Pmmc Ch3 Completed (06.03.11)

7/31/2019 Pmmc Ch3 Completed (06.03.11)

1/46

3.TEXT AND IMAGE COMPRESSION

INTRODUCTION.

COMPRESSION PRINCIPLES.

TEXT COMPRESSION.

IMAGE COMPRESSION.


2/46

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


3/46

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.


4/46

1. Source encoders and Destination decoders.

Compression algorithm and Decompression algorithm.


5/46

Source encoders and Destination decoders contd


6/46

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.


7/46

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.


8/46

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


9/46

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.


10/46

TRANSFORM ENCODING: involves transforming the source fromone form into another


11/46

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.


12/46


13/46

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


14/46

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:


15/46


16/46


17/46

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.


18/46

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 ).


19/46

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.


20/46

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 :-


21/46


22/46

Dynamic mode using LZWcoding


23/46


24/46

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).


25/46

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.


26/46

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 :-


27/46

Flow chart.


28/46

JPEG contd.. :-


29/46

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


30/46


31/46

Block preparation


32/46

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.


33/46

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


34/46

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.


35/46


36/46

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


37/46

4. Entropy Encoding

This stage comprises 4 steps, they are:

1. Vectoring

2. Differential encoding

3. Run-length encoding

4. Huffman encoding


38/46

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.


39/46

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.


40/46


41/46


42/46


43/46


44/46


45/46


46/46

Documents

Pmmc Ch3 Completed (06.03.11)