VTI6MET1'F DIP

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International standard organizations

• ISO/IEC (International Organization for
  Standardization)
• Deals with information processing, e.g., image
  storage en retrieval
• ITU-T (International Telecommunnications
  Union-Telecommunications Sector)
• Deals with information transmission

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Image Compression Standards

• Binary (bi-level) images
• Group 34 JBIG (1994)
• Continues-tone still images
• JPEG (1994) JPEG-2000
• Image sequences (moving pictures)
• H.261(1990) H.263(1995)
• MPEG1(1994)MPEG2(1995)
• MPEG4(2000) MPEG7 MPEG21

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Compression System
compressed signal
bit rate
signal in
signal out
Coder
Decoder
Quantify the numerical/perceptual difference
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Compression Framework
Compressed Image data
Original Image data
Lossless
Transformation or Decomposition
Symbol Encoding
Quantization
Lossy
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Decomposition or transformation

• A reversible process (or near reversible due to
  finite arithmetic) that provides an alternate
  image representation that is more amenable to
  efficient extraction and coding of relevant
  information
• Examples Lineair block transformations, e.g.
  discrete fourier transform (DCT) wavelet
  transform, colorspace transformatie etc

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Example block from Lena image
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DCT of 8x8 Image block
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Quantization

• A many-to-one mapping (maps a range of input
  values to a single output value) that reduces the
  number of possible signal values at the cost of
  introducing error.
• Acts as a control knob for trading off image
  quality for compression ratio (bit rate)
• Examples are scalar uniform or nonuniform
  quantization, vector quantization (VQ)

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Uniform Quantization

• Unquantized value 18.1
• Scaled (normalized) value18.1/121.51
• Quantizer output 2
• Dequantized value 2x1224

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Symbol modeling and encoding

• The process of defining a statistical model for
  the symbols to be encoded and assigning a binary
  codeword to each output symbol based on its
  statistics
• The resulting code should be uniquely decodable
• Examples are Huffman coding, arithmetic coding.
  Lempel-Ziv Welch (LZW) coding

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Variable-Length encoding

• Average length of Code I 2.0 bits/symbol
• Average length of Code II 1.5 bits/symbol

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Variable-length codes

• Code II is a prefix condition code, i.e. no
  codeword is a prefix of any other codeword. This
  allows any bit stream generated by code II to be
  uniquely decodable
• Example
• Transmitted bitstream 0011010111010
• Decoded stream 0/0/110/10/111/0/10
• Decode message A,A,C,B,D,A,B

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Huffman Coding

• For a given source with given symbol
  probabilities, a Huffman code is a code whose
  average length is less than or equal to the
  average length of all other uniquely decodable
  codes
• In global (static) Huffman coding, the codeword
  table is preset, wheras in local (custom) huffman
  coding the table is computed on the fly for each
  input image.

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Entropy of a source

• The average amount of information obtained per
  source symbol from an information source is
  called the entropy of the source
• H(S)Sp(s)LOG(1/P(s))

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Huffman coding en entropy

• No uniquely decodable code can have an average
  length less than the source entropy
• For the previous example, H(S)1.40 bits/symbol,
  while code II achieved 1.50 bits/symbol
• By Huffman coding larger blocks of source symbols
  at once, the average length of the code per
  original source symbol can be made arbitrarily
  close to the source entropy

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framework
Original Image data
Compressed Image data
Lossless
Transformation or Decomposition
Symbol Encoding
Quantization
Lossy
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The JPEG Standard Toolkit

• The JPEG (Joint Photographic Experts Group)
  standard concerns with the compression of
  continuous-tone still-frame monochrome and
  color-images
• It describes a family of image compression
  techniques and provides a toolkit from which
  applications can select the elements that satisfy
  their particular requirements

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JPEG Encoder Block diagram
Header
Compresseddata
8x8 blocks
FDCT
Quantizer
Entropy encoder
Huffman tables
Quantization tables
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JPEG Decoder Block diagram
Header
Compresseddata
Reconstructed image data
IDCT
Dequantizer
Entropy decoder
Quantization tables
Huffman tables
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JPEG Encoding Example

• The image is first segmented into 8x8 blocks.
  Each block is encode independent of the other
  blocks (except for the DC coefficient of the DCT)
• The value of 128 is subtracted from each pixel
  value prior to the DCT (for implementation
  facility)
• A 3-component color image is treated as three
  separate images

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Original block
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Level-Shifted block
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Discrete Cosine Transform (DCT)

• The heart of both the JPEG and the MPEG family of
  standards is the DCT operation
• For each 8x8 block of an 8-bit input image with
  pixel values in the range of (-128, 127), the
  forward DCT produces an 8x8 set of 11-bit
  coefficients in the range (-1024, 1024).
• DCT coefficients are much less correlated and the
  signal energy is usually redistributed among a
  few coefficients.

