This document discusses image compression. It begins by defining an image as a two-dimensional function with spatial coordinates and pixel intensities. Images contain redundancy from similar neighboring pixels (spatial redundancy) and fixed codeword assignments (coding redundancy). Compression aims to reduce this redundancy to decrease data size for storage and transmission. The amount of compression is quantified by the compression ratio, with higher ratios indicating more redundant original data. Compression provides an efficient way to optimize resource usage for transmitting and storing large volumes of image data.

1. K. Punnam Chandar
Asst. Professor
Dept. of Electronics and Comm. Eng.
University College of Engineering
Kakatiya University
84th Orientation Course
Academic Staff College
University of Hyderabad
K. Punnam Chandar

2. 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 x
and y are spatial (plane) coordinates, and the amplitude of f at any pair of
coordinates (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

3. Images are every where
Medical Images
Photography
First Picture of Moon
Size: 1024x1024
Size: 512x512
K. Punnam Chandar

4. Storage & Transmission
• To store 100 images of
size 1024x1024 the
amount of memory
required:
One Image
1024x1024 = 1MB
100 Images
100x1MB= 100MB
• To transmit 10 images
of size 1024x1024 the
amount of time
required on a
communication link of
speed 10kbs is 1Hour .
Solution: Compression
K. Punnam Chandar

5. 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
Compression
Information
Data: N1
Information
Data: N2
K. Punnam Chandar

6. If N1 and N2 denote the number
of information –carrying Units in
two data sets that represent the
same information.
The relative data redundancy RD of
the first data set (the one
characterized by N1) can be
defined as
Quantifying Redundancy
Mathematically: 1 2
1
1 2
2 1
2
1
1
1
1
1
2
1
1
D
D
D
D
D
R
N N
R
N
N N
R
N N
N
R
N
R
N
N
R
C


 
 
 
 
Where CR , commonly called the
compression ratio
K. Punnam Chandar

7. Case i. N2=N1
Indicating that the first representation of the
information contains no redundant data.
Case ii. N2<<N1
Implying significant compression and highly
redundant data.
Case iii. N2>>N1
indicating that the second data set contains much
more data than the original representation.
Compression
Information
Data: N1
Information
Data: N2
K. Punnam Chandar

8. Redundancy in Images
• In digital images, neighboring samples on a
scanning line are normally similar (spatial
redundancy)
K. Punnam Chandar

9. Coding Redundancy
Coding 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: aaaaad
Data N1: 000000000011
Data N2: 00000001
N1=12
N2= 8
Cr = 12/8=1.5
1.5:1
K. Punnam Chandar

10. 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

11. Reference
• The Images are taken from Digital Image
Processing, Gonzalez 2nd Edition.
K. Punnam Chandar