Chapter 6 Image Compression

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Chapter 6 Image Compression
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Necessary of Image Compression
Every day, an enormous amount of
information is stored, processed, and transmitted
digitally. Image compression addresses the
problem of reducing the amount of data required
to represent a digital image.
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Such a large amount of data has brought the issue
of data transfer and storage
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Purpose of Image Compression

• Saving storage space
• Saving transfer time
• Easy processing reduce cost?

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Image Compression Coding
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General compression system model
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Three basic data redundancies

• Coding redundancy
• Interpixel redundancy
• Psychovisual redundancy

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Data Redundancies
Psychovisual redundancy
Interpixel redundancy
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Objective fidelity criteria
Objective fidelity criteria root-mean-square
(rms) error between an input and output image.
Let f(x, y) represent an input image and let
g(x,y) denote an approximation of f(x, y), x, y
0, 1, 2,,N-1,
(1)The root-mean-square error
(2)The rms value of the signal-to-noise ratio
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Subjective fidelity criteria
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Huffman Coding

• Huffman coding is an entropy encoding algorithm
  used for lossless data compression.
• Huffman coding uses a specific method for
  choosing the representation for each symbol,
  resulting in a prefix code that expresses the
  most common characters using shorter strings of
  bits than are used for less common source
  symbols. A method was later found to do this in
  linear time if input probabilities are sorted.

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Huffman Coding Algorithm

• The simplest construction algorithm uses a
  priority queue where the node with lowest
  probability is given highest priority
• (1)Create a leaf node for each symbol and add
  it to the priority queue. While there is more
  than one node in the queue, remove the node of
  highest priority (lowest probability) twice to
  get two nodes.
• (2)Create a new internal node with these two
  nodes as children and with probability equal to
  the sum of the two nodes' probabilities. Add the
  new node to the queue.
• (3)Repeat step 2 until the remaining node is
  the root and the tree is complete.

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Example of Huffman Coding
For example, a source generates 5 different
symbols A, B, C, D, E with probability 0.16
0.51 0.09 0.13 0.11.
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Run Length Encoding

• Run-length encoding (RLE) is a very simple form
  of data compression in which runs of data (that
  is, sequences in which the same data value occurs
  in many consecutive data elements) are stored as
  a single data value and count, rather than as the
  original run. This is most useful on data that
  contains many such runs for example, relatively
  simple graphic images such as icons, line
  drawings, and animations.

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Example of RLE

• Let us take a hypothetical single scan line, with
  B representing a black pixel and W representing
  white
• WWWWWWWWWWWWBWWWWWWWWWWWWBBBWWWWWWWWWWWWWWWWWWWWW
  WWWBWWWWWWWWWWWWWW

If we apply the run-length encoding (RLE)
data compression algorithm to the above
hypothetical scan line, we get the
following12W1B12W3B24W1B14W
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Predictive Coding
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The principle of Predictive Coding

• The system consists of an encoder and a decoder,
  each containing an identical predictor. As each
  successive pixel of the input image, is
  introduced to the encoder, the predictor
  generates the anticipated value of that pixel
  based on some number of past inputs. The output
  of the predictor is then rounded to the nearest
  integer.

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Predictive coding model I
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Predictive coding model II
The predictor
The symbol encoder generate the next element of
the compressed data stream
Decoder perform the inverse of encoding
The linearity predictor
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Delta Modulation I
Delta modulation (DM or ?-modulation) is an
analog-to-digital and digital-to-analog signal
conversion technique used for transmission of
voice information where quality is not of primary
importance. DM is the simplest form of
differential pulse-code modulation (DPCM) where
the difference between successive samples is
encoded into n-bit data streams. In delta
modulation, the transmitted data is reduced to a
1-bit data stream.
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Delta Modulation II
Quantify the bands
Analog signal input range
Slope overload
Granular noise
Coding output
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Differential Pulse Code Modulation

• Differential Pulse Code Modulation (DPCM)
  compares two successive analog amplitude values,
  quantizes and encodes the difference, and
  transmits the differential value.