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Discrete cosine transform (DCT)

• The discrete cosine transform for an 8x8 block
  with input image pixel values f(j,k) and output
  DCT coefficient values F(u,v) is given by

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DCT of 8x8 Image block
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DCT Basis functions

• The DCT can be viewed as a spectral decomposition
  of the original image block into a set of 8x8
  cosine basis functions (templates) of varying
  frequencies
• The transform coefficients can be viewed as
  weighting factors that, when applied tot the
  cosine basis functions, will reconstruct the
  original block

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DCT coefficient quantization

• Each DCT coefficient is uniformly quantized with
  a quantization step that is taken from a
  user-defined quantization table
• A q-table is characterized by 64, 1-byte elements
• For the baseline system, in order to meet the
  needs of the various color components, four
  different quantization tables are allowed.

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DCT coefficient quantization

• The quality and compression ratio of an encoded
  image can be varied by changing the q-table
  elements (usually by scaling up or down the
  values of an initial q-table)
• The q-table is often designed according to the
  perceptual importance of the DCT coefficients
  (e.g. by using HSV data CSF data) under the
  intended viewing conditions

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Quantization matrix
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Uniform Quantization

• Unquantized value 18.1
• Scaled (normalized) value18.1/121.51
• Quantizer output 2
• Dequantized value 2x1224

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Quantized DCT coefficient
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Coding of quantized coefficients

• After quantization, the DCT coefficients are
  recordered into a 1-D format using a zigzag
  pattern in order to create long runs of zero.
• 20 -20 2 0 0 2 -1 -1 EOB
• The en-of-block (EOB) symbol implies that all the
  quantized coefficients from that position until
  the end of the block are zero

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Zigzag pattern
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DCT pattern
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Discrete Cosine Transform example
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Discrete Cosine Transform example
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8
8
1
0
-1
1
0
2
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
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1
0
0
64 pixels
0
0
-1
1
0
0
0
0
0
0
0
1
0
0
0
0
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0
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0
0
0
Cosine patterns/DCT basis functions
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Coding of quantized coefficients

• 20 -20 2 0 0 2 -1 -1 EOB
• DC coefficient The difference between the
  quantized DC coefficient of the current block and
  that of the previous block is Huffman coded
• AC coefficient The magnitude of a nonzero AC
  coefficient combined with the runlength of the
  zero-valued AC coefficients preceding it is
  encoded by a Huffman code.

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Dequantization

• At the receiver, the normalized and quantized DCT
  coefficients are invers scaled (dequantized) by
  multiplying them by the corresponding
  quantization table values
• The resulting coefficients are then inverse
  transformed and the value of 128 is added to each
  pixel. This result in an approximation (due to
  quantization) to the original block

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Dequantized DCT coefficients
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Inverse Discrete cosine transform (IDCT)

• The JPEG inverse DCT with input DCT coefficients
  values F(u,v) and output pixel f(j,k) is given
  by

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Reconstructed 8x8 image block
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Difference image
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SummaryJpeg

• Lossy
• DCT
• Uniform quantization
• Huffman coding
• Manipulating quality

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The MPEG compression standard

• The MPEG (Moving Picture Experts Group) has
  developed a series of algorithms for the
  compression of motion sequences
• The MPEG algorithm is similar to JPEG (in
  principle) for the compression of individual
  frames, but is also capable of exploiting the
  temporal redundancy by estimating and
  compensating for object motion from one frame to
  another.

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The MPEG compression standard

• MPEG1 compression of video and audio for storage
  and retrieval on CD-rom at a combined data rate
  up to 1.5 Mb/s.
• MPEG2 higher rates than MPEG1, e.g., DVD and
  digital satelites use MPEG2 at 3-6 Mb/s HDTV
  at 20 Mb/s
• MPEG4 supports new functionalities such as
  content-based access, manipulation and
  scalability, and improved coded efficiency

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MPEG Family of standards

• It is a generic standard that standarizes a
  syntax for the representation of the encoded
  bit-stream and a method of decoding
• The syntax supports operations such as motion
  estimation, DCT, quantization and Huffmann
  encoding.
• Substantial flexibility is left in the design of
  the encoder, e.g. the motion estimation algorithm
  has not been standardized

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MPEG hierarchie
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MPEG frame types

• Intra-coded or I-frame coded independently from
  all other frames
• Predictive-coded or P-frame coded based on a
  prediction from a past I or P frame
• Bi-directionally predictive-coded or B-frame
  coded based on a prediction from the past and/or
  future I or P frames
• The I and P frames are also called reference
  frames

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MPEG frame types

• I frames use the most number of bits. Followed by
  the P frames and the B frames. A typical ratio of
  compressed frame sizes IPB is 621
• The proportion of the I,P and B frames is
  application-dependent and is left to the user. An
  example is placing a reference frame every 0.1
  second
• I B B P B B P B B P B B P B B I

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-
Frame k
Frame k-1
Variance 1400
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Video Stream Compositie
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Motion Compensation