Image Compression

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Image Compression
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Data and information

• Data is not the same thing as information.
• Data is the means with which information is
  expressed. The amount of data can be much larger
  than the amount of information.
• Data that provide no relevant information
  redundant data or redundancy.
• Image coding or compression has a goal to
  reduce the amount of data by reducing the amount
  of redundancy

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Definitions

• n1 data.
• n2 data - redundancy (i.e., data after
  compression).
• Compression ratio CR n1/n2
• Relative redundancy RD 1 - 1/CR

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Definitions

• n1 data.
• n2 data - redundancy (i.e., data after
  compression).
• Compression ratio CR n1/n2
• Relative redundancy RD 1 - 1/CR

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Different Types of Redundancy
CR Coding Redundancy.IR Interpixel
Redundancy.PVR Psycho-Visual Redundancy
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Image compression and decompression
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Image Compression

• Image compression can be
• Reversible (loss less), with no loss of
  information.
• A new image is identical to the original image
  (after decompression).
• Reversibility is necessary in most image analysis
  applications.
• The compression ratio is typically 2 to 10 times.
• Examples are Huffman coding and run-length
  coding.
• Non reversible (lossy), with loss of some
  information.
• Lossy compression is often used in image
  communication, video,WWW, etc.
• It is usually important that the image visually
  is still nice.
• The compression ratio is typically 10 to 30 times.

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Objective measures of image quality
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Subjective measures of image quality

• Let a number of test persons grade the images as
  bad/acceptable/good etc.

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Coding redundancy

• Use shorter code words fore the more common gray
  levels and longer code words for the less common
  gray levels. This is called Variable Length
  Coding.
• The amount of data in an M N image with L gray
  levels is equal to M N Lavg, where
• l(rk ) is the number of bits used to represent
  gray level rk , and p(rk ) is the probability of
  gray level rk in the image.

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Example 3-bit image
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Interpixel Redundancy

• There is often correlation between adjacent
  pixels, i.e., the value of the neighbors of an
  observed pixel can often be predicted from the
  value of the observed pixel.
• Coding methods
• Run-Length coding.
• Difference coding

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Run-length coding

• Every code word is made up of a pair (g, l) where
  g is the gray level, and l is the number of
  pixels with that gray level (length, or run).
• E.g.,
• 56 56 56 82 82 82 83 80
• 56 56 56 56 56 80 80 80
• creates the run-length code (56, 3)(82, 3)(83,
  1)(80, 4)(56, 5).
• The code is calculated row by row.
• Very efficient coding for binary data.
• Important to know position, and the image
  dimensions must be stored with the coded image.
• Used in most fax machines.la University) Image
  Coding an

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Run-length coding
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Run-length coding
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Run-length coding
Compression Achieved Original image requires 3
bits per pixel (in total - 8x8x3192
bits). Compressed image has 29 runs and needs
336 bits per run (in total - 174 bits or 2.72
bits per pixel).
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Difference coding

• f (xi )
• E.g.,
• original 56 56 56 82 82 82 83 80 80 80 80
• Code f(xi ) 56 0 0 26 0 0 1 -3 0 0
  0
• The code is calculated rob by row.
• Both run-length coding, and difference coding are
  reversible, and can be combined with, e.g.,
  Huffman coding

Xi if i 0,xi - xi-1 if i gt 0
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Example of difference
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Example of difference
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The Huffman code

• Yields the smallest possible number of unique
  code symbols per source symbol.
• Step 1.
• 1 1. Sort the gray levels by decreasing
  probability.
• 2 2. Add the two smallest probabilities.
• 3. Sort the new value into the list.
• 4. Repeat until only two probabilities
  remain.
• Step 2.
• 2. 1. Give the code 0 to the highest
  probability, and the code 1
  to the lowest probability in the present node.
• 2. Go backwards through the tree and
  add 0 to the highest and 1 to the lowest
  probability in each node until all gray levels
  have a unique code

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Example Huffman coding
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Huffman code of original image
Lavg 3.1 la
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Example of Huffman coding
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Example of Huffman coding
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The Huffman code

• The Huffman code results in unambiguous code.
• The code is reversible without loss.
• The table for the translation of the code has to
  be stored together with the coded image.
• The Huffman code does not take correlation
  between adjacent pixels into consideration.

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Chain Coding
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Chain Coding
Eight directions are represented with 3 bits.
Upper left corner of the object (7,3) is selected
to be the starting point (upper left corner of
the image is (0,0)). The edge of the object is
followed clockwise until we get back to the
starting point.
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Chain Coding
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Chain Coding
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Chain Coding
We get the following chain code for the
object 7,6,7,7,6,6,5,6,3,3,3,3,4,1,1,1,2. Binary
code starting point directions 0111 0011
111 110 111 111 110 . . . 010 Bits needed
2x417x359 (against 256 for uncompressed image)
7? 0.23 bits/pixel (against 1 bit/pixel for
uncompressed image).
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Lossy Compression

• Transform Coding
• Coefficients can be quantized, dropped and coded
  causing a controlled damage to the image.
• Possible Transforms
• DFT, DCT, Hadamard etc.
• MixedTime-Frequency presentations e.g. Gabor,
  Waveletsetc

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Transform coding

• Divide the image into n n sub-images.
• Transform each sub-image using a reversible
  transform (e.g., the Hotelling transform, the
  discrete Fourier transform (DFT) or the discrete
  cosine transform (DCT)).
• Quantify, i.e., truncate the transformed image
  (e.g., by using DFT,and DCT frequencies with
  small amplitude can be removed without much
  information loss). The quantification can be
  either image dependent (IDP) or image independent
  (IIP).
• Code the resulting data, normally using some kind
  of variable length coding, e.g., Huffman code.
• The coding is not reversible (unless step 3 is
  skipped). Divide the image into n n sub-images.
• 2

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Some common image formats

• JPEG Joint Photographic Experts Group - Exists in
  many different versions but is always some kind
  of transformation coding. JPEG is not reversible
  due to quantification.
• MPEG Motion Picture Experts Group - Similar to
  JPEG, but the motion in comparison to the
  previous image is calculated,and used in the
  compression.

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Example of JPEG compression
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Some more common image formats

• LZW (Lempel-Ziv-Welch) A word-based code. The
  data is represented by pointers to a library of
  symbols (see Huffman code). LZW compression is
  loss less, and can often be chosen when TIFF
  (Tagged Image File Format) images are stored.
  The result is a smaller file which usually takes
  a bit longer to decode. An image file directory
  (set of symbols) is included in the header.
• GIF (Graphics Interchange Format) Creates a
  coding for color images where each color is coded
  by only a few bits (usually three). GIF also uses
  LZW compression for storage and transfers. GIF is
  fully reversible (loss less) if less then 256
  colors are present in the original image.
• Remember that the time used for coding, and
  decoding is important when choosing coding method

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Choice of image formats

• Images used for image analysis should always be
  stored in a loss less format.
• Images for the WWW have to be either GIF, JPEG or
  PNG (due to the license issues GIF).
• Chose GIF for graphs and hand drawn figures with
  few color shades (JPEG transform coding and
  truncation can cause artifacts around sharp
  edges).
• Chose JPEG for photos and figures with many
  colors, and smooth transitions between colors
  (GIF reduces the number of colors to 256).

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JPEG Encoding and Decoding
Reconstructed