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The principle of DPCM
A natural refinement of this general approach is
to predict the current sample based on the
previous M samples utilizing linear prediction
(LP), where LP parameters are dynamically
estimated. Block diagram of a DPCM encoder and
decoder is shown below. Part (a) shows DPCM
encoder and part (b) shows DPCM decoder at the
receiver.
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Transform Coding I

• Transform coding is a type of data compression
  for "natural" data like audio signals or
  photographic images.
• The transformation is typically lossy, resulting
  in a lower quality copy of the original input.

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Transform Coding II
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Transform Coding III
A transform coding system
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Joint Picture Expert Group

• The name "JPEG" stands for Joint Photographic
  Experts Group, the name of the committee that
  created the standard. The group was organized in
  1986, issuing a standard in 1992, which was
  approved in 1994 as ISO 10918-1. JPEG is a
  commonly used method of compression for
  photographic images. The degree of compression
  can be adjusted, allowing a selectable tradeoff
  between storage size and image quality.

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Steps of JPEG

• The image is subdivided into pixel blocks of size
  8 8, which are processed left to right, top to
  bottom. As each 8 8 block or subimage is
  encountered, its 64 pixels are level shifted by
  subtracting the quantity 2n-1, where 2n is the
  maximum number of gray levels.
• The 2-D discrete cosine transform of the block is
  then computed, quantized and reordered.
• Use the zigzag pattern, to form a 1-D sequence of
  quantized coefficients.
• Use the DPCM (differential pulse code modulation)
  code the DC coefficients.
• The nozero AC coefficients are coded using a
  run-length encoding.
• Entropy coding

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JPEG Model
DCT-based encoder
Image block
Entropy coder
Quantizer
Compressed image data
The original image data
Quantization table
Entropy coding table
DCT-based compression encoding steps
DCT-based encoder
Inverse quantizer
Entropy coder
Compressed image data
Reconstruction of image data
Quantization table
Entropy coding table
DCT-based compression encoding steps
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JPEG2000

• JPEG 2000 is a wavelet-based image compression
  standard. It was created by the Joint
  Photographic Experts Group committee in the year
  2000 with the intention of superseding their
  original discrete cosine transform-based JPEG
  standard (created about 1991).

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MPEG

• MPEG was an early standard for lossy compression
  of video and audio.
• Development of the MPEG standard began in May
  1988.

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MPEG-1

• MPEG-1 was designed to compress VHS-quality raw
  digital video and CD audio down to 1.5 Mbit/s
  (261 and 61 compression ratios respectively)
  without excessive quality loss, making Video CDs,
  digital cable/satellite TV and digital audio
  broadcasting (DAB) possible.
• The MPEG-1 standard consists of the following
  five Parts Systems?Video?Audio? Conformance
  testing?Reference software

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MPEG-2

• MPEG-2 describes a combination of lossy video
  compression and lossy audio compression methods
  which permit storage and transmission of movies
  using currently available storage media and
  transmission bandwidth. MPEG-2 is widely used as
  the format of digital television signals that are
  broadcast by terrestrial (over-the-air), cable,
  and direct broadcast satellite TV systems.
• MPEG-2 Audio section enhances MPEG-1's audio by
  allowing the coding of audio programs with more
  than two channels. This method is
  backwards-compatible, allowing MPEG-1 audio
  decoders to decode the two main stereo components
  of the presentation.

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MPEG-4

• MPEG-4 provides the following functionalities
• Improved coding efficiency?Ability to encode
  mixed media data?Error resilience to enable
  robust transmission?Ability to interact with the
  audio-visual scene generated at the receiver .
• MPEG-4 was aimed primarily at low bit-rate video
  communications however, its scope was later
  expanded to be much more of a multimedia coding
  standard.

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MPEG-7

• MPEG-7 is a multimedia content description
  standard. This description will be associated
  with the content itself, to allow fast and
  efficient searching for material that is of
  interest to the user.
• The objectives of MPEG-7 are Provide a fast and
  efficient searching, filtering and content
  identification method Describe main issues about
  the content Index a big range of applications
  Audiovisual information( Audio, voice, video,
  images, graphs and 3D models) Inform about how
  objects are combined in a scene Independent
  between description and the information itself.

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MPEG-21

• MPEG-21 is based on two essential concepts the
  definition of a fundamental unit of distribution
  and transaction, which is the Digital Item.
• Digital Items can be considered the kernel of
  the Multimedia Framework and the users can be
  considered as who interacts with them inside the
  Multimedia Framework.