Lecture 1

Contemporary issues in IT

Lecture 1Monday

Lecture 10:00 – 12:00, Room 3.27Lab 13:00 – 15:00, Lab 6.12 and 6.20

Lecturer: Dr Abir HussainRoom 633, a.hussain@ljmu.ac.uk

Lecture contents

Introduction to image compression Image compression measures. Image compression system. Image compression methods.

Recommendation

Digital compression of still images and videos, by Roger Clarke, Academic press, 1995

Image compression introductions and basic concepts on the following web site: www.cms.livjm.ac.uk/cmsahus1

Introduction Images are very important representative

objects. The application of image compression for

transmission purposes is limited by real-time considerations.

the application of image compression for storage purposes is less strict.

There are two types of compression methods, lossless and lossy image compression

Introduction The application of image compression has

widened and its benefits are far from being counted digital computers in printing publishing and video production in television or satellite transmission video conferencing facsimile transmission of printed material graphics sensing images obtained from

reconnaissance aircraft archiving of medical images

Introduction There are three classical approaches to image

compression In the fist approach, the compression is performed by

removing the redundancy in the image data (example predictive coding)

The second approach of image compression is the one that aims at reducing the number of coefficient of the transformed image parameters while preserving the energy (transform coding, JPEG)

The final classical approach of image compression divides the image into nonoverlapped blocks, transforms the image blocks into one-dimensional vectors, which are subsequently quantised (vector quantisation)

Image compression measures

compression ratio and defined by:

mean-square error defined for an size image by

Compressed

OriginalR n

nC

M

1i

N

1j

2

rms )j,i(S)j,i(SNM

1e

Image compression measures

Another form of fidelity measure that depends on the mean square error is the signal to noise ratio (SNR)

dB

data image theof peak value tolog10

2

10

rmse

PeakSNR

Redundant Information

There are three types of redundant data that can be identified and removed by a digital image compression algorithm. coding redundancy interpixel redundancy psychovisual redundancy

Image compression system Image compression systems consist of two

parts, the encoder and the decode

Source encoder

Channel encoder

Channel Source decoder

Channel decoder

Encoder Decoder

f(i,j) f(i,j) ^

Image compression system

^ f(i,j) Channel Symbol

decoder Inverse mapper

Mapper Quantiser Symbol encoder f(i,j) Channel

Source encoder (a)

Source decoder (b)

Image compression methods two methods can be used, lossless and

lossy image compression techniques. In lossless image compression, the quantiser is

not utilised at the encoder and the aim of the compression is to reduce coding and interpixel redundancies.

lossy image compression methods use the correlation among the pixel data and the properties of the visual process to reduce the interpixel and psychovisual redundancies

Lossless image compression

Lossless image compression methods can provide compression ratios of 2 to 10 and they can be applied to both grey level and binary images Huffman coding Arithmetic coding Lossless predictive coding

Huffman coding Huffman coding was introduced by Huffman

in 1952. The coding process starts by examining the

probabilities of different grey levels in the image.

These probabilities are tabulated in a descending order with the highest probability at the top and the lowest probability at the bottom.

The two lowest probabilities are added together and the order of the probabilities is reorganised in a descending order for the proceeding process.

Huffman coding The next stage in Huffman coding is to

assign to the two remaining probabilities the binary symbols 0 and 1.

Then, we go backwards and assign to the two joined probabilities in the previous stage the symbol of the next stage plus the binary symbols 0 and 1 assigned to each probability.

Such process is repeated until the first stage of the process is achieved

ExampleSymbol Probability 1 2 3 4 5

a1 0.4 0.4 0.4 0.4 0.4 0.5

a2 0.2 0.2 0.2 0.2 0.3 0.4

a3 0.1 0.1 0.12 0.18 0.2

a4 0.08 0.08 0.1 0.12

a5 0.05 0.07 0.08

a6 0.04 0.05

a7 0.03

Arithmetic coding

Arithmetic coding can be used to minimise coding redundancy in the image data.

It outperforms Huffman coding The basic idea of arithmetic coding is

as simple as Huffman coding.

Arithmetic coding

Initially, the range of the input message is specified between 0 and 1.

Each probability is represented by a two end interval, the left end is closed while the right end is open

Arithmetic coding

The next step in the coding is to look at the message, since the first appearing symbol will limit the range of the message according to its specified interval.

Arithmetic coding Suppose that the current message is specified

in the interval Suppose that the range of the present

incoming symbol is [Qa1, Qa2), this means that the new range of the message is

)high,low[ oldold

2oldoldnew

1oldoldnew

Qarangelowhigh

Qarangelowlow

Example

Consider the message a2, a1, a3, a4, with the initial probability interval between 0 and 1.

Symbol Probability Initial Subinterval

a1 0.4 [0.0, 0.4)

a2 0.3 [0.4, 0.7)

a3 0.2 [0.7,0.9)

a4 0.1 [0.9, 1.0)

Example..

a4 a3 a2 a1

1 0.9

0.7

0.4

0

a4 a3 a2 a1

0.7

0.4

a4 a3 a2 a1

0.52

0.4

a4 a3 a2 a1

0.508

0.484

a4 a3 a2 a1

0.508

0.5056

Lossless predictive coding

In lossless predictive image compression approach, the interpixel redundancies are removed by predicting the current pixel value

using closely spaced pixel values and generating new values for coding.

The new values represent the error generated from the subtraction of the predicted value from the original value

Lossless predictive coding

Predictor Nearest integer

Symbol encoder

Input image

Sn

-

+ en Compressed

image

(a)

Compressed image

Symbol decoder

en

Predictor

Decompressed image

(b)

Sn

Sn ^

Sn ^ +

+

Practical

In today’s lab, we will have a look at various compressed images and compare them with the uncompressed images

Various techniques will be used Standard and medical images will be

used in the lab.

Summary

In today’s lecture, we gave an introduction to image compression

We studied various lossless image compression methods

In tomorrow’s lecture, we will go through the concept of lossy image compression techniques.