Compression and Decompression techniques

7/27/2019 Compression and Decompression techniques

1/68

By:

Shubhra goyal


2/68

Definition

Why Compression

Types of compression Binary image compression scheme

Video image compression

Audio image compression Fractal image compression


3/68

Compression: the process of coding that will

effectively reduce the total number of bits

needed to represent certain information.

Encoder

(compression)storage

decoder

(decompression)

Input

data

output

data


4/68

compression is possible due to:

Redundancy in digital audio, image, and video data(silence removal, spatial redundancy, temporalredundancy)

Properties of human perception.

(Compressed version of digital audio, image, video

need not represent the original information exactly

Perception sensitivities are different for different signal

patterns

Human eye is less sensitive to the higher spatial

frequency components than the lower frequencies

(transform coding)

)


5/68

Video and audio have much higher storage

requirements than text.

Data transmission rates (in terms of bandwidthrequirements) for sending continuous media

are considerably higher than text.

Efficient compression of audio and video data,

including some compression standards, will be

considered in this lesson.


6/68


7/68

Data compression is about storing and sending a smaller number

of bits. Therere two major categories for methods to compress data:

lossless and lossy methods

Data compression

methods

Lossless

methodsLossy methods

Run-

lengt

h

LZW

Ccitt

grp 3

2D

Ccitt

grp 4

Ccitt grp

3 1 DJPEG Ccitt

h.261

fractals

Intel

DVIMPEG


8/68

In lossless methods, original data and the data after compression anddecompression are exactly the same.

Redundant data is removed in compression and added during decompression.

It achieve reduction in size in the range of 1/10 to 1/50 of the originaluncompressed size.

Lossless methods are used when we cant afford to lose any data: eg. TextCompression like legal and medical documents, computer programs.


9/68

There are five common lossless methods:

Run length encoding

CCITT Group 3 1D

CCITT Group 3 2D

CCITT Group 4

Lempel-Ziv and welch algorithm LZW


10/68

Run-length encoding is the simplest method of

compression.

It can be used to compress data made of any

combination of symbols.

The general idea behind this method is to replace

consecutive repeating occurrences of a symbol by one

occurrence of the symbol followed by the number of

occurrences.

The method can be even more efficient if the data uses

only two symbols (for example 0 and 1) in its bit

pattern and one symbol is more frequent than the other.


11/68


12/68

This is disadvantageous for a busy image. In busyimage, adjacent pixels or groups of adjacent pixelschange rapidly. These lead to shorter run lengths of

black pixels or white pixels.

In this, it could take more bits for the code torepresent the run length which generates more

bytes than the original number of bytes in animage.

This effect is called as reverse compression ornegative compression.

It was designed for black and white images only,not for gray scale or color images.


13/68

Many facsimile and document imaging file formatssupport a form of lossless data compression oftendescribed as CCITT encoding.

The CCITT (International Telegraph and Telephone

Consultative Committee) is a standards organizationthat has developed a series of communications

protocols for the facsimile transmission of black-and-white images over telephone lines and data networks.

The CCITT actually defines three algorithms for the

encoding of image data:

Group 3 One-Dimensional (G31D)

Group 3 Two-Dimensional (G32D)

Group 4 (G4)


14/68

Huffman encoding is used for encoding the pixel run length in CCITT

Group 3 and Group 4.

It is a variablelength encoding scheme generating the shortest code for

frequently occurring run lengths and longer code for less frequently

occurring run lengths.

Algorithm:

Make a leaf node for each code symbol

Add the generation probability of each symbol to the leaf node

Take the two leaf nodes with the smallest probability and connectthem into a new node

Add 1 or 0 to each of the two branchesThe probability of the new node is the sum of the probabilitiesof the two connecting nodes

If there is only one node left, the code construction is completed. Ifnot, go back to (2)


15/68


16/68


17/68


18/68


19/68


20/68

Advantages

- it is simple to implement in both hardware

and software.

Disadvantages

- it is one-dimensional as it encodes each row or

line separately.

- it assumes a reliable communication link and does

not provide any protection mechanism.


21/68

CCITT Group 3 - 2D compression scheme is also known asmodified run-length encoding. This scheme is morecommonly used for software based document imagingsystem.

While CCITT Group 3- 2D scheme provides fairly goodcompression, it is easier to compress in software thanCCITT Group 4 standard. The compression ratio averagessomewhere between 10-25, between Group 3 and Group 4.

The compression scheme is based on statistical nature ofimages. For example, the image data across the adjacentscan line may normally be redundant, if black and whitetransitions occur within plus or minus 3 pixels in the nextline as well. Depending upon the scan resolution one line oftext may consist of 20-30 scan lines.


