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JPEG 2000
Marcela Iregui Guerrero
Université catholique de Louvain
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JPEG 2000 Overview
Image
Rate Control
Arithmetic coding
ROI
Pre- processing
Wavelet Transform
Quant.
Coefficient bit model
Data Ordering
Codestream
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JPEG 2000 Overview
Image
Pre- processing
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Image pre-processing

• Tile partition (each component of each tile
  encoded independently)
• DC level shifting
• Unsigned sample values ? Signed values
• Colour transformation
• To de-correlate the colour data
• RGB ? YCbCr (ICT)
• RGB ? YUV (RCT)

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High resolution grid, image components and tiling
(XTsiz)
(0,0)
(ax,ay)
(YTsiz)
(bx-1, by-1)
Image Area
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JPEG 2000 Overview
Image
ROI
Pre- processing
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DWT

• DWT intra-component decorrelation
• ? concentrate image energy in a small area
• No blocking artefacts at high compression ratios
  
• Enables multi-resolution image representation

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1-D DWT

• Application of a pair of low-pass high-pass
  filter

• Filter-bank charateristics symmetric,
  bi-orthogonal
• 2 filter-banks defined in JPEG2000
• reversible (5,3) and irreversible (9,7)

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1-D DWT (ctd)

• After a decomposition, most of the energy is
  located at the low-pass output.
• Successive applications of the filters on the
  low-pass outputs
• ? dyadic decomposition

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2-D DWT

• 2-D DWT 1-D DWT on the columns
• followed by 1-D DWT on the rows
• ? four filtered and subsampled images
  (subbands)

• In JPEG 2000 5 decompositions by default

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DWT the lifting scheme

• Problem straightforward DWT implementation
  requires storage of the entire image in memory
• Alternative implementation lifting scheme
• Memory ?
• Compute load ?
• In-place computation
• Principle

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Example (5,3) filter
In general
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Integer-to-integer transforms

• Problem precision required on coefficients ??
  with every level of the DWT
• Solution insert quantizers in the lifting
  scheme

Quantizer truncation or rounding to the
nearest integer (still mathematically
invertible !)
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JPEG 2000 Overview
Image
Pre- processing
Wavelet Transform
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Quantization

• Uniform quantizer
• Separate stepsize for each sub-band

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JPEG 2000 Overview
Image
Pre- processing
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Entropy coding

• Requirements
• embedded bit-stream
• distortion progressive ordering
• resolution scalability
• localized random access to the image
• efficient rate control
• error resilience

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Code-blocks and Bit-planes

• Each sub-band of each tile component is
  partitioned
• into code-blocks
• Each code-block is compressed independently
  using
• bit-plane coding

Bit-plane i
LSB
MSB
DWT
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Arithmetic coding

• Removes the redundancy in the encoding of the
  data
• Assigns short code-words to more probable events
  and
• longer code-words to the less probable
• AC estimates the probability of the events to
  assign the
• code-words
• A statistical encoder must work in conjunction
  with a
• modeller that estimates the probability of each
  possible
• event at each point in the coding

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Arithmetic entropy coding
Bit
Arithmetic coding
Coefficient bit model
Compressed image data
Quantified Coefficient
Context

• The context represents the status of the
  neighbour
• coefficients
• The MQ-coder estimates the probability of the
  current
• coding symbol.

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Bit-plane coding

• Quantized coefficients are represented in
  sign-magnitude
• Leading all-zero bit-planes are skipped.
• Each bit-plane is coded in three phases
• Significance Propagation
• Magnitude Refinement
• Clean up

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Significance State

• Each coefficient in a code-block has an
  associated binary state variable called its
  significance state.
• The significance state changes from
  insignificant to significant at the bit-plane
  where the most significant bit equal to 1 is
  found.

