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TRANSCRIPT
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3.TEXT AND IMAGE COMPRESSION
INTRODUCTION.
COMPRESSION PRINCIPLES.
TEXT COMPRESSION.
IMAGE COMPRESSION.
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INTRODUCTION
In almost all multimedia application a technique known as
compression is first applied prior to its transmission.
Why Do We Need Compression?
Requirements may outstrip the anticipatedincrease of storage space and bandwidthFor data storage and data transmission
- DVD- Video conference- Printer
The bit rate of uncompressed digital cinema
data exceeds 1 Gbps
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COMPRESSION PRINCIPLES
Compression is done either to reduce the VOLUME of
information to be transmitted ( text, fax or images) or to reduce
the BAND-WIDTH that is required for its transmission.
Different compression principles are:
Source encoders and Destination decoders.
Lossless and Lossy compression.
Entropy encoding.
Source encoding.
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1. Source encoders and Destination decoders.
Compression algorithm and Decompression algorithm.
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Source encoders and Destination decoders contd
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2. Lossless and Lossy compression.
Lossless compression algorithm is used to reduce
the amount of source information to be transmitted and to
decompress the information without any losses. It is also
called as REVERSIBLE.
Lossy compression algorithm does not reproduce an
exact copy of the source information but rather a version ofit which is perceived by the recipient as a true copy.
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3. Entropy encoding.
It is a lossless and independent type of compression it is
concerned with how the information is represented. It includes
two widespread algorithm, they are:
1. Run-length encoding : Source information comprises long
sub-strings of same character or binary digit.
2. statistical encoding : It exploits the property of using a
variable length code words. In this encoding the destination must
aware of code words set. A code word set that avoids the wrongcode word is said to posses the PREFIX PROPERTY.
HAFFUMAN CODING is the better example of having a
prefix property.
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Minimum average number of bits that are required to transmit a sourcestream is known as ENTROPY and can be coded by using
SHANNON ENTROPY formula.
entropy (H)= Pi log 2 (Pi)N number of different symbols
Piprobability of occurrence of symbol I.
Efficiency is the ratio ofentropy of source to the average
number of bits per codeword
Average number of bits per codeword is = Ni Pi
Problem (1) pg no. 142
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4. Source encoding.
It uses an alternative form of representation of a compressed version
of original information. This can be used in two ways, they are:
1. Differential encoding.
2. Transform encoding.
DIFFERENTIAL ENCODING: in this type of encoding, instead of
using a set of relatively large code words, a set of small code words
is used which indicates only the difference in amplitude between the
current value and the next Immediately preceding value.
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TRANSFORM ENCODING: involves transforming the source fromone form into another
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Rate of change in magnitude as one transverses the matrix
gives rise to a term known as SPATIAL FREQUENCY.
DISCRETE COSINE TRANSFORM (DCT) is used as
mathematical analysis for transferring of 2-D matrix.
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TEXT COMPRESSION:-
All the three types of text are represented as string of characters
selected from a defined set.
any compression algorithm associated with text must be lossless
.
text compression uses statistical encoding.
For the text compression this statistical encoding can be used in
mainly in three types, they are HUFFMAN CODING
ARITHMETIC CODING
LEMPEL-ZIV (LZ) CODING
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HUFFMAN CODING
Huffman coding is a type of text compression which can be
clearly analyzed by static Huffman coding and Dynamic
Huffman coding.
STATIC HUFFMAN CODING: character string is first
analyzed and their relative frequency is determined. Coding
involves creating an unbalanced tree with some branches shorter
than others.
DYNAMIC HUFFMAN CODING:
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ARITHMETIC CODING
Huffman coding achieves shannon value only if the
character or the symbol are all integers of (1/2). And set
codeword obtained are optimum
ARITHMETIC CODING results a set of codewords
sent as a block of data known as binary arithmetic coding.
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LEMPEL-ZIV CODING
Instead of using a single character we are using a strings
of characters. The occurrence of the character in the text to be
transmitted is held by both the encoder and decoder in a table.
This table is used as dictionary and the LZ algorithm is known as
Dictionary based compression algorithm.
LEMPEL-ZIV- WELSH CODING
This algorithm is used to build the contents of thedictionary dynamically as the text being transferred . Initially
the encoder and decoder uses the character that has been used
to create the text. The remaining entries are then built up
dynamically by both ( the encoders and decoders ).
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IMAGE COMPRESSION:-
Images are of two types, they are:
1. Computer generated (Graphical) images are represented via a
form of program written in a particular graphics programming
languages.
