LosslessImg Cmprsn Report

8/7/2019 LosslessImg Cmprsn Report

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2/10/2011 ABSTRACT

mage compression is the application of data

compression on digital image. It is a technique bywhich image information can be represented by lessnumber of bits. In effect, the objective is to reduce theredundancy of image data in order to be able to store ortransmit data in efficient form. Image compression isthe application of Data compression on digital images. Ineffect, the objective is to reduce redundancy of the imagedata in order to be able to store or transmit data in anefficient form. Image compression can be lossy orlossless. Lossless compression is sometimes preferred forartificial images such as technical drawings, icons orcomics. This is because lossy compression methods,especially when used at low bit rates, introducecompression artifacts. Lossless compression methodsmay also be preferred for high value content, such asmedical imagery or image scans made for archivalpurposes. Lossy methods are especially suitable for

natural images such as photos in applications whereminor (sometimes imperceptible) loss of fidelity isacceptable to achieve a substantial reduction in bit rate.Various techniques of both lossy and losslesscompression are there .Some compression techniques,presented here, are derived from standard signal/Datacompression methodologies, while others are developedby exploiting the characteristics of digital images.

I


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CONTENTS

Page

no.

INTRODUCTION

3

DIGITAL IMAGE REPRESENTATION4

DIGITIZING IMAGE

5

REDUNDANCY VS COMPRESSION RATIO

7

TYPES OF REDUNDANCY

9

IMAGE COMPRESSION MODELS

11

LOSSLESS IMAGE COMPRESSION ALGORITHMS

13

APPLICATIONS

21


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CONCLUSION

22

REFERENCES

23

INTRODUCTION

An enormous amount of data is produced when a 2-D

light intensity function is sampled and quantized tocreate a digital image. In fact , the amount of data

produced may be so great that it results in impractical

storage, processing, and communication requirements.

For instance more than 25GB of data are required to

represent Encyclopedia Britannica in digital form.

Image compression addresses the problem of reducing

the amount of data required to represent a digital image. The underlying basis of the reduction process is the

removal of redundant data. From a mathematical point of

view, this amounts to transforming a 2-D pixel array into


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a statistically uncorrelated data set. The transformation is

applied prior to storage or transmission of the image. At

some later time the compressed image is decompressed

to get the original image or an approximation to it.

WHY WE NEED IMAGE COMPRESSION

We need image compression for the following reasons:

1. Computational Expenses

2.Storage Requirement

3. Transmission time and cost

4. Utilizations of resourses

TYPES OF IMAGE COMPRESSION

There are two forms of compressionlossless and lossyand digital cameras use both forms.

Lossless compression. Lossless compressionuncompresses an image so its quality matches theoriginal sourcenothing is lost. Although losslesscompression sounds ideal, it doesnt provide muchcompression and files remain quite large. For this reason,lossless compression is used mainly where detail isextremely important, as it is when planning to make largeprints. Lossless compression normally providecompression ratio < 10:1.


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Lossy compression. Because lossless compressionisnt practical in many cases, all popular digital camerasoffer a lossy compression. This process degrades imagesto some degree and the more they're compressed, the

more degraded they become. In many situations, such asposting images on the Web or making small to mediumsized prints, the image degradation isn't obvious. Heremaximum compression ratio is the function ofreconstruction quality. It provides compression ratio >10:1.

DIGITAL REPRESENTATION OF IMAGE

A digital image is an image f(x,y) that has been

discretized both in spatial coordinate and brightness .A

digital can be considered a matrix whose row and column

indices identify a point in the image and the

corresponding matrix element value identifies the gray

level at that point. The elements of such a digital array

are called image elements, picture elements, pixels or

pels.


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DIGITIZATION OF IMAGE

First of all a physical device called image sensor

converts the visual image into electrical signal. Digitizer

then converts the electrical signal to digital form. Itinvolves two steps.

1.Sampling: Sampling is a process by which formed

over a patch in continuous domain is mapped into a

discrete point with integer coordinates.

A continuous image function can be sampled

using a discrete grid of sampling points in the plane.

