Introduction to Image Compression

Any Differences?
Lecture by Kalyan Acharjya
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Disclaimer
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 All images/contents used in this presentation are
copyright of original owners.
 The PPT has prepared for academic use only.

So True?
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Unit 5
Image Compression
(Part 1)
Kalyan Acharjya
Jaipur National University, Jaipur
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JPEG
Image Compression.
Size-270 KB Size-22 KB
“Without Compression a CD store only 200 Pictures or 8
Seconds Movie”
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What is Image Compression?
 Image compression is the process of reducing
the amount of data required to represent an
image.
Encoder 0101100111... Decoder
Original Image Decoded Image
Bitstream
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Why Compression?
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Storage
Ease of Transmission

Compression Fundamentals
 Image compression involves reducing the size of image
data files, while retaining necessary information
 Retaining necessary information depends upon the
application
 Image segmentation methods, which are primarily a data
reduction process, can be used for compression
 The ratio of the original, uncompressed image file and the
compressed file is referred to as the compression ratio
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Why Compression?
 Now, consider the transmission of video images, where we need
multiple frames per second, If we consider just one second of video
data that has been digitized at 640x480 pixels per frame, and requiring
15 frames per second for interlaced video, then:
 Waiting 35 seconds for one second’s worth of video is not exactly real
time.
 Even attempting to transmit uncompressed video over the highest
speed Internet connection is impractical
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Image Compression General Models
 Some image Compression Standard
 JPEG-Based on DCT
 JPEG 2000-Based on DWT
 GIF-Graphics Interchange Format etc.
Source
Encoder
Channel
Encoder
Channel
Decoder
Source
Decoder
Channel/
Store
F(x, y)
F’(x, y)
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Data ≠ Information
 Data and information are not synonymous terms.
 Data is the means by which information is conveyed.
 Data compression aims to reduce the amount of data required
to represent a given quantity of information while preserving
as much information as possible.
 Image compression is an irreversible process.
 Some Transform used in Image Compression
 DCT-Discrete Cosine Transform
 DWT-Discrete wavelet Transform etc.
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Compression Steps
 Preparation: analog to digital conversion.
 Processing: transform data into a domain easier to
compress.
 Quantization: reduce precision at which the output is
stored.
 Entropy Encoding: remove redundant information in the
resulting data stream.
Picture
Preparation
Picture
Processing
Quanti-
zation
Entropy
Encoding
Input Image Compressed Image
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Image Compression-Lossy or Lossless
 But its resolution or features should be unchanged for human
perception.
 Relative Data Redundancy Rd of the first data set is Rd=1-1/CR
 Where CR-Compression Ratio=n1/n2.
 n1 and n2 denote the nos. of information carrying units in two data
sets that represent the same information.
• In Digital Image Compression, the basics data redundancies are-
 Coding Redundancy
 Inter pixel Redundancy
 Psycho-visual Redundancy
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Compression algorithms are developed by taking advantage of the
redundancy that is inherent in image data
Coding Redundancy
 Occurs when the data used to represent the image is not utilized in
an optimal manner
Interpixel Redundancy
 Occurs because adjacent pixels tend to be highly correlated, in
most images the brightness levels do not change rapidly, but
change gradually.
Psychovisual Redundancy
 Some information is more important to the human visual system
than other types of information
Data Redundancies

Lecture by Kalyan Acharjya 15
Part II
Image Compression
Unit V

Trade Off: Quality vs. Compression
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 Lossless Compression (Information Preserving) -
Original can be recovered exactly. Higher quality,
bigger.
 Lossy Compression- Only an approximation of
the original can be recovered. Lower quality,
smaller.

