about a fundamentals and image compression models

1. Presented by
M.Lavanya
M.Sc (cs & it)
Nadar Saraswathi College of arts & science
Theni.

2.  Need for Compression:
 Huge amount of digital data
 Difficult to store and transmit
 Solution:
 Reduce the amount of data required to represent a digital image
 Remove redundant data
 Transform the data prior to storage and transmission
 Categories:
 Information Preserving
 Lossy Compression

3.  Data compression
 Difference between data and information
 Data Redundancy
 If n1 and n2 denote the number of information-carrying units
in two datasets that represent the same information , the
relative data redundancy RD of the first dataset is defined as
RD = 1-1/CR ,
where CR = n1/n2 is called the compression ratio

4. In digital image compression, three basic data
redundancies can be identified and exploited:
 Coding Redundancy
 Interpixel Redundancy
 Psychovisual Redundancy
 Fidelity Criteria

5.  Let a discrete random variable r k in [0,1] represent the gray
levels of an image.
 pr(rk ) denotes the probability of occurrence of r
Pr(rk) = nk / n , k=0,1,2,….L-1
 If the number of pixels used to represent each value of rk is
l(rk ), then the average number of bits required to represent
each pixel is
L-1
Lavg = £ l(rk)pr(rk)
k=0
CODING REDUNDANCY

6.  Hence, the total number of bits required to code an MxN image is
MNLavg
 For representing an image using an m-bit binary code , Lavg= m.
Example of variable length coding

7.  Related to interpixel correlation within an image.
 The value of a pixel in the image can be reasonably predicted
from the values of its neighbors.
 Information carried by individual pixels is relatively small.
These dependencies between values of pixels in the image
are called interpixel redundancy

10.  Based on human perception
 Associated with real or quantifiable visual information.
 Elimination of psychovisual redundancy results in loss
of quantitative information. This is referred to as
quantization.
 Quantization - mapping of a broad range of input values to a
limited number of output values.
 Results in lossy data compression.

13.  Criteria
 Subjective: based on human observers
 Objective : mathematically defined criteria

15. Encoder - Source encoder + Channel encoder
Source encoder
Removes coding, interpixel, and psychovisual
redundancies in input image and outputs a set of symbols.
Channel encoder
To increase the noise immunity of the output of source
encoder.
Decoder - Channel decoder + Source decoder

16. Mapper
• Transforms input data into a format designed to reduce interpixel redundancies
in input image.
• Reversible process generally
• May or may not reduce directly the amount of data required to represent the
image.
Examples
• Run-length coding(directly results in data compression)
•Transform coding

18.  Essential when the channel is noisy or error-prone.
 Source encoded data - highly sensitive to channel noise.
 Channel encoder reduces the impact of channel noise by
inserting controlled form of redundancy into the source
encoded data.
 Example:
Hamming Code – appends enough bits to the data being
encoded to ensure that two valid code words differ by a
minimum number of bits.

19.  7-bit Hamming(7,4) Code
 7-bit code words
 4-bit word
 3 bits of redundancy
 Distance between two valid code words (the minimum number
of bit changes required to change from one code to another) is
3.
 All single-bit errors can be detected and corrected.
 Hamming distance between two code words is the number of
places where the code words differ.
 Minimum Distance of a code is the minimum number of bit
changes between any two code words.
 Hamming weight of a codeword is equal to the number of non-
zero elements (1’s) in the codeword

20.  The 7-bit Hamming (7,4) code word h1,h2,….h5,h6,h7
associated with a 4-bit binary number b3,b2,b1,b0 is

21.  The principal objectives of digital image compression to
describe the most commonly used compression methods that
form core of technology as it exits currently.
 Gray – scale imagery , compression methods are playing an
increasingly important role in document image storage and
transmission.