These sampling points are ordered in the plane and

their geometric relation is called the grid. Grids used in

practice are mainly square or hexagonal

Origin

x


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2.Quantization :

A magnitude of the sampled image is expressed as adigital value in image processing.

The transition between continuous values of theimage function (brightness) and its digital equivalentis called quantization.

The number of quantization levels should be highenough for human perception of fine shading detailsin the image.

The occurrence of false contours is the main problemin image which has been quantized with insufficientbrightness levels. This effect arises when the numberof brightness levels is lower than that which humanscan easily distinguish.


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This number is dependent on many factors -- forexample, the average local brightness -- but displayswhich avoid this effect will normally provide a rangeof at least 100 intensity levels.

This problem can be reduced when quantization intointervals of unequal length is used; the size ofintervals corresponding to less probable brightnesses in the image is enlarged. These gray-scaletransformation techniques are considered in latersections.

Most digital image processing devices usequantization into k equal intervals.

If bits are used ... the number of brightness levels is.

Eight bits per pixel are commonly used, specializedmeasuring devices use 12 and more bits per pixel

COMPRESSION RATIO ANDREDUNDANCY

Compression ratio is the ratio between uncompressedand compressed image

Compression ratio (CR)= #bits in the original data

#bits in the compressed data

Data and information are not same. Data are the means

to convey information. Various amounts of data can

convey same information. If data provides no relevantinformation or simply restate what is already known, it is

called data redundancy. It can be defined as


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Data Redundancy (RD) = 1 1/Compression ratio

0 < CR <

- < RD

< 1


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TYPES OF REDUNDANCY

Coding redundancy

Interpixel redundancy

Psychovisual redundancy

CODING REDUNDANCY:

If the gray levels of an image are coded in a way that

uses more code symbols than absolutely necessary to

represent each gray level, the resulting image is said to

contain coding redundancy.

In general, coding redundancy is present when the codes

assigned to a set of events have not been selected to

make full advantages of probabilities of the events.

The underlying basis for coding redundancy is that image

are typically composed of objects that have a regular and

somewhat predictable morphology(shape) and are

sampled so that the objects being depicted are much

larger than the picture elements.

The natural consequence is that, in most images, certain

graylevels are more probable than others(that ishistograms of most images are not uniform).


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PSYCHOVISUAL REDUNDANCY:

Psychovisual redundancy stem from the fact that the

human eye does not respond with equal intensity to all

visual information. The human visual system does not

rely on quantitative analysis of individual pixel values

when interpreting an image an observer searches for

distinct features and mentally combines them into

recognizable groupings

In this process certain information is relatively less

important than other this information is calledpsychovisually redundant

Psychovisually redundant image information can be

identified and removed a process referred to as

quantization

Quantization eliminates data and therefore results in

lossy data compressionReconstruction errors introduced by quantization can be

evaluated objectively or subjectively depending on the

application need & specifications

Quantization effects


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(a) (b) (c)

(a) Original image

(b) Uniform quantization to 16 levels

(c) IGS quantization to 16 levels

INTERPIXEL REDUNDANCY:

Interpixel redundancy is defined as failure to identifyand utilize data relationshipsIf a pixel value can be reasonably predicted from itsneighboring (or preceeding/ following) pixels the image

is said to contain interpixel redundancyInterpixel redundancy depends on the resolution of theimage


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The higher the (spatial) resolution of an image, themore probable it is that two neighboring pixels willdepict the same object The higher the frame rate in a video stream, the

more probable it is that the corresponding pixel in thefollowing frame will depict the same objectThese types of predictions are made more difficult by

the presence of noise

IMAGE COMPRESSION MODEL

We discussed individually three general techniques for

reducing or compressing the amount of data required torepresent an image. However, these techniques typically

are combined to form practical image compression

systems.

Source Encoder removes input redundancies

Channel Encoder increases noise immunity of

encoders output. If channel between encoder and

decoder is noisefree then channel encoder and

decoder are omitted.

