K. Punnam ChandarAsst. Professor

Dept. of Electronics and Comm. Eng.University College of Engineering

Kakatiya University

84th Orientation CourseAcademic Staff College

University of Hyderabad

K. Punnam Chandar

IMAGE

10 12 35 54 34 23 201 2 10 12

4 5 6 7 8 9 9 9 0 0

87 6 8 0 7 68 8 9 09 6

5 87 88 7 9 9 8 8 8 8

8 8 8 8 8 89 9 90 0 0

00 5 54 4 55 6 76 7 4

3 65 7 7 89 7 6 6 8 99

7 6 6 6 78 9 166 6 77 6

4 44 4 5 55 43 2 54 87 5

45 6 54 67 45 7 3 7 98 54

An image may be defined as a two-dimensional function f(x, y) where xand y are spatial (plane) coordinates, and the amplitude of f at any pair ofcoordinates (x, y) is called the intensity or gray level of the image at that

point. A small region in the digital image is shown in matrix.

K. Punnam Chandar

Images are every where

Medical Images

Photography

First Picture of Moon

Size: 1024x1024

Size: 512x512

K. Punnam Chandar

Storage & Transmission

• To store 100 images ofsize 1024x1024 theamount of memoryrequired:

One Image

1024x1024 = 1MB

100 Images

100x1MB= 100MB

• To transmit 10 imagesof size 1024x1024 theamount of timerequired on acommunication link ofspeed 10kbs is 1Hour .

Solution: CompressionK. Punnam Chandar

Compression

• To reduce the volume of data to be transmitted • To reduce the storage requirements• How is compression possible?

– Redundancy in image data– Properties of human perception

CompressionInformationData: N1

InformationData: N2

K. Punnam Chandar

If N1 and N2 denote the numberof information –carrying Units intwo data sets that represent thesame information.

The relative data redundancy RD ofthe first data set (the onecharacterized by N1) can bedefined as

Quantifying Redundancy Mathematically: 1 2

1

1 2

2 1

21

1

11

1

2

11

D

D

D

D

D

R

N NR

N

N NR

N N

NR

N

RN

N

RC

Where CR , commonly called the compression ratio

K. Punnam Chandar

Case i. N2=N1Indicating that the first representation of the information contains no redundant data.

Case ii. N2<<N1Implying significant compression and highly redundant data.

Case iii. N2>>N1indicating that the second data set contains much more data than the original representation.

CompressionInformationData: N1

InformationData: N2

K. Punnam Chandar

Redundancy in Images• In digital images, neighboring samples on a

scanning line are normally similar (spatial redundancy)

K. Punnam Chandar

Coding RedundancyCoding Redundancy: assigning fixed code words to

all the symbols results in Coding Redundancy

Symbol Fixed Code Variable code

a 00 0

b 01 01

c 10 10

d 11 001

Information: aaaaadData N1: 000000000011Data N2: 00000001

N1=12N2= 8Cr = 12/8=1.5

1.5:1K. Punnam Chandar

Summary

• Data (Images) contains redundancy.

• The type of redundancy present, need to be identified for processing .

• Processed (compressed) data is suitable for transmission and storage.

• The type of compression depends on application.

• Compression is a viable technique to utilize the communication and storage resources optimally.

K. Punnam Chandar

Reference

• The Images are taken from Digital Image Processing, Gonzalez 2nd Edition.

K. Punnam Chandar