Image compression in digital image processing

Digital Image Processing
Image Compression

2
Data vs. information
• Data is not the same thing as information
• Data are the means to convey information; various
amounts of data may be used to represent the same
amount of information Part of data may provide no
relevant information: data redundancy
• The amount of data can be much larger expressed
than the amount of information.

3
Data Redundancy
• Data that provide no relevant information=redundant data or
redundancy.
• Image compression techniques can be designed by
reducing or eliminating the Data Redundancy
• Image coding or compression has a goal to reduce the amount of
data by reducing the amount of redundancy.

5
Data Redundancy
Three basic data redundancies
 Coding Redundancy
 Interpixel Redundancy
 Psychovisual Redundancy

6
Coding Redundancy
A natural m-bit coding method assigns m-bit to each gray
level without considering the probability that gray level occurs
with: Very likely to contain coding redundancy
Basic concept:
 Utilize the probability of occurrence of each gray level
(histogram) to determine length of code representing that
particular gray level: variable-length coding.
 Assign shorter code words to the gray levels that occur most
frequently or vice versa.

10
Coding Redundancy (Example)

Spatial and Temporal Redundancy
• Interpixel Spatial redundancy is due to the correlation between the neighboring
pixels in an image.
• That means neighboring pixels are not statistically independent. The gray levels
are not equally probable.
• The value of any given pixel can be predicated from the value of its neighbors that
is they are highly correlated.
• The information carried by individual pixel is relatively small. To reduce the
interpixel Spatial redundancy the difference between adjacent pixels can be used
to represent an image.

Spatial and Temporal Redundancy
• Interpixel temporal redundancy is the statistical correlation between pixels from
successive frames in video sequence.
• Temporal redundancy is also called interframe redundancy. Temporal redundancy
can be exploited using motion compensated predictive coding.
• Removing a large amount of redundancy leads to efficient video compression.

Irrelevant Information
• Information that is not used by the human visual system are psychovisually
redundant.
 The eye does not respond with equal sensitivity to all visual information.
 Certain information has less relative importance than other information in normal
visual processing psychovisually redundant (which can be eliminated without
significantly impairing the quality of image perception).
 The elimination of psychovisually redundant data results in a loss of quantitative
information lossy data compression method.
 Image compression methods based on the elimination of psychovisually redundant
data (usually called quantization) are usually applied to commercial broadcast TV
and similar applications for human visualization.

18
Image Compression Models
 The encoder creates a set of symbols (compressed) from the input
data.
 The data is transmitted over the channel and is fed to decoder.
 The decoder reconstructs the output signal from the coded symbols.
 The source encoder removes the input redundancies, and the
channel encoder increases the noise immunity.

Some Basic Compression Methods

Variable-length Coding Method: Huffman Coding
21

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Huffman coding: give the smallest possible number of
code symbols per source symbols.
Step 1: Source reduction

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Step 2: Code assignment procedure
The code is instantaneous uniquely decodable without referencing
succeeding symbols.

24

(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
Nonblock code: one-to-one correspondence between source symbols
And code words does not exist.
Concept: The entire sequences of source symbols is assigned a single
arithmetic code word in the form of a number in an interval of real
number between 0 and 1.
Arithmetic Coding

Arithmetic Coding Example
0.2x0.4 0.04+0.8x0.04 0.056+0.8x0.016
0.2x0.2 0.04+0.4x0.04 0.056+0.4x0.016
The number
between 0.0688
and 0.06752
can be used to
represent the
sequence
a1 a2 a3 a3 a4

In this type of arithmetic coding, symbol probabilites that are based on
predefined neighborhood of pixels called context are updated as symbols
are coded or become known.
Example : Q-Coder and MQ-Coder in JBIG,JPEG 2000
Adaptive Context Dependent Probability Estimates

LZW Coding
Lempel-Ziv-Welch (LZW) coding assigns fixed length code
words to variable length sequences of source symbols.
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LZW Coding Algorithm
0. Initialize a dictionary by all possible gray values (0-255)
1. Input current pixel
2. If the current pixel combined with previous pixels
form one of existing dictionary entries
Then
2.1 Move to the next pixel and repeat Step 1
Else
2.2 Output the dictionary location of the currently recognized
sequence (which is not include the current pixel)
2.3 Create a new dictionary entry by appending the currently
recognized sequence in 2.2 with the current pixel
2.4 Move to the next pixel and repeat Step 1

LZW Coding
Lempel-Ziv-Welch coding : assign fixed length code words to
variable length sequences of source symbols.
24 Bits
9 Bits

LZW Coding Example
Input
pixel
39
39
126
126
39
39
126
126
39
39
126
126
Dictionary
Location Entry
0 0
1 1
… …
255 255
256 39-39
257 39-126
258 126-126
259 126-39
260 39-39-126
261 126-126-39
262 39-39-126-126
Encoded
Output (9 bits)
39
39
126
126
256
258
260
Currently
recognized
Sequences
39
39
126
126
39
39-39
126
126-126
39
39-39
39-39-126
126

Bit-Plane Decomposition (Example)

Image compression in digital image processing

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Image compression in digital image processing