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JPEG 2000
Marcela Iregui Antonin Descampe François-Olivier
Devaux
Université catholique de Louvain
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Presentation plan

• JPEG 2000 Features
• Main coding blocks
• Encoding process
• JPEG 2000 standardization

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Presentation plan

• JPEG 2000 Features
• Main coding blocks
• Encoding process
• Standardization process

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JPEG 2000 Features

• Improved compression efficiency
• Lossy to lossless compression
• Multiple resolution representation
• SNR scalability
• Progressive decoding
• ROI coding
• Error resilience
• Random codestream access

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Improved Image Quality
JPEG 1137
JPEG2000 1137
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Improved Image Quality
JPEG 1126
JPEG2000 1126
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Single compression / Multiple decompression
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Progressive transmissions

Progression in quality
Compression
Storage
Progression in resolution
Spatial Progression
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Wavelet transform
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Wavelet transform 1
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Wavelet transform 2
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Wavelet transform 3

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Multiresolution compression by wavelets


2.6 kBytes (1100)
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Reduced Quality Reconstruction
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Progressive Quality
1.6 download
2.2 download
8.0 download
26.4 download
100 download
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Regions of Interest
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Robustness to Errors
Compression 152 13.4 KB Embedded Error 16
Bytes set to zero in the middle of the files
JPEG
JPEG2000
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Presentation plan

• JPEG 2000 Features
• Main coding blocks
• Encoding process
• Standardization process

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Main coding blocks
Discrete Wavelet Transform (DWT)
Entropy Coding Unit (ECU)
Original image
Compressed data
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Main coding blocks
Discrete Wavelet Transform (DWT)
Entropy Coding Unit (ECU)
Original image
Compressed data
Goal Concentrate the image information in a very
localized (and small) area ? Enable a higher
compression ratio in other areas Ouput 4
subbands with the upper left one containing low
frequencies
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Main coding blocks
Discrete Wavelet Transform (DWT)
Entropy Coding Unit (ECU)
Original image
Compressed data
Successive decompositions are applied on the
low frequencies.
?
?
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Main coding blocks
Discrete Wavelet Transform (DWT)
Entropy Coding Unit (ECU)
Original image
Compressed data
Each subband is then divided into code-blocks
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Main coding blocks
Discrete Wavelet Transform (DWT)
Entropy Coding Unit (ECU)
Original image
Compressed data

• The ECU contains two blocks
• Context Modeling Unit (CMU)
• Arithmetic Coding Unit (ACU)

The CMU handles first the bits bringing the
highest distortion reduction?3 groups of bits
encoded in different passes?Algorithm used
EBCOT
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Main coding blocks
Discrete Wavelet Transform (DWT)
Entropy Coding Unit (ECU)
Original image
Compressed data

• The ECU contains two blocks
• Context Modeling Unit (CMU)
• Arithmetic Coding Unit (ACU)

010011011100

• ACU coder itself
• Removes redundancy present in the binary
  sequence
• Algorithm used MQ

010100
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Presentation plan

• JPEG 2000 Features
• Main coding blocks
• Encoding process
• Standardization process

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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 ??
  at
• 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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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

• 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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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 amount of data
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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Presentation plan

• JPEG 2000 Features
• Main coding blocks
• Encoding process
• Standardization process

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Standardization process

• Part 1, Core coding system
• (intended as royalty and license-fee free)
• Part 2, Extensions
• (adds more features and sophistication to the
  core)
• Part 3, Motion JPEG 2000
• Part 4, Conformance
• Part 5, Reference software
• (Java and C implementations are available)
• Part 6, Compound image file format
• (document imaging, for pre-press and fax-like
  applications, etc.)
• Part 7 has been abandoned

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Standardization process

• Part 8, JPSEC (security aspects)
• Part 9, JPIP (interactive protocols and API)
• Part 10, JP3D (volumetric imaging)
• Part 11, JPWL (wireless applications)
• Part 12, ISO Base Media File Format
• (common with MPEG-4)

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Open JPEG

• Open source JPEG 2000 coder and decoder
• Implemented in C language
• Developped here at UCL
• http//www.openjpeg.org/

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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