, n].
stochastic and blue-noise half toning like DBS. The strategy
here is that i n each microcell, we set up an area called
cores. In the cores, the microcell growth order is not
obeyed. Instead, p i x e l s grow randomly i n the cores
chosen DBS. What‟s more is that the macro dot growing
order is determined by the growing order of the first turned-
on p i x e l in each core.
F.Multilevel Clustered-dot, Periodic Multi toning
Our choice of the prototype h a l f t o n e texture that
we try to maintain across the entire tone scale is based
on two criteria: (1) it should be the texture that would
be used with a bi-level multi toning process to represent
a gray value near a = 1/2; and (2) it should have a
simple and regular geometric shape. The prototype half
 obtained for various possible absorptance levels η ∈ [0, 1]. To obtain a specific
multi tone screening output q [m, n] by threshold the stacking constraint is applied
during the screen construction: Iη [m, n] ≥ Iη−1/L [m, n], where L = 255 denotes
the maximum gray scale value [Chandu et al (2014)]

Fig. 3.2
Three steps to realize one-level-contrast multi toning .

I. INTER-ITERATIVE CLUSTERED-DOT DIRECT MULTI-

BIT SEARCH (CLU-DMS) SCREEN DESIGN
The method of generating stochastic clustered-
dots for a green-noise property preferred by laser printers is Fig. 3.4 Generated screening outputs of size 32 × 32 with
first introduced. Subsequently, the screen construction which Chandu et al.’s method (2014), where Dmin = 4. (a) η = 1/32.
exploits the benefits of generated homogenous multi tone
(b) η = 2/32. (c) η = 4/32. (d) η = 8/32. (e) η = 16/32. (f)
outputs is detailed.
η = 24/32. (g) η = 28/32. (h) η = 30/32. (i) η = 31/32.
J.INTER-ITERATIVE CLU-DMS
CLU-DBS generated halftone clusters for a green-noise IV EXISTING SIMULATION
property with the use of two-component cost function, which was majorly RESULTS A.HALF TONING
formulated by both initial filter ci p˜ p˜ [m, n] and update filter cu p˜ p˜ [m, n]. Its
purpose is to minimize the perceived errors between the continuous tone image f
Digital half toning is a technique for converting
[m, n] ∈ [0, 1] and the multi tone image g [m, n] ∈ continuous-tone images into binary images. These binary
{αi|0 ≤ αi ≤ 1}S i=1. There are two main stages, trial and update, involved in the images resemblethe original images when viewed from a
iterative process for each pixel of an image. Prior to these stages, an initialization
stage is required to form an initial ci p˜e˜0 [m, n] with ci p˜ p˜ [m, n] for simulating distance because ofthe low-pass nature of human visual
the perceived error as ci p˜e˜0 [m, n] = e0 [m, n] ∗ ci p˜ p˜[m, n], where e0 [m, n] =
g0 [m, n] − f [m, n], where the operator „∗‟ denotes convolution, and g0 [m, n] system (HVS).Many image rendering technologies only have
denotes the initial multi tone pattern for being optimized. Subsequently, the trial binary output. For example, printers can either “fire a dot” or
and update stages are performed with a different filter cu p˜ p˜ [m, n] in opposed to
the use of ci p˜ p˜ [m, n]. not. Halftoning is a method for creating the illusion of
continuous tone output with a binary device. Effective digital
halftoning can substantially improve the quality of rendered
images at minimal cost.

Fig 3.3 Algorithm for CLU-

DMS K.Screen Design
The screens can be decomposed into
multiple multi tone masks In generated by the proposed inter-
iterative CLU-DMS algorithm as introduced in Section 3.5
with the given f [m, n] = η. In a practical case of screening a
gray scale image with 256 tones, there are 256 masks Iη

Fig 4.1 Half Toning Input image

 Fig 4.2 Half Toning Output
image B. SPATIAL FREQUENCY
Spatial frequency refers to the level of detail
present in a stimulus per degree of visual angle. A scene with
small details and sharp edges contains more high spatial
frequency information than one composed of large coarse
stimuli.

Fig 4.5 Multi Toning Output image

Fig 4.3 Half Toning Spatial Frequency for Pixels/cycles

Fig 4.6 Multi Toning Spatial Freq For Cycles

Fig 4.4 Half Toning Threshold Values

Multi-Toning Technique:
The first multi tone screening method to generate Fig 4.7 Multi Toning Threshold Values
stochastic clustered-dots for a much better visual quality. The V CONCLUSION AND FUTURE
pixel validation map is mainly utilized to restrain the possible WORK A.CONCLUSION
dot growing region to form dot clusters. In this method, the In this work, the inter-iterative CLU-DMS is
quantization error at each pixel was diffused to neighbors for proposed to design screens for the generation of stochastic
error compensation. clustered dot multi tone results. For the optimization, the tactic
of coordinating intra-iteration and inter-iteration is proposed to
circumvent the potential issue of trapping in a local minimum
cost in the conventional approaches such as DBS and CLU-
DBS. Formerly, simply one inter-iteration is involved in the
conventional methods. This works for the DBS since the terms
in its cost function are updated for approaching the minimum
cost. Yet, this is not feasible for CLU-DBS, since the
optimized output highly relies on the initial multi tone pattern.
To ease this effect and achieve a greater clustering rendition,
the inter-iteration method is proposed to ensure that the initial
multi tone pattern can also be gradually updated to form a
uniformly distributed cluster. As documented in the
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In this method, the quantization error at each pixel was Capturing Images, Systems (PICS) Conference
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[11] P.Allebach and Q.Lin, “FM screen design using DBS
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[12] C. H. Lee and J. P. Allebach,(2012) “The hybrid
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