Image Compression Techniques.docmentation55555555555555555555555555

INSTITUTE OF SCIENCE &

TECHNOLOGY

Dissertation approval Sheet THIS IS CERTIFY THAT DISSERTATION TITLED

IMAGE COMPRESSION TECHNIQUES By

Raju Kumar

Rabbul Hussain

Md. Minhaj Alam

Is approved for the degree of Bachelor of technology (B.TECH)

In COMPUTER SCIENCE AND ENGINEERING (C.S.E)

Ms. Pubali Das

Project Guide Faculty

Signature of Project

Coordinator Signature of Project Guide

Ms. Pubali Das

Signature of HOD

Mr. Gouranga Mondal

HOD, CSE&IT, IST

CERTIFICATE

This Is To Certify That The Project Entitled Image Compression Techniques Submitted By Raju Kumar (Roll no: 18200111025), Rabbul Hussain (Roll No:18200111024) and Md.Minhaj Alam

(Roll No:18200111022)For The Partial Fulfillment Of The Degree Of Bachelor Of Technology In Computer Science, Under

West Bengal University Of Technology Is Actually Based Upon

His Group Work Under The Supervision Of Ms. Pubali Das department Of Computer Science And Information Technology,

Institute Of Science & Technology, West Midinipur,West Bengal,

Neither His Project Nor Any Of The Either Project Has Been Submitted For Any Degree Or Diploma Or Any Other Academic

Award Anywhere Before.

Raju Kumar Roll no-18200111025

Rabbul Hussain Roll no-18200111024

Md.Minhaj Alam Roll no-18200111022

AKNOWLEDGEMENT

We take this opportunity to express my profound gratitude and

deep regards to our guide Mr. Gouranga Mondal, HOD(Head of

the Department), department of CSE & IT of Institute of

Science & Technology, for his exemplary guidance, monitoring

and constant encouragement throughout the course of this

thesis. The blessing, help and guidance given by him time to

time shall carry us a long way in the journey of our life on

which we are about to embark. We would also like to thanks

our project coordinator and our dear friends for helping us in

this project. Without their help we wouldn't be able to make it.

Thanks once again.

Raju kumar Roll no-18200111025

Rabbul Hussain Roll no-18200111024

Md.Minhaj Alam Roll no-18200111022

DECLARATION

This is to certify that the project work entitled Image Compression Techniques which is almost completed and

performed by us in partial fulfillment of the completion

Bachelors degree in Computer Science from Institute of Science & Technology Which Comprises of our Original Work.

ABSTRACT

Digital image compression technology is of special interest for

the fast transmission and real-time processing of digital image

information on the internet. Although still image compression is

a technique developed for a long time, plus there are several

approaches which reduce the compression rate, and accelerate

computation time, there are still a lot to go to improve the

efficacy of compression. In this tutorial, several important

image compression algorithms at present are examined,

including DCT and the derived tools such as JPEG, JPEG 2000,

fractal image compression and wavelet transformation. These

use different aspects to help image processing smoother and

faster.

In the following tutorial, I would like to talk about the

background of image compression first, including when we will

need image compression, categories of techniques, and their

properties. Secondly, I would briefly introduce some common

image compression methods nowadays such as JPEG,

JPEG2000, wavelet-based, fractal-based, and several other

techniques and neural networks. When they can be applied,

how to implement the algorithms, their advantages and

disadvantages, how they differ and their development prospect

will be described as well.

CONTENT

Abstract

I. Introduction

1. Introduction to Image Compression 1.1 Image

Pixel RGB Grayscale YUV

1.2 Image Compression Techniques Advantages of image compression Techniques Categories

2. Lossy Compression Techniques 2.1 Introduction 2.2 Techniques

Transform Coding Vector Quantization Fractal Image Compression Compression can Fractal achieve

Encoding Images

3. Lossless Compression Techniques 3.1 Introduction 3.2 Techniques

Run Length Encoding Huffman Encoding Area Coding

II. Commonly Used Techniques

4. JPEG 4.1 JPEG

JPEG Encoder The 2D 8x8 DCT Quantization Differential Coding of DC Coefficients

Summary

1. Introduction to Image Compression The digital multimedia is popular nowadays because of their highly

perceptual effects and the advanced development its corresponding

technology. However, it often requires a large amount of data to store

these multimedia contents due to the complex information they may

encounter. Besides, the requirement of resolution is much higher than

before, such that the data size of the image is surprisingly large.

In other words, a still image is a sensory signal that contains significant

amount of redundant information which exists in their canonical forms.

