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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

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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