22/68

2 dimensional coding

Images are divided into several groups of K lines

the first line of each group is encoded using CCITT Group 3 1D method

The rest of lines are encoded using some "differential schemes"

Typically compression ratio 10 ~ 20

The "K-factor" allows more error-free transmission World-wide fassimile standard

The 2D scheme uses a combination of additional codes called vertical code,

pass code, and horizontal code.

Only one pass code, i.e. 0001 and one horizontal code, i.e. 001

If vertical code and horizontal code are not applied, then the horizontal code is

applied.

Horizontal Code + Group 3 1D Code = 001 + markup code + terminating code


23/68


24/68

Parse the coding line and look for the change in the

pixel value. The pixel value change is found at the

a1 location (a1 is the indicator that the pixel

changed from binary 0 to binary 1.)

Parse the reference line and look for the change in

the pixel value. The change is found at the b1

location.

Find the difference in the location between b1 anda1: Delta = b1-a1.


25/68


26/68


27/68


28/68

Advantages

- the implementation of the K factor allows

error-free transmission.

- it is a worldwide facsimile standard.- due to its 2-dimensional nature, the compressionratios achieved with this scheme are better thanCCITT Group 3 1D.

Disadvantages- it does not provide a dense compression

- it is complex and relatively difficult to implementin software.


29/68

The compression ratio was not sufficient for serious, high-

resolution document imaging.

This is a 2D coding scheme without the k-factor, the k-factor in

this scheme is the entire page of lines.

Here, the first reference line is an imaginary all-white line abovethe top of the image.

The first group of pixels is encoded using the imaginary white line

as reference line.

The new coded line becomes the reference line for the next scan

line. Each successive line is coded relative to the previous line.

This provides very large level of compression


30/68


31/68

There are no EOL markers before the start of

the compressed data.

Fillers are not used for the scan line .There is an EOP (End-Of-Page) mark consisting

of

- two concatenated EOLs

- padding bits are added immediately

after the end of compressed data


32/68


33/68

Advantages:

- Better resolution

Disadvantages:

- Slow- Complex

- As there is no reference line, a single error

error can result in the rest of the pagebeing skewed.


34/68


35/68

It is dictionary-basedencoding algorithm.

It creates a dictionary (a table) of strings used during

the communication session.

If both the sender and the receiver have a copy of the

dictionary, then previously-encountered strings can be

substituted by their index in the dictionary to reduce

the amount of information transmitted.


36/68

In this phase there are two concurrent events:

- building an indexed dictionary and

- compressing a string of symbols.

The algorithm extracts the smallest substring that

cannot be found in the dictionary from the remaininguncompressed string.

It then stores a copy of this substring in the dictionary

as a new entry and assigns it an index value.

Compression occurs when the substring, except for thelast character, is replaced with the index found in the

dictionary.

The process then inserts the index and the last

character of the substring into the compressed string.


37/68


38/68

Decompression is the inverse of the compression

process.

The process extracts the substrings from the

compressed string and tries to replace the indexes with

the corresponding entry in the dictionary, which is

empty at first and built up gradually.

The idea is that when an index is received, there is

already an entry in the dictionary corresponding to that

index.


39/68


40/68

Used for compressing images and video

files (our eyes cannot distinguish subtle

changes, so lossy data is acceptable).

These methods are cheaper, less time andspace.

Several methods: JPEG: compress pictures and graphics

MPEG: compress video MP3: compress audio


41/68

Color characteristics:

Luminance : This is the measure of the light

emitted or reflected by an object.

Hue: This is the color sensation producedin an observer due to the presence of certain

wavelengths of color.

Saturation: Depth of a color

Difference between red and pink


42/68

A color model is an orderly system for creating a

whole range of colors from a small set of primary

colors.

There are two types of color models,

- Subtractive

- Additive

Additive color models use light to display color while

subtractive models use printing inks.

Colors perceived in additive models are the result oftransmitted light. the typical technique

on color displays.

Colors perceived in subtractive models are the result of

reflected light, the typical technique in printers/plotters.


43/68

CMYK model:

The Cyan ,Magenta ,Yellow and Black (CMYK)

model is used in color printing devices.

It is a color subtractive model.HSI MODEL (HSB MODEL):

The Hue, Saturation and Intensity model

represents tint, shade and tone.

This model is used in IP for filtering and

smoothing images.

Requires high level of computation


44/68

YUV MODEL:

Its a 3-D and Subtractive model.

Y is Luminance component

UV is chrominance components.

Used in full motion video.

Black and white

information

Coloured information

U = red-cyan

V= magenta-green


45/68

RGB Model:

This model is additive in

nature.intensities of Red, Green and Blue

are added to generate various colors.

Used in design of image capture devices,

television, and color monitors.