Image data compression is the technique of reducing the redundancies

in image data required to maintain a given quantity of information.

Therefore, how to improve image compression becomes an important

question. Great progress has been made in applying digital signal

processing or wavelet transform techniques in this area.

There are two different technique groups including lossy compression

and lossless compression depending on if the information can be

recovered after compression. I would like to briefly introduce different

methods included in these two techniques. As for JPEG and JPEG2000,

they are very popular compression tools, which will be described in

details in the latter chapters.

1.1 Image An image is essentially a 2-D signal processed by the human visual

system. The signals representing images are usually in analog form.

However, for image processing, storage and transmission, they are

converted from analog to digital form. A digital image is basically a 2-

D array of pixels.

Images are formed of the significant part of data, particularly in remote

sensing, biomedical and video conferencing applications. The use of

and dependence on information and computers continue to grow, so

does our need for efficient ways of storing and transmitting large

amounts of data.

Pixel In digital image, a pixel is a single point in a raster image. It is the

smallest unit of picture that can be controlled, and is the smallest

addressable screen element as shown in Fig. Each pixel has its own

address. The address of a pixel corresponds to its coordinates. They are

usually arranged in a 2-D grid, and are often represented with dots or

squares.

Each pixel is a sample of an original image. More samples typically

provide more accurate representations of the original. The intensity of

each pixel is variable. In color image systems, a color is typically

represented by three or four component intensities such as red, green,

and blue.

Pixel is smallest element of an image

RGB When the eye perceives an image on a computer monitor, it is in actually

perceiving a large collection of finite color elements, or pixels [1]. Each of

these pixels is in and of itself composed of three dots of light; a green dot, a

blue dot, and a red dot. The color the eye perceives at each pixel is a result

of varying intensities of green, red, and blue light emanating from that

location. A color image can be represented as 3 matrixes of values, each

corresponding to the brightness of a particular color in each pixel.

Therefore, a full color image can be reconstructed by superimposing these

three matrices of RGB.

A color image is made of 3 matrices

Grayscale If an image is measured by an intensity matrix with the relative

intensity being represented as a color between black and white, it

would appear to be a grayscale image.

A grayscale image

The intensity of a pixel is expressed within a given range between

a minimum and a maximum. This range is represented in a range

from 0 to 1 with incremental steps according to the bit-depth of

the image. The greater the number of steps is, the larger the bit-

depth is. If each intensity value is represented as an 8-bit number,

then there are 256 variations. If the intensity values are

represented as 16-bit numbers, there are 32,000 variations

between absolute black and pure white. Fig. 4 demonstrates a

black to white gradient in 4-bits of intensity.

4-bit black to white gradient

YUV In the case of a color RGB picture a point-wise transform is made

to the YUV (luminance, blue chrominance, red chrominance)

color space. This space in some sense is more efficient than the

RGB space and allows better quantization. The transform is given

by

0.299 0.587 0.114 0

0.1687 0.3313 0.5 0.5

0.5 0.4187 0.0813 0.5

Y R

U G

V B

, (1)

and the inverse transform is

1 0 1.402

1 0.344.4 0.71414 0.5

1 1.772 0 0.5

R Y

G U

B V

. (2)

1.2 Image Compression Techniques Image compression is an application of data compaction that can

reduce the quantity of data. The block diagram of image coding

system is shown in Fig.

Object

R-G-B

coordinate

Transform to

Y-Cb-Cr

coordinate

Downsample

ChrominanceEncoder

DecoderR-G-B

coordinate

Transform to

R-G-B

coordinate

Upsample

Chrominance

Monitor

C

Camera

C

V

HDDRate-

Dstortion

Comparison

The block diagram of the general image storage system.

The camera captures the reflected light from the surface of the

object, and the received light will be converted into three primary

color components R, G and B. These three primary color

components are processed by coding algorithms afterward.

Image compression addresses the problem of reducing the amount

of data required to represent a digital image. It is a process

intended to yield a compact representation of an image, thereby

reducing the image storage/transmission requirements.

Compression is achieved by the removal of one or more of the

following three basic data redundancies:

1. Coding Redundancy

2. Inter-pixel Redundancy

3. Perceptual Redundancy

Coding redundancy occurs when the codes assigned to a set of

events such as the pixel values of an image have not been selected

to take full advantage of the probabilities of the events.

Inter-pixel redundancy usually results from correlations between

the pixels. Due to the high correlation between the pixels, any

given pixel can be predicted from its neighboring pixels.

Perceptual redundancy is due to data that is ignored by the human

visual system. In other words, all the neighboring pixels in the

smooth region of a natural image have a high degree of similarity

and this insignificant variation in the values of the neighboring

pixels is not noticeable to the human eye.

