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Only Size needs to be Huffman coded in the above scheme, since, within a given Size, all the input values havesufficiently similar probabilities for there to be little gain from entropy coding the Additional Bits (hence they are codedin simple binary as listed). Each coded Size is followed by the appropriate number of Additional Bits (equal to Size) todefine the sign and magnitude of the coefficient difference exactly.

There are only 12 Sizes to be Huffman coded, so specifying the code table can be very simple and require relatively few bitsin the header.

In JPEG all Huffman code tables are defined in the image header. Each table requires 16 n bytes, where n is the number of codewords in the table.

The first 16 bytes list the number of codewords of each length from 1 to 16 bits (codewords longer than 16 bits areforbidden). The remaining n bytes list the decoded output values of the n codewords in ascending codeword order ( n 256 ).

Hence 16 12 28 bytes are needed to specify the code table for DC coefficients.

The jpeg run-amplitude code

The remaining 63 coefs (the AC coefs) of each 64-element vector usually contain many zeros and so are coded with acombined run-amplitude Huffman code.

The codeword represents the run-length of zeros before a non-zero coef and the Size of that coef. This is then followed by the Additional Bits whichdefine the coef amplitude and sign precisely. Size and Additional Bits are defined just as for DC coefs.

This 2-dimensional Huffman code (Run, Size) is efficient because there is a strong correlation between the Size of acoef and the expected Run of zeros which precedes it - small coefs usually follow long runs; larger coefs tend to followshorter runs. No single 2-D event is so probable that the Huffman code becomes inefficient.

In order to keep the code table size n below 256, only the following Run and Size values are coded: Run 0 15 Size 1 10 These require 160 codes. Two extra codes, corresponding to (Run,Size) = (0,0) and (15,0) are used for EOB (End-of-block)and ZRL (Zero run length).

EOB is transmitted after the last non-zero coef in a 64-vector. It is the most efficient way of coding the finalrun of zeros. It is omitted in the rare case that the final element of the vector is non-zero.

ZRL is transmitted whenever Run 15 , and represents a run of 16 zeros (15 zeros and a zero amplitude coef) which can be part of a longer run of anylength. Hence a run of 20 zeros followed by -5 would be coded as

(ZRL) (4,3) 010

When the code tables are defined in the image header, each codeword is assigned to a given (Run,Size) pair by making thedecoded output byte Code Byte equal to ( 16 Run Size ).

The default JPEG code for (Run,Size) of AC luminance DCT coefficients is summarised below in order of decreasing codeprobability:

(Run,Size) Code Byte (hex) Code Word (binary) (Run,Size) Code Byte (hex) Code Word (binary)
(0,1) 01 00 (0,6) 06 1111000
(0,2) 02 01 (1,3) 13 1111001
(0,3) 03 100 (5,1) 51 1111010
(EOB) 00 1010 (6,1) 61 1111011
(0,4) 04 1011 (0,7) 07 11111000
(1,1) 11 1100 (2,2) 22 11111001
(0,5) 05 11010 (7,1) 71 11111010
(1,2) 12 11011 (1,4) 14 111110110
(2,1) 21 11100
(3,1) 31 111010 (ZRL) F0 11111111001
(4,1) 41 111011

As an example, let us code the following 8 8 block: -13 -3 2 0 0 0 1 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Concerting this to (DC Size) or (Run,Size) and values for the Additional Bits gives:

(4) -13 (0,2) -3 (0,3) 6 (2,2) 2 (3,1) -1 (ZRL) (1,1) 1 (EOB) 101 0010 01 00 100 110 11111001 10 111010 0 11111111001 1100 1 1010

The compressed bitstream for this block is listed on the lower line, assuming that the default Huffman code tables, givenabove, are used.

shows the histogram of probabilities for the (Run,Size) codewords used to code Lennausing the Q lum quantisation matrix. The bin number represents the decoded byte value.

shows the equivalent histogram when the quantisation matrix is 2 Q lum .

Histogram of the (Run,Size) codewords for the DCT of Lenna, quantised using Q lum .
Histogram of the (Run,Size) codewords for the DCT of Lenna, quantised using 2 Q lum .

Note the strong similarity between these histograms, despite the fact that represents only 2 3 as many events. Only the EOB probability changes significantly, because its probability goes up as the number of events (non-zero coefs) per block goes down.

It turns out that the (Run,Size) histogram remains relatively constant over a wide range of image material and acrossdifferent regions of each image. This is because of the strong correlation between the run lengths and expected coefsizes. The number of events per block varies considerably depending on the local activity in the image, but theprobability distribution of those events (except for EOB) changes much less.

and also give the mean bit rates to code Lenna for the two quantisation matrices. Comparingthese with the theoretical entropies from this figure (lower row) we get:

Q matrix Mean Entropy (b/pel) JPEG Bit Rate (b/pel) JPEG efficiency
Q lum 0.8595 0.8709 98.7%
2 Q lum 0.5551 0.5595 99.21%

Hence we see the high efficiency of the (Run,Size) code at two quite different compression factors. This tends to apply overa wide range of images and compression factors and is an impressive achievement.

There is even very Little efficiency lost if a single code table is used for many images, which can avoid the need totransmit the 16 n (168 bytes) of code definition in the header of each image. Using the recommended JPEG default luminance tables(Annex K.3.3) the above efficiencies drop to 97.35% and 95.74% respectively.

Questions & Answers

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
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
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
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Image coding. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10206/1.3
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