No color model is better than the other,the choice depends on the application


46/68

Color component conversion

Y 0.299R + 0.587G + 0.114B

U 0.596R 0.247G 0.322B

V 0.211R 0.523G + 0.312B

Color component conversion

R 1.0Y + 0.956U + 0.621V

G 1.0Y 0.272U 0.647V

B 1.0Y -1.1061U 1.703V


47/68

JPEG standard is a collaboration among :

International Telecommunication Union (ITU)

International Organization for Standardization

(ISO)

International Electrotechnical Commission

(IEC)

The official names of JPEG :

Joint Photographic Experts Group ISO/IEC 10918-1 Digital compression and coding

of continuous-tone still image

ITU-T Recommendation T.81


48/68

It should address image quality where visual

fidelity is very high and an encoder can be

parameterized to allow the user to set the

compression or the quality level.

Should compress any kind of continuous-tone

digital source image and is not restricted by

dimensions, color, aspect ratios etc.

Should be scalable from completely losslessto lossy.


49/68

Four operation modes: Sequential encoding component is encoded

in left to right and top to bottom scan.

Progressive encoding the image is

decompressed so that a coarser image isdisplayed first and filled in with more

components when decompressed to a finer

version of the image.

Hierarchical encoding- the image iscompressed to multiple resolution levels.

Lossless encoding the image can be

guaranteed to provide full detail at the

selected resolution when decompressed.


50/68

A codecis a device or computer program

capable of encoding and decoding a digital

stream of data or signal.

They differ within an operation modeaccording to the precision of source image

they can handle or the entropy coding

method they use.


51/68

It have three levels of defination:Baseline System- it decompress color images,

maintain a high compression ratio, and handle

from 4 bits/pixels to 16 bits/pixels. It ensures s/w

implementation are cost effective.Extended System it covers various encoding

aspects such as variable-length, progressive and

hierarchical mode of encoding.

Special Lossless function it ensures there is noloss of detail in the compression and

decompression process, but there is some loss in

scanning process.


52/68

Baseline sequential codec- It consist of three steps:

formation of DCT coefficients, quantization, andentropy encoding. Itsa rich compression scheme.

DCT progressive mode- key steps of DCT coefficients

and quantization are same as above with a diff. that

each component is coded in multiple scans instead ofsingle scan.

Predictive lossless encoding-defines a means of

approaching lossless continuous-tone compression.

Predictor combines sample areas and predictsneighboring areas.

Hierarchical mode- provides a means of carrying

multiple resolutions. Each successive encoding is

reduced by a factor of two, either in horizontal orvertical dimension.


53/68


54/68

The main steps in JPEG encoding are the following

Transform RGB to YUV or YIQ and subsample color

DCT on 8x8 image blocks

Quantization

Zig-zag ordering and run-length encoding

Entropy coding


55/68

The image is divided up into 8x8 blocks

2D DCT is performed on each block

The DCT is performed independently for each

block

This is why, when a high degree of compression is

requested, JPEG gives a blocky image result


56/68

7 7

0 0

1 (2 1) (2 1)( , ) ( ) ( ) ( , )cos cos

4 16 16

for 0,...,7 and 0,...,7

x y

x u y vF u v C u C v f x y

u v

1/ 2 for 0where ( )

1 otherwise

kC k

7 7

0 0

1 (2 1) (2 1)( , ) ( ) ( ) ( , )cos cos

4 16 16

for 0,...,7 and 0,...,7

u v

x u y vf x y C u C v F u v

x y

Forward DCT:

Inverse DCT:


57/68


58/68

0 1 2 3 4 5 6 70

1

2

3

4

5

6

7

u

v


59/68

Y

the luminance of an image

W

H

8x8 values of luminance

48 39 40 68 60 38 50 121

149 82 79 101 113 106 27 62

58 63 77 69 124 107 74 125

80 97 74 54 59 71 91 66

18 34 33 46 64 61 32 37

149 108 80 106 116 61 73 92

211 233 159 88 107 158 161 109

212 104 40 44 71 136 113 66

DCT699.25 43.18 55.25 72.11 24.00 -25.51 11.21 -4.14

-129.78 -71.50 -70.26 -73.35 59.43 -24.02 22.61 -2.05

85.71 30.32 61.78 44.87 14.84 17.35 15.51 -13.19

-40.81 10.17 -17.53 -55.81 30.50 -2.28 -21.00 -1.26

-157.50 -49.39 13.27 -1.78 -8.75 22.47 -8.47 -9.23

92.49 -9.03 45.72 -48.13 -58.51 -9.01 -28.54 10.38

-53.09 -62.97 -3.49 -19.62 56.09 -2.25 -3.28 11.91

-20.54 -55.90 -20.59 -18.19 -26.58 -27.07 8.47 0.31


60/68

Quantization in JPEG aims at reducing the

total number of bits in the compressed image

Divide each entry in the frequency space block

by an integer, then round

Use a quantization matrix Q(u, v)


