This presentation involves a mathematical view of image compression having a brief introduction of its theory,major techniques along with their algorithm and examples.

1. Image Compression: Techniques and Application
By- Nidhi Baranwal
University of Allahabad

2. What and Why?
• Image compression is the technique of reducing the amount of data
required to represent an image
• It involves:
- reducing the storage required to save an image
-reducing the bandwidth required to transmit it
• Why?
- to handle large amount of information such as multimedia
- to fulfill the goal of representing an image with minimum number of bits
of an acceptable image quality
- for focusing on removal or reduction of several types of redundancy in
data or information

3. Compression Algorithm
• The role of compression algorithm is to reduce the source data to a
compressed form and decompress it to get the original data
• Any compression algorithm has two major components:
- modeler: its purpose is to condition the image data for compression using
the knowledge of data
- coder: encoder codes the symbols using the model while decoder decodes
the message from the compressed data

4. Compression Techniques
• Lossess:
1.Runlength
2.Huffma
3.Shannon Fano
4.Arithmetic
5.Dictionary based
• Lossy:
1.Lossy Predictive
2.VectorQuantization
3.Block Transform
4.JPEG
5.MPEG

5. Redundancy and its Types
• Redundancy means repetitive data that may be present implicitly or
explicitly
• Types:
- coding redundancy : caused due to poor selection of coding technique
- inter-pixel redundancy : called spacial/geometrical redundancy.It may be
inter frame or intra frame
- psychovisual redundancy : images that convey little or no information to
the human observer are said to be psychovisually redundant
- chromatic redundancy: it refers to the presence of unnecessary colors in
an image

6. Arithmetic Coding
Algorithm/Pseudocode
Input symbol is l
Previouslow is the lower bound for the old interval
Previoushigh is the upper bound for the old interval
Range is Previoushigh - Previouslow
Let Previouslow= 0, Previoushigh = 1, Range = Previoushigh – Previouslow =1
WHILE (input symbol != EOF)
get input symbol l
Range = Previoushigh - Previouslow
New Previouslow = Previouslow + Range* intervallow of l
New Previoushigh = Previouslow + Range* intervalhigh of l
END

7. Example
5 symbol message, a1a2a3a3a4 from 4 symbol source is coded.
Source Symbol Probability Initial Subinterval
a1 0.2 [0.0, 0.2)
a2 0.2 [0.2, 0.4)
a3 0.4 [0.4, 0.8)
a4 0.2 [0.8, 1.0)

8. Contd..
a1 a2 a3 a3 a4
1 0.2 0.08 0.072 0.0688
a4 a4 a4 a4 a4
a3 a3 a3 a3 a3
a2 a2 a2 a2 a2
a1 a1 a1 a1 a1
0 0 0.04 0.056 0.0624

9. Contd..
a1 a2 a3 a3 a4
1 0.2 0.08 0.072 0.0688
a4 a4 a4 a4 a4
a3 a3 a3 a3 a3
a2 a2 a2 a2 a2
a1 a1 a1 a1 a1
0 0 0.04 0.056 0.0624

10. Contd..
a1 a2 a3 a3 a4
1 0.2 0.08 0.072 0.0688
a4 a4 a4 a4 a4
a3 a3 a3 a3 a3
a2 a2 a2 a2 a2
a1 a1 a1 a1 a1
0 0 0.04 0.056 0.0624

11. Contd..
a1 a2 a3 a3 a4
1 0.2 0.08 0.072 0.0688
a4 a4 a4 a4 a4
a3 a3 a3 a3 a3
a2 a2 a2 a2 a2
a1 a1 a1 a1 a1
0 0 0.04 0.056 0.0624

12. Contd..
a1 a2 a3 a3 a4
1 0.2 0.08 0.072 0.0688
a4 a4 a4 a4 a4
a3 a3 a3 a3 a3
a2 a2 a2 a2 a2
a1 a1 a1 a1 a1
0 0 0.04 0.056 0.0624

13. Contd..
a1 a2 a3 a3 a4
1 0.2 0.08 0.072 0.0688
a4 a4 a4 a4 a4
a3 a3 a3 a3 a3
a2 a2 a2 a2 a2
a1 a1 a1 a1 a1
0 0 0.04 0.056 0.0624
.06752
.0688

14. Dictionary based Techniques_1.LZ77
Algorithm/Pseudocode

15. Example

16. Dictionary based Techniques_2.LZ78
Algorithm/Pseudocode

17. Example

18. Dictionary based Techniques_3.LZW
Algorithm/Pseudocode

19. Example
•

20. Applications of Image Compression
• Broadcast Television
• Remote sensing via satellite
• Military communication via radar, sonar
• Tele conferencing
• Computer communications
• Facsimile transmission
• Medical images : in computer tomography
• Magnetic Resonance Imaging(MRI)
• Satellite images, geological surveys, weather maps