JPEG2000

1
JPEG-2000

• The JPEG-2000 Still Image Compression Standard,
  M.D. Adams
• Embedded Block Coding in JPEG2000,Taubman,Ordent
  lich, Ueno

By Mona Vajihollahi Roozbeh Farahbod
2
Agenda

• Introduction
• JPEG-2000 Coding Engine
• Codec Structure
• Preprocessing
• Core Processing
• Bit-Stream Formation
• Representation
• Remarkable Features
• Progression
• Region of Interest Coding
• Scalability
• Error Resilience

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Introduction

• Image Compression has to
• Reduce storage and bandwidth requirements
• Allow different extraction modes
• JPEG-2000 provides
• Low bit-rate compression performance
• Progressive transmission by quality, resolution,
  component, or spatial locality
• Lossy and Lossless compression
• Random access to the bitstream
• Region of Interest coding
• Robustness to bit errors

4
Agenda

• Introduction
• JPEG-2000 Coding Engine
• Codec Structure
• Preprocessing
• Core Processing
• Bit-Stream Formation
• Representation
• Remarkable Features
• Progression
• Region of Interest Coding
• Scalability
• Error Resilience

5
Codec Structure
6
Agenda

• Introduction
• JPEG-2000 Coding Engine
• Codec Structure
• Preprocessing
• Core Processing
• Bit-Stream Formation
• Representation
• Remarkable Features
• Progression
• Region of Interest Coding
• Scalability
• Error Resilience

7
Preprocessing

• Source Image Model
• Reference Grid
• Image Tiling
• DC Level Shifting
• Intercomponent Transform

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Source Image Model

• One or Several Components in the image
• Components can be at different resolutions
  (different sizes)

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Preprocessing

• Source Image Model
• Reference Grid
• Image Tiling
• DC Level Shifting
• Intercomponent Transform

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Reference Grid

• A rectangular gird of size