61/68

Use larger entries in Q for the higher spatialfrequencies These are entries to the lower right part of the

matrix

The following slide shows the default Q(u, v)values for luminance and chrominance Based on psychophysical studies intended to maximize

compression ratios while minimizing perceptualdistortion

Since after division the entries are smaller, we can usefewer bits to encode them


62/68


63/68

F(u,v)8x8 DCT coefficiences

16 11 10 16 24 40 51 61

12 12 14 19 26 58 60 55

14 13 16 24 40 57 69 56

14 17 22 29 51 87 80 62

18 22 37 56 68 109 103 77

24 35 55 64 81 104 113 92

49 64 78 87 103 121 120 101

72 92 95 98 112 100 103 99

Q(u,v)Quantization matrix

699.25 43.18 55.25 72.11 24.00 -25.51 11.21 -4.14

-129.78 -71.50 -70.26 -73.35 59.43 -24.02 22.61 -2.05

85.71 30.32 61.78 44.87 14.84 17.35 15.51 -13.19

-40.81 10.17 -17.53 -55.81 30.50 -2.28 -21.00 -1.26

-157.50 -49.39 13.27 -1.78 -8.75 22.47 -8.47 -9.23

92.49 -9.03 45.72 -48.13 -58.51 -9.01 -28.54 10.38

-53.09 -62.97 -3.49 -19.62 56.09 -2.25 -3.28 11.91-20.54 -55.90 -20.59 -18.19 -26.58 -27.07 8.47 0.31


64/68

43.70 3.93 5.52 4.51 1.00 -0.64 0.22 -0.07-10.82 -5.96 -5.02 -3.86 2.29 -0.41 0.38 -0.04

6.12 2.33 3.86 1.87 0.37 0.30 0.22 -0.24

-2.91 0.60 -0.80 -1.92 0.60 -0.03 -0.26 -0.02

-8.75 -2.25 0.36 -0.03 -0.13 0.21 -0.08 -0.12

3.85 -0.26 0.83 -0.75 -0.72 -0.09 -0.25 0.11

-1.08 -0.98 -0.04 -0.23 0.54 -0.02 -0.03 0.12

-0.29 -0.61 -0.22 -0.19 -0.24 -0.27 0.08 0.00

( , )( , )

F u vQ u v

44 4 6 5 1 -1 0 0

-11 -6 -5 -4 2 0 0 0

6 2 4 2 0 0 0 0

-3 1 -1 -2 1 0 0 0

-9 -2 0 0 0 0 0 0

4 0 1 -1 -1 0 0 0

-1 -1 0 0 1 0 0 0

0 -1 0 0 0 0 0 0

( , )

( , )( , )

qF u v

F u vRoundQ u v


65/68

0 1 5 6 14 15 27 28

2 4 7 13 16 26 29 42

3 8 12 17 25 30 41 43

9 11 18 24 31 40 44 53

10 19 23 32 39 45 52 54

20 22 33 38 46 51 55 60

21 34 37 47 50 56 59 61

35 36 48 49 57 58 62 63

The zigzag sequence starts at the DC coefficient value.It is designed to facilitate entropy coding by placing low-frequency

coefficients (which are non- zero) before high frequency coefficients.


66/68

44 4 6 5 1 -1 0 0

-11 -6 -5 -4 2 0 0 0

6 2 4 2 0 0 0 0

-3 1 -1 -2 1 0 0 0

-9 -2 0 0 0 0 0 0

4 0 1 -1 -1 0 0 0

-1 -1 0 0 1 0 0 0

0 -1 0 0 0 0 0 0

( , )q

F u v

Zig-Zag Reordering :

44,

4,-11,

6,-6,6,5,-5,2,-3,

-9,1,4,-4,1,

-1,2,2,-1,-2,4,

-1,0,0,-2,0,0,0,

0,0,0,1,0,1,-1,0,

-1,0,-1,0,0,0,0,

0,0,0,-1,0,0,

0,1,0,0,0,0,0,0,0,

0,0,0,

0,0,

0


67/68

Entropy is used in thermodynamics for the study of heat and work.

In data compression, it is a measure of the information content ofa message in number of bits.

Entropy in no. of bits = log2(probabilityofobject)

Object can be a character

Eg. If the probability of character T present in a string is 1/8, the

entropy is 3 bits. i.e. If there are 7 Ts in a text string, then the

message can be represented by 21 bits.

JPEG uses two entropy coding schemes: huffman and arithmetic

coding.

Huffman coding requires one or more sets of huffman code tablesfor coding as well as decoding.

Arithmetic coding uses DC and AC coefficients. The coefficient at

0,0 position in the matrix is called DC coefficients and other 63

are called as AC coefficients.


68/68

Compression and Decompression techniques

Documents