2. Digitized images (both document & picture) 2-D matrix
representation is used.
There are several formats used to compress the image and
are sent via a network to the destination. Mainly run length and
statistical coding, transform and differential coding is used.
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It is used extensively with the INTERNET for the
representation and compression of the graphical images. The color
images uses 24 pels of 8-bits each for R,G and B by selecting 256
colors from the original set.
Instead of sending each pels as a 24-bit value only 8-bit
index to the table entry is sent.
This table of colors relate either to the whole image {global
color table} or to a portion of the image (local color table}.
LZW coding algorithm is used.
Graphics Interchange Format :-
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Dynamic mode using LZWcoding
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DIGITIZED DOCUMENT :-
Scanned lines consist only of long strings of white picture
element while other comprise a mix of long strings of
white pels and long string of black pels. Facsimile machie
is the best example of this format.
ITU-T has produced standards they are:
1. T2(group1)
2. T3(group2)
3. T4(group3)
4. T6(group4).
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DIGITIZED DOCUMENT contd.. :-
Codeword are fixed and grouped in to 2 separate tables, they are
1. The termination code table: are for white and black run-length
of from 0 to 63 pels
2. Make-up codes table : code words for white or black run length
that are multiples of 64 pels
Run-length coding are associated with a coding line as one of the three
possibilities or modes they are
1. Pass mode.
2. vertical mode.
3. horizontal mode.
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DIGITIZED PICTURE :-
The most widely adopted standard relating to the compression
of digitized picture has been introduced by an international
standard body known as Joint Photographic Experts Group
(JPEG).
It is a standard that was developed by a team of experts working
on behalf of ISO, The ITU, & the TEC. JPEG is defined in theinternational standards IS10918.
JPEG defines a number of format (modes), we will study only the
lossy sequential mode used in this case. This mode is also known
as BASELINE MODE.
JPEG :-
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Flow chart.
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JPEG contd.. :-
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JPEG contd.. :-
There are 5 different stages associated with this mode,
they are
1. Image / block representation.
2. Forward DCT.
3. Quantization.
4. Entropy encoding .5. Frame building
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Block preparation
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2. Forward DCT
P[x,y] is the input 2-D matrix. F[i,j] is the transformed matrix.
C(i) and c(j) = For I,j=0
= 1 for all other value of I & j.
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2. Forward DCT contd..
The following steps are remembered during the DCT:
1. All 64 values in the input p[x,y] contributes to each entry in
the transformed matrix f[i,j].
2. For i=j=0, two cosine terms are 0. the value in the location
f[0,0] of the transformed matrix is a summation of all the
values in the input. It is the mean of all the values in the
matrix and is known as DC-COEFFICIENTS.
3. All the other values has the coefficients either in horizontal
(x=1-7 for y=0), vertical (x=0 for y=1-7)or both (x=1-7 for
y=1-7) they are known as AC-COEFFICIENTS
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2. Forward DCT contd..
4. If j=0, only horizontal frequency components are presented
for i=1-7. If i=0, only vertical frequency components are
presented for j=1-7.
5. In other loaction both horizontal and vertical frequencycomponents are present to varying degree.
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Example: assuming a quantization threshold value of 16, derive
the resulting quantization error for each of the following DCT
co-efficient of 127,72,64,56,-56,-64,-72,-128.
Co-efficient
Quantizedvalue
Roundedvalue
Dequantizedvalue
Error
127 127/16=7.937
8 128 -1
72 4.5 5 80 -8
64 4 4 64 0
56 3.5 4 64 8
-56 -3.5 -4 -64 -8
-64 -4 -4 -64 0
-72 -4.5 -5 -80 -8
-128 -8 -8 -128 0
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4. Entropy Encoding
This stage comprises 4 steps, they are:
1. Vectoring
2. Differential encoding
3. Run-length encoding
4. Huffman encoding
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5. Frame Building
Frame building is to encapsulate all the information relating toan encoded image / picture. It consists of the parameters like, at
the top level the complete frame plus header is encapsulated
between a start of frame and a end of frame.
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5. Frame Building contd..
Frame header contains:
1. Overall width and height of the image in pixels.
2. Number & type of component that are used to represent the
image (CLUT, R/G/B, Y/Cb/Cr).
3. Digitization format used (4:2:2, 4:2:0).
At second level the frame consist of :
1. Identity if the components used.
2. Number of bits used to digitize each component.
3. Quantization table of values that have been used to encode
each component.
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