• Compression is the reduction in size of data in order to save space or transmission time. And its used just about everywhere. All the images you get on the web are compressed, typically in the JPEG (Joint Photographic Experts Group ), Medical Images , Libraries and Video Conferences, ….etc.

• Image compression is the application of data compression. The objective is to reduce redundancy of the image data in order to be able to store or transmit data in an efficient form. The reduction in file size allows more images to be stored in a given amount of disk or memory space. It also reduces the time required for images to be sent over the Internet or downloaded from Web pages.

♣The two fundamental principles used in image compression are redundancy and irrelevancy.

☻Redundancy removes redundancy from the image. ☻irrelevancy omits pixel values which are not noticeable by human eye.

♣ The information in an image can be minimized by removing the redundancy present in it.

♣ There are three types of redundancies: (i) spatial redundancy, which is due to the correlation

or dependence between neighboring pixel values(ii) spectral redundancy, which is due to the correlation

between different color planes or spectral bands.(iii) temporal redundancy, which is present because of

correlation between different frames in images. Image compression aims to reduce the number of

bits required to represent an image by removing the spatial and spectral redundancies as much as possible.

♣ JPEG and JPEG 2000 are two important techniques used for image compression

1. The need to efficiently store, manipulate, and transmit large masses of information is growing more rapidly than the capacity of systems to handle it.

2. Uncompressed images take too much space, require larger bandwidth for transmission and longer time to transmit.

3. easier exchange of image files between different devices and applications.

Compression system consists of two components which are encoder and

decoder .

Pre processing

quantizer Symbol encoder

Symbol encoder

Dequantizer InverseDCT

8x8 blockextraction

quantizer Symbol encoder

DCT

Symbol encoder

Dequant-izer

InverseDCT

8x8 blockmersor

Original Lena image 8x8 block divided

Fourier transform

DCT transform

Wavelet transform

Or any linear transform

used

QuantizerSymbol encoder

compressed Lena Image With 4 coefficients

Decoding processing

For examplelet the input pixel matrix is

136147147152155136155148

147140144162167123156136

162136140155155140167147

162147136140148156148162

160136155152160156145168

172152162163167136155152

179167148140147140152144

175179155140140147144140

1

0

1

0

),(1

)0,0(N

x

N

y

yxfN

c

The coefficient of DCT can be compute as follow :

vyuxyxfN

vucN

x

N

y

)12cos()12cos(),(2

1),(

1

0

1

03

vyuxvuCN

CN

yxfN

u

N

v

)12cos()12cos(),(2

1)0,0(

1),(

1

1

1

13

Original Lena image

Output DCT matrix

06412280

21714319

714881824

1518181118103

8338151458

120318622410

71411119263421

191492391518186

DC coefficient is at position 0,0 in the upper left corner of the matrix.

Zigzag sequence

7.77.67.57.47.37.27.17.0

6.76.66.56.46.36.26.16.0

5.75.65.55.45.35.25.15.0

4.74.64.54.44.34.24.14.0

3.73.63.53.43.33.23.13.0

2.72.62.52.42.32.22.12.0

1.71.61.51.41.31.21.11.0

0.70.60.50.40.30.20.10.0

Original Lena image Compressed Lena imagewith 4 coefficients

Compressed imagewith 16 coefficients

Compressed imagewith 25 coefficients

Compressed imagewith 40 coefficients

Compressed imagewith 50 coefficients

• There are two important compression schemes which are lossy and lossless compression

• is a type of data compression in which actual information is lost. the goal is to use lossy compression such that there is not much observable loss in the final product, while saving enormously on file size over lossless compression. In a lossy compression scheme, some of the original information is discarded when it is compressed. Therefore, it is impossible to produce an exact replica of the original image when the image is reconstruct.

Orginal imageMedium compression

92% less information

High compression 98% less information

• Lossless compressors produce an exact replica of the original image.

• Lossless compression is a compression technique that does not lose any data in the compression process. It assumes you want to get everything back that you put in.

Lossy CompressionLossloss Compression

The reconstruction image is not identical to the origin

The reconstruction image is identical to the origin

Compration ratio 20:1 up to 50:1 or more

Compration ratio 2:1 up to 3:1

It is used for Any type of media file, image files e.g GIF and JPEG for, music e.g MP3 real media and for example of videos files

It is not used for image files but is usually applied to text files and other files.