Technicques Image compression techniques reduce the number of bits required

to represent an image by taking advantage of these redundancies.

An inverse process called decoding is applied to the compressed

data to get the reconstructed image. The objective of compression

is to reduce the number of bits as much as possible, while keeping

the resolution and the quality of the reconstructed image as close

to the original image as possible.

Image compression systems are composed of two distinct

structural blocks: an encoder and a decoder, as shown in Fig.

Image compression system

Image f(x, y) is fed into the encoder, which creates a set of

symbols form the input data and uses them to represent the image.

If we let n1 and n2 denote the number of information carrying

units in the original and encoded images respectively, the

compression that is achieved can be quantified numerically via

the compression ratio, CR = n1/n2

As shown in Fig, the encoder is responsible for reducing the

coding, inter-pixel and perceptual redundancies of input image.

In first stage, the mapper transforms the input image into a format

designed to reduce inter-pixel redundancies. The second stage,

qunatizer block reduces the accuracy of mappers output in

accordance with a predefined criterion. In third and final stage, a

symbol decoder creates a code for quantizer output and maps the

output in accordance with the code. These blocks perform, in

reverse order, the inverse operations of the encoders symbol

coder and map per block. As quantization is irreversible, an

inverse quantization is not included.

Advantages of image Compression The benefits of image compression can be listed as follows:

1. It provides a potential cost savings associated with sending less data over switched telephone network where cost of call is

really usually based upon its duration. 2. It not only reduces storage requirements but also overall

execution time.

3. It reduces the transmission errors since fewer bits are transferred.

4. It also provides a level of security against illicit monitoring.

Categories The image compression techniques are broadly classified into two

categories depending whether or not an exact replica of the

original image could be reconstructed using the compressed

image. These are:

1. Lossy technique 2. Lossless technique

2. Lossy Compression Techniques

2.1 Introduction Lossy schemes provide much higher compression ratios than

lossless schemes. Lossy schemes are widely used since the

quality of the reconstructed images is adequate for most

applications. By this scheme, the decompressed image is not

identical to the original image, but reasonably close to it.

Lossy image compression

As shown in Fig, this prediction transformation

decomposition process is completely reversible. The quantization

process results in loss of information. The entropy coding after

the quantization step, however, is lossless. The decoding is a

reverse process. Firstly, entropy decoding is applied to

compressed data to get the quantized data. Secondly, de-

quantization is applied to it and finally the inverse transformation

to get the reconstructed image.

Major performance considerations of a lossy compression scheme

include:

1. Compression ratio 2. Signal - to noise ratio 3. Speed of encoding and decoding.

Lossy compression techniques includes following schemes:

1. Transform coding

2. Vector quantization

3. Fractal Image Compression

2.2 Techniques

Transform Coding In this coding scheme, transforms such as DFT (Discrete Fourier

Transform) and DCT (Discrete Cosine Transform) are used to

change the pixels in the original image into frequency domain

coefficients. These coefficients have several desirable properties.

One is the energy compaction property that results in most of the

energy of the original data being concentrated in only a few of the

significant transform coefficients. Only those few significant

coefficients are selected and the remaining is discarded. The

selected coefficients are considered for further quantization and

entropy encoding. DCT coding has been the most common

approach to transform coding.

DCT

Vector Quantization The basic idea in this technique is to develop a dictionary of

fixed-size vectors, called code vectors. As shown in Fig, a vector

is usually a block of pixel values. A given image is then

partitioned into non-overlapping blocks (vectors) called image

vectors. Each in the dictionary is determined and its index in the

dictionary is used as the encoding of the original image vector.

Thus, each image is represented by a sequence of indices that can

be further entropy coded.

(a)

(b)

(a) Vector quantization coding procedure (b) decoding procedure

Fractal Image Compression The essential idea here is to decompose the image into segments

by using standard image processing techniques such as color

separation, edge detection, and spectrum and texture analysis.

Then each segment is looked up in a library of fractals. The

library actually contains codes called iterated function system

codes, which are compact sets of numbers. Using a systematic

procedure, a set of codes for a given image are determined, such

that when the IFS codes are applied to a suitable set of image

blocks yield an image that is a very close approximation of the

original. This scheme is highly effective for compressing images

that have good regularity and self-similarity.

Original image and self-similar portions of image

Now, we want to find a map W which takes an input image and

yields an output image. If we want to know when W is

contractive, we will have to define a distance between two

images. The distance is defined as

where f and g are value of the level of grey of pixel (for grayscale

image), P is the space of the image, and x and y are the

coordinates of any pixel. This distance defines position (x, y)

where images f and g differ the most.