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Compression algorithms are developed by taking advantage of the
redundancy that is inherent in image data
Coding Redundancy
 Occurs when the data used to represent the image is not utilized in
an optimal manner
Interpixel Redundancy
 Occurs because adjacent pixels tend to be highly correlated, in
most images the brightness levels do not change rapidly, but
change gradually.
 Some information is more important to the human visual system
than other types of information
Data Redundancies

Coding Redundancy
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 Length of the code words (e.g., 8-bit codes for grey value
images) is larger than needed.
 Coding redundancy is associated with the representation of
information.
 The information is represented in the form of codes.
 If the gray levels of an image are coded in a way that uses
more code symbols than absolutely necessary to represent
each gray level then the resulting image is said to contain
coding redundancy.

Coding Redundancy
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Coding Redundancy
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Measuring the
Information
I=Log[1/P(E)]
=-log P(E)

Measuring Information
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 These methods, from information theory, are not limited to
images, but apply to any digital information. Here uses
“symbols” instead of “pixel values” and “sources” instead of
“images”

Shanon’s First Theorem
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 Shanon looked at group of n consecutive source symbols with a
single code word (rather than one code word per source symbol)
and showed that-
 Where Lavg is the average number of code symbols required to
represents all n symbols groups.

Coding Redundancy
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Two common algorithms: Huffman coding and LZW coding

Fidelity Criteria
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RMS Error
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The rms of the three images are 5.17, 15.67, and 14.17.

Image Compression
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Inter-Pixel Redundancy
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 Inter-Pixel Spatial Redundancy:
 Inter-pixel redundancy is due to the correlation between the neighboring
pixels in an image.
 The value of any given pixel can be predicated from the value of its
neighbors (Highly Correlated).
 The information carried by individual pixel is relatively small.
 To reduce inter-pixel redundancy the difference between adjacent pixels can
be used to represent an image.
 Inter-Pixel Temporal Redundancy
 Inter-Pixel temporal redundancy is the statistical correlation between pixels
from successive frames in video sequence.
 Temporal redundancy is also called inter-frame redundancy.
 Removing a large amount of redundancy leads to efficient video
compression.
Algorithm: Run Length Coding

Spatial Redundancy
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Its Histogram (Ignore White Background)
Just variable length coding is not
sufficient?
0 255

Run Length Algorithm
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 Lets Discuss (During Lecture!)
 Consider one Binary Image
 Its vector representation
 Size without compression
 Size after run length algorithm
1 1 1 1 1 1
1 1 1 1 0 0
1 1 1 1 1 1
0 0 1 1 1 1
1 1 1 1 1 1
0 0 0 0 0 0

Which have higher intensity (Centre Circle)?
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 The Psychovisual redundancies exist because human perception does not
involve quantitative analysis of every pixel or luminance value in the image.
 It’s elimination is real visual information is possible only because the
information itself is not essential for normal visual processing.

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 We’re more sensitive to differences between dark intensities than
bright ones. Encode log(intensity) instead of intensity.
 We’re more sensitive to differences of intensity in green than red
or blue.
 Use variable quantization: devote most bits to green, fewest to
blue.

Some Basic Compression Methods
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 Huffman coding (Will Discuss in this Lecture- Coding Redundancy)
 Golomb Coding
 Arithmetic Coding
 LZW Coding
 Run Length Coding (Already Discussed)
 Symbol Based Coding
 Bit Plane Coding (You are familiar)
….many more for detail:
Image Processing Gonzalez Book (Chapter 8-Image Compression)

Huffman Coding
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Huffman Coding
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Efficiency=H/Lavg x 100 %

Channel Encoder & Decoder
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Remember
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 To study some standard image compression methods
Like JPG, JPEG2000 etc.
Suggested Further Reading
Gonzalez & Woods, Digital Image
Processing Book
Chapter 8: Image Compression

Thank You!
Any Question Please?
kalyan.acharjya@gmail.com
kalyan5.blogspot.in
Lecture by Kalyan Acharjya 39
Suggested Further Reading
Gonzalez & Woods, Digital Image Processing Book
Chapter 8: Image Compression

Introduction to Image Compression

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