SOURCE

ENCODE

CHANNEL

ENCODER

CHANNEL CHANNE

L

SOURCE

DECODE

x,y)f

ENCODER DECODER

MAPPER QUANTIZE

R

SYMBOL

ENCODERf(x,y


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Symbol decoder and inverse mapper have inverse

function as that of symbol encoder and mapper

respectively.

LOSSLESS IMAGE COMPRESSION

SYMBOL

DECODER

INVERSE

MAPPER

SOURCE ENCODER

SOURCE DECODER

Chan

Channel f(x,y)


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Data reduction can be achieved by encoding the pixel

values in such a way that the average number of bits b

used to represent each pixel be much less than b, the

number of bits used to represent each pixel originally.

Here we are not discarding any information, but we

represent more frequently occurring valuesby shorter

codes.

Average no. of bits used to represent each pixel (b)

Suppose the image contains L different graylevels

i=0,1,2L-1,

ni denotes frequency of occurrence of pixels having

graylevel i.


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Then probability of occurrence of graylevel i in the image

is

Entropy : A measure of amount of information. It is the

degree of randomness in the occurrence of graylevels in

an image.L-1 L-1

H = pi log2ni b = pili

i=0 i=0

For lossless image compression b should approximate H

i.e. H is lower bound of b

LOSSLESS IMAGE COMPRESSION

ALGORITHMS:

Lossless means the reconstructed image does not

lose any information according to the original one.

There is a huge range of lossless data compression

technique.

The common techniques used are:

Huffman coding

ni

L-1

ni

i=0


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Arithmetic coding

Run-length coding

Predictive coding

HUFFMAN CODING

Huffman coding provides a data representation with the

smallest possible number of code symbols (when coding

the symbols of an information source individually).This is

done by assigning fewer number of bits to the symbols

that appear more often and more number of bits to thesymbols that appear less often. It is more efficient when

occurrence probability vary widely.

Huffman code construction is done in two steps:

1) Source reductions

We create a series of source reductions by ordering

the probabilities of the symbols and then combine thesymbols of lowest probability to form new symbols

recursively.

2) Code assignment

When only two symbols remain, step 1) is retraced

and a code bit is assigned to symbol in each steps.

Encoding and decoding is done using these codes in alookup table manner.

Original Source Source Reduction


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Symbol Probability 1 2 34

a2 0.4 0.4 0.4 0.40.6

a6 0.3 0.3 0.3 0.30.4a1 0.1 0.1 0.2 0.3a4 0.1 0.1 0.1a3 0.06 0.1a5 0.04

Original Source Source reductionSym. Prob. Code 1 2 3

a2 0.4 1 0.4 1 0.4 1 0.4 1 0.0a6 0.3 00 0.3 00 0.3 00 0.3 00 0

1a1 0.1 011 0.1 011 0.2 010 0.3 01

a4 0.1 0100 0.1 0100 0.1 011a3 0.06 01010 0.1 0101a5 0.04 01011

Lavg = 0.4*1 + 0.3*2 + 0.1*3 + 0.1*4 + 0.06*5 +

0.04*5= 2.2 bits/symbol

Huffman source reduction

Huffman code assignment


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Entropy = 2.14 bits/symbol

Huffman coding efficiency is 0.973

ARITHMETIC CODING

Provides a data representation where the entire symbol

sequence is encoded as a single arithmetic code word

(which is represented as an interval of real numbers

between 0 and 1)

Arithmetic code construction is done in three steps:

1) Subdivide the half-open interval [0,1) based on

probabilities of the source symbols

2) For each source symbol recursively

a) Narrow the interval to the sub-interval designated by

the encoded symbol.

b) Subdivide the new interval among the source symbolsbased on probability

3) Append an end-of-message indicator.

Encoding is done by choosing any number in the interval

to represent the data.

Decoding is done by retracing the steps in the code

construction.

Encoding sequence

Arithmetic coding procedure


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a1 a2 a3 a4 a5

1 a4 0.2 a4 0.08 a4 0.072 a4 0.0688 a4

a3 a3 a3 a3 0.06752a3

a2 a2 a2 a2 a2

a1 a1 a1 a1 a10 0 0.04 0.056 0.0624

In the above example three decimal digits are used to

represent the five-symbol message. This translates into0.6 decimal digits per source symbol and compares

favorably with the entropy of the source which is 0.58

digits per source symbol.