Natural images are not exactly self similar. Lena image, a typical

image of a face, does not contain the type of self-similarity that

can be found in the Sierpinski triangle. But next image shows that

we can find self-similar portions of the image. A part of her hat is

similar to a portion of the reflection of the hat in the mirror.

Compression can Fractal achieve

The compression ratio for the fractal scheme is hard to measure since the image can be decoded at any scale. For example, the

decoded image in Figure 3 is a portion of a 5.7

to 1 compression of the whole Lena image. It is decoded at 4 times its original size, so the full decoded image contains 16 times as many pixels and hence this compression ratio is 91.2 to

1. This many seem like cheating, but since the 4-times later image has detail at every scale, it really is not.

Encoding Images

The previous theorems tell us that transformation W will have a

unique fixed point in the space of all images. That is, whatever

image (or set) we start with, we can repeatedly apply W to it and we will converge to a fixed image. Suppose we

are given an image f that we wish to encode. This means we want

to find a collection of transformations w1 , w2 , ...,wN and want f to be the fixed point of the map W (see fixed Point Theorem). In other

words, we want to partition f into pieces to which we apply the

transformations wi , and get back the original image f. A typical image of a face, does not contain the type of self-similarity like the

fern in Figure The image does contain other type of self-similarity.

Lena identical, and a portion of the reflection of the hat in the mirror is similar to the original. These distinctions form the kind of

self-similarity here the image will be formed by copies of properly transformed parts of the original. These transformed parts do not fit

together, in general, to form an exact copy of the original image,

and so we must allow some error in our representation of an image as a set of transformations.

3. Lossless Compression Techniques

3.1 Introduction In lossless compression techniques, the original image can be

perfectly recovered from the compressed image. These are also

called noiseless since they do not add noise to the signal. It is also

known as entropy coding since it use decomposition techniques to

minimize redundancy.

Following techniques are included in lossless compression:

1. Run length encoding

2. Huffman encoding

Techniques

Run Length Encoding This is a very simple compression method used for sequential

data. It is very useful in repetitive data. This technique replaces

sequences of identical pixels, called runs by shorter symbols. The

run length code for a gray scale image is represented by a

sequence {Vi, Ri} where Vi is the intensity of pixel and Ri refers

to the number of consecutive pixels with the intensity Vi as

shown in the figure. If both Vi and Ri are represented by one byte,

this span of 12 pixels is coded using eight bytes yielding a

compression ration of 1: 5.

Run-length encoding

Huffman Encoding This is a general technique for coding symbols based on their

statistical occurrence frequencies.

Huffman encoding

The pixels in the image are treated as symbols. The symbols that

occur more frequently are assigned a smaller number of bits,

while the symbols that occur less frequent are assigned a

relatively larger number of bits. Huffman code is a prefix code.

The binary code of any symbol is not the prefix of the code of any

other symbol. Most image coding standards use lossy techniques

in earlier stages of compression and use Huffman coding as the

final step.

Area Coding Area coding is an enhanced form of run length coding, reflecting

the two dimensional character of images. This is a significant

advance over the other lossless methods. For coding an image it

does not make too much sense to interpret it as a sequential

stream, as it is in fact an array of sequences, building up a two

dimensional object. The algorithms for area coding try to find

rectangular regions with the same characteristics. These regions

are coded in a descriptive form as an element with two points and

a certain structure. This type of coding can be highly effective but

it bears the problem of a nonlinear method, which cannot be

implemented in hardware. Thus, the performance in terms of

compressio time is not competitive, although the compression

ratio is.

4. JPEG

4.1 JPEG JPEG (Joint Photographic Expert Group) standard will be simply

described in this section, and the flow chart, and the algorithm

will be introduced.

JPEG Encoder The block diagram of the JPEG standard. The YCbCr color

transform and the chrominance subsampling format are not

defined in the JPEG standard, but most JPEG software will

perform this processing because it makes the JPEG encoder

reduce the date quantity more efficient. However, we dont

discuss the basic concept of subsampling format here. We will

focus on JPEG encoder as follows.

88 DCTSource

ImageBitstream

Huffman

Table for AC

Quantization

Quantization

Table

DC

AC

Differential

Coding

Zero-Run-

Length Coding

Entropy

Encoder

Entropy

Encoder

Huffman

Table for DC

The flow chart of JPEG standard

2D 8x8 DCT As we learned, we know that the energy of nature image are

concentrated in low frequency, so we can used DCT transform to

separate low frequency and high frequency. And then reserve the

low frequency component as far as possible, and subtract the high

frequency component to achieve reduction of compression rate.