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Context

• The context is a state governed by the past
  sequence
• of symbols

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Bit-plane coding

• Bit-plane blocks scan pattern

• The first bit-plane is coded in the clean up
  pass
• Next bit-planes are coded in three phases
• Significance Propagation
• Includes the coefficients that are predicted or
  most-likely to become significant and their
  sign bit as appropriated
• Magnitude Refinement
• Includes bits from already significant
  coefficients
• Clean up Significance Propagation
• Includes all the remaining coefficients

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Significance propagation pass

• The current bit is coded in this pass
• Only if the past bits of the coefficient were
  insignificant (the
• significance state for this coefficient has
  yet to be set) and
• the bit has a non-zero context (it has almost
  one significant
• neighbour)
• If the bit is one
• the significance state is set
• the bit is coded (MQcoder (1, CTX))
• the next bit to code is the sign bit
• If the bit is zero
• The bit is coded (MQcoder (0, CTX))
• The significance state remains 0

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Contexts for the significance propagation pass
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Sign-bit coding
If the current bit has become significant, the
sign bit is coded using another context vector
from the neighbourhood.
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Magnitude Refinement pass
Includes bits from coefficients that are already
significant (except those that have just become
significant in the immediately preceding
significance propagation pass)
First refinement for this coefficient
SH0 SV0 SD0
Context label
x ? 1 0
false true true
16 15 14
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Clean up pass

• The first bit-plane in a new block is coded in
  the clean up pass
• Run length encoding (if 4 coeff. Have context0)
• Run-length context (17)
• If there is almost 1 different to zero UNIFORM
  context (18)
• It includes the remaining coefficients that are
  insignificant and had the context of 0 in the
  significance propagation pass
• The neighbour contexts are the same than for the
  significance pass

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Bit-plane coding example
Scan Pattern for bit-plane coding
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JPEG 2000 Overview
Image
Arithmetic coding
ROI
Pre- processing
Wavelet Transform
Quant.
Coefficient bit model
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Compressed data
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Distortion Estimation
Ex. Significant bit y 22 00010110 y4
24 00011000
DDDb-Da(y-0)2-(y-y4)2
20
22
23
24
25
21
1.524
0
22
24
2
8
16
32
4
1
Da
Db
Ex. Refinement bit y 22 00010110 y320
00010100
DDDb-Da(y-y4)2-(y-y3)2
20
22
23
24
25
21
1.2524
1.7524
0
22
24
20
2
8
16
32
4
1
Db
Da
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Rate-Distortion Optimisation
truncation point ni distortion data quantity
The Image is divided in code-blocks
and
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The optimisation principle

• for each code-block, find the truncation points
  ni which minimise

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Layers Abstraction
Rate-distortion optimisation (non standardised)
A layer is a quality increment for an entire
tile
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JPEG 2000 Overview
Image
Rate Control
Arithmetic coding
Pre- processing
Wavelet Transform
Quant.
Coefficient bit model
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Precincts and packets
Packet k Bitstream of precinct p, at resolution
r layer l, comp. c
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Codestream syntax
Tile-body (Data)
Tile- header
Tile header
Tile- header
Main header
Tile- header
Tile-body (Data)
Tile-body (Data)

P1
P2
P3
Pn
EOC

packet header
Code-block i Entropic Data
Code-block n Entropic Data
SOP
EPH

• Code block inclusion
• Zero bit plane information
• Number of coding passes
• Data length

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JPEG 2000 Overview
JPEG 2000 Overview
Image
Rate Control
Arithmetic coding
Pre- processing
Wavelet Transform
Quant.
Coefficient bit model
Data Ordering
Codestream
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Region of Interest

• Spatial random access to the codestream is
  possible by
• tiles, precincts and code-blocks
• A ROI mask can be created which contains the bit
  map
• describing the coefficients that must be
  encoded
• with better quality
• The ROI coefficients are placed in higher
  bit-planes than
• the background by shifting
• The bit-planes associated
• with the ROI are coded before
• the background information.

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J2K parts under development

• Part 8, JPSEC (security aspects)
• Part 9, JPIP (interactive protocols and API)
• Part 10, JP3D (volumetric imaging)
• Part 11, JPWL (wireless applications)

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References

• ISO, JPEG 2000 International Standard
• Taubman, D. and Marcellin, M. (November 2001)
  JPEG2000 Image compression
• fundamentals, standards and practice, Boston,
  Kluwer Academic Publishers, 795 pgs.
• Taubman, High performance scalable image
  processing with EBCOT, IEEE Trans. on Image
  processing, July 2000.
• Rabbani, Joshi, An overview of the JPEG2000
  still image compression standard, Signal
  processing Image communication 17(2002) p 3-48.
• Special issue on JPEG2000, Signal Processing
  Image Communication. Elsevier, Volume 17, Issue
  1, January 2002