RUN-LENGTH CODING

Run-length encoding (RLE) is a very simple form of

data compression in which runs of data (that is,

sequences in which the same data value occurs in many

consecutive data elements) are stored as a single data

value and count, rather than as the original run. This ismost useful on data that contains many such runs: for

example, relatively simple graphic images such as icons,

line drawings, and animations.
http://en.wikipedia.org/wiki/Data_compressionhttp://en.wikipedia.org/wiki/Data_compression


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For example, consider a screen containing plain black

text on a solid white background. There will be many long

runs of white pixels in the blank space, and many short

runs of black pixels within the text. Let us take ahypothetical single scan line, with B representing a black

pixel and W representing white:

WWWWWWWWWWWWBWWWWWWWWWWWWBBBWWWWWWW

WWWWWWWWWWWWWWWWWBWWWWWWWWWWWWWW

If we apply the run-length encoding (RLE) data

compression algorithm to the above hypothetical scanline, we get the following:

12WB12W3B24WB14W

Interpret this as twelve W's, one B, twelve W's, three B's,

etc.

The run-length code represents the original 67 charactersin only 16. Of course, the actual format used for the

storage of images is generally binary rather than ASCII

characters like this, but the principle remains the same.

Another example :
http://en.wikipedia.org/wiki/Pixelhttp://en.wikipedia.org/wiki/Scan_linehttp://en.wikipedia.org/wiki/ASCIIhttp://en.wikipedia.org/wiki/Pixelhttp://en.wikipedia.org/wiki/Scan_linehttp://en.wikipedia.org/wiki/ASCII


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First row of image consists of 128 pixels

Instead of using 384 bytes (128 * 3)

Only 4 bytes (3 for color & 1 for count)

Works well on images with areas of flat

Color (not continuously blended tones)

PREDICTIVE CODING

Provides a data representation where code words expresssource symbol deviations from predicted values ( usually

values of neighboring pixels )

Predictive coding efficiently reduces interpixel

redundancies

1D & 2D pixels are predicted from neighboring pixels

Works well for all images with a high degree of interpixelredundancies

Works in the presence of noise (just not as efficiently)


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I/P data

22222222222666666666666669999999999999999

Code

20000000000400000000000003000000000000000

Predictive coding can be used in both lossless & lossy

Compression schemes

Encoder circuit

Decoder circuit

The amount of compression achieved in lossless

predictive coding is related directly to the entropy


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reduction that results from mapping the input image into

the prediction error sequence.

APPLICATIONS

In numerous applications error-free compression is the

only acceptable means of data reduction. Such

applications are:

Archival of medical and business documents, where

lossy compression usually prohibited for legal

reasons.

Processing of LANDSAT imagery, where both the use

and cost of collecting data makes any loss

undesirable.

Digital radiography, where loss of any informationcan compromise diagnostic accuracy.


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Control of remotely piloted vehicles in military,

space, and hazardous waste control application.

CONCLUSION

Image compression techniques, by which image

information can be represented by less number of

bits, are very useful for image transmission from one

point to other and also for image archival purpose.

Image compression has been and continues to be

crucial to the growth of multimedia computing.


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In addition to medical imaging, compression is one of

the few areas of image processing that has received

a sufficiently broad commercial appeal to warrant the

adoption of widely accepted standards.

In short, an ever expanding number of applications

depend on the efficient manipulation, storage and

transmission of binary, grayscale or color images.

REFERENCES:

[1] Rafael C. Gonzalez and Richard E. Woods, Digital

Image

Processing Pearson Prentice Hall, 2nd Edition, pp. 431

480, 2006


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[2] B. Chanda and D. Dutta Majumdar, Digital Image

Processing, PHI Publication, pp. 145 165, 2006

[3] Kenneth R. Castleman, Digital Image Processing,Pearson Education, 1st Edition, 2007

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