The encoder performs the DCT on these macroblocks to achieve

decorrelation and frequency analysis. Because the transform are

performed on the 8x8 blocks, the forward 2-D DCT formula is

defined in (3), and x[m,n] and X[u,v] represent the input signal

and the DCT coefficients, respectively.

7 7

0 0

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

4 16 16

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

x y

m u n vX u v C u C v x m n

u v

(3)

where

5.

1,for 0

( ) 2

1 ,otherwise

kC k

The discrete cosine transform shown is closely related to the

Discrete Fourier Transform (DFT). Both take a set of points from

the spatial domain and transform them into an equivalent

representation in the frequency domain. The difference is that

while the DFT takes a discrete signal in one spatial dimension and

transforms it into a set of points in one frequency dimension and

the Discrete Cosine Transform (for an 8x8 block of values) takes

a 64-point discrete signal, which can be thought of as a function

of two spatial dimensions x and y, and turns them into 64 DCT

coefficients which are in terms of the 64 unique orthogonal 2D

spectrum.

The DCT coefficient values are the relative amounts of the 64

spatial frequencies present in the original 64-point input. The

element in the upper most left corresponding to zero frequency in

both directions is the DC coefficient and the rest are called AC

coefficients.

64 two-dimensional spatial frequencies

Because pixel values typically change vary slowly from point to

point across an image, the FDCT processing step lays the

foundation for achieving data compression by concentrating most

of the signal in the lower spatial frequencies. For a typical 8x8

sample block from a typical source image, most of the spatial

frequencies have zero or near-zero amplitude and need not be

encoded.

At the decoder the IDCT reverses this processing step. It takes the

64 DCT coefficients and reconstructs a 64-point output image

signal by summing the basis signals. Mathematically, the DCT is

one-to-one mapping for 64-point vectors between the image and

the frequency domains. In principle, the DCT introduces no loss

to the source image samples; it merely transforms them to a

domain in which they can be more efficiently encoded.

Quantization After DCT, the encoder performs quantization to reduce precision

of the data and discard the less important high frequency

coefficients. As mentioned above, the human eyes are more

sensitive to the low frequency components than the high

frequency components, the JPEG quantization assigns large

quantization step size to high frequency components to discard

the redundant information, and assign small quantization step size

to the low frequency components to preserve the significant

information. Fig. 18 shows two quantization tables defined in

JPEG, where Qr is the luminance quantization table and Qc is the

chrominance quantization table.

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

17 18 24 47

18 21 26 66

24 26 56 99

47 66 9

Y

C

Q

Q

99 99 99 99

99 99 99 99

99 99 99 99

9 99 99 99 99 99

99 99 99 99 99 99 99 99

99 99 99 99 99 99 99 99

99 99 99 99 99 99 99 99

99 99 99 99 99 99 99 99

Quantization table

The quantization step size is smaller in the upper left region to

preserve the low frequency components. On the other hand, the

quantization step is larger in the lower right region to reduce the

less important high frequency components to zero. Since the

distortion of the high frequency features of the image is less

sensitive to the human eyes, it is not easy for us to observe the

difference between the original image and the quantized image.

Differential Coding of DC Coefficients

After 2-D DCT and quantization, we can find that the component

of AC terms in 88 block will consist of many zeros such as Fig.

19. And the DC coefficient is the mean of each corresponding

block, and the current DC coefficient is very similar to the DC

coefficients in its neighboring blocks. Thus, the JPEG encoder

performs the predictive coding on the DC coefficients to reduce

the redundancy, as shown in Fig. 20. The differential coding of

DC coefficient is denoted as difference of DCi and DCi-1.

DC 10 -6 2

4 -5 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 0 0

0 0 0 0

8x8 block after 2-D DCT and quantization

DCi-1 DCi

Blocki-1 Blocki

Diffi = DCi - DCi-1

Differential coding of DC coefficients

SUMMARY

This tutorial starts from the introduction of backgrounds of why

we need image compression, how image is formed, what kind of

image processing tools are there, what we can do via image

compression techniques, to how each method is implemented.

I didnt talk much on how to implement JPEG and JPEG2000, but

focus more on introducing different kinds of compression

techniques. The drawback is that each cannot be discussed in

details, but since the topic is development of compression

techniques, so I would like to talk more broadly. Therefore,

different methods are covered.

There are still many other analysis tools with more complex

algorithms that have not been introduced here. Readers who are

interested can find more information in the references.