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Depending on the pixel size, you sometimes need to view a halftoned image from a short distance to appreciate the effect. The natural filtering (blurring) of the visual system allows you to perceive many different shades, even though the only colors displayed are black and white!
Random noise binarization.

Ordered dithering

Halftone images are binary images that appear to have a gray scale rendition.Although the random thresholding technique described in "Binary Images" can be used to produce a halftone image, it is not often used in real applications since it yields very noisy results.In this section, we will describe a better halftoning technique known as ordered dithering .

The human visual system tends to average a region around a pixel instead of treating each pixel individually, thusit is possible to create the illusion of many gray levels in a binary image, even though there are actually only two gray levels.With 2 × 2 binary pixel grids, we can represent 5 different “effective” intensity levels, as shown in [link] . Similarly for 3 × 3 grids, we can represent 10 distinct gray levels. In dithering, we replace blocks of the original image with these typesof binary grid patterns.

Five different patterns of 2 × 2 binary pixel grids.

Remember from "Binary Images" that false contouring artifacts can be reduced if we can reduce the signal dependence or the quantization error.We showed that adding uniform noise to the monochrome image can be used to achieve this decorrelation. An alternative methodwould be to use a variable threshold value for the quantization process.

Ordered dithering consists of comparing blocks of the original image to a 2-D grid, known as a dither pattern . Each element of the block is then quantized using the corresponding valuein the dither pattern as a threshold. The values in the dither matrix are fixed, but are typically different from each other. Because the thresholdvalue varies between adjacent pixels, some decorrelation from the quantization erroris achieved, which has the effect of reducing false contouring.

The following is an example of a 2 × 2 dither matrix,

T ( i , j ) = 255 * 5 / 8 3 / 8 1 / 8 7 / 8

This is a part of a general class of optimum dither patterns known as Bayer matrices . The values of the threshold matrix T ( i , j ) are determined by the order that pixels turn "ON".The order can be put in the form of an index matrix . For a Bayer matrix of size 2, the index matrix I ( i , j ) is given by

I ( i , j ) = 3 2 1 4

and the relation between T ( i , j ) and I ( i , j ) is given by

T ( i , j ) = 255 ( I ( i , j ) - 0 . 5 ) / n 2

where n 2 is the total number of elements in the matrix.

[link] shows the halftone image produced by Bayer dithering of size 4.It is clear from the figure that the halftone image provides good detail rendition. Howeverthe inherent square grid patterns are visible in the halftone image.

The halftone image produced by Bayer dithering of size 4.

Error diffusion

Another method for halftoning is random dithering by error diffusion . In this case, the pixels are quantized in a specificorder (raster ordering Raster ordering of an image orients the pixels from left to right, and then top to bottom. This is similar to the order that a CRT scans theelectron beam across the screen. is commonly used), and the residual quantization error for the current pixel is propagated (diffused) forward tounquantized pixels. This keeps the overall intensity of the output binary imagecloser to the input gray scale intensity.

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
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Source:  OpenStax, Purdue digital signal processing labs (ece 438). OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col10593/1.4
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