Image compression

IMAGE COMPRESSION
By Garima Shakya

● The objective of image compression is to reduce irrelevance and
redundancy of the image data in order to be able to store or transmit
data in an efficient form.
● Sometimes the given data contains data which has no relevant
information,or restates/repeats the known information: Data
redundancy.
Image=Information+redundant data
Need of compression...

What are the data
Redundancies used in
image compression??

Data redundancies:
There are three main data redundancies used in image compression:
● Coding redundancy: The uncompressed image usually is coded with each
pixel by a fixed length.
➔ Using some variable length code schemes such as Huffman coding and
arithmetic coding may produce compression.
● Interpixel redundancy: Spatial redundancy,it exploit the fact that an
image very often contains strongly correlated pixels, large regions whose
pixel values are the same or almost the same.

● Psychovisual redundancy: Human eye does not respond with equal
sensitivity to all incoming visual information.
➔ Some piece of information are more important than others.
➔ Removing this type of redundancy is a lossy process and the lost
information can not be recovered.

Types of compression:
Lossless:
● In lossless data compression, the integrity of the data is preserved,i.e. no
part of the data is lost in the process.
● Lossless compression methods are used when we cannot afford to lose
any data.
Lossy:
● Lossy compression can achieve a high compression ratio, since it allows
some acceptable degradation. Yet it cannot completely recover the
original data

Lossless Compression:
Two-step algorithms:
1. Transforms the original image to
some other format in which the
inter-pixel redundancy is reduced.
2. Use an entropy encoder to remove
the coding redundancy.
The lossless decompressor is a perfect
inverse process of the lossless
compressor.

Lossless
compression
● Huffman Coding
● Run-length Coding
● Arithmetic Coding
● Lempel-Ziv Coding

Lossless
compression
● Huffman Coding
● Run-length Coding
● Lempel-Ziv Coding
● Arithmetic Coding

Huffman Coding:
Huffman coding assigns shorter codes to symbols that occur more frequently
and longer codes to those that occur less frequently.
For example,
Character A B C D E
Frequency 17 12 12 27 32

Run-Length Coding
● It can be used to compress data made of any combination of symbols.
● It does not need to know the frequency of occurrence of symbols.
● The method is to replace consecutive repeating occurrences of a symbol
by one occurrence of the symbol followed by the number of occurrences.

The method can be even more efficient if the data uses only two symbols (for
example 0 and 1) in its bit pattern and one symbol is more frequent than the
other.

Arithmetic Coding
A sequence of source symbols is assigned to a sub-interval in [0,1) which can
be represented by an arithmetic code.
For example, message: a1a2 a3 a3 a4
1) Start with interval [0, 1) :
Source symbol Probability
a1 0.2
a2 0.2
a3 0.4
a4 0.2
0 1

2) Subdivide [0, 1) based on the probabilities of
symbols:
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)
0 1
0.2 0.2 0.4 0.2
Initial Subinterval
[0.0,0.2)
[0.2,0.4)
[0.4,0.8)
[0.8,1.0)

[0.06752, 0.0688)
or 0.068
Encode a1 a2 a3 a3 a4
(must be inside sub-interval)

Lempel-Ziv Coding
● It is an example of a category of algorithms called dictionary-based
encoding .
● The idea is to create a dictionary (a table) of strings used during the
communication session.
● If both the sender and the receiver have a copy of the dictionary, then
previously-encountered strings can be substituted by their index in the
dictionary to reduce the amount of information transmitted.

References:
● https://en.wikipedia.org/wiki/Data_compression
● https://en.wikipedia.org/wiki/Lossless_compression
● https://en.wikipedia.org/wiki/lossy_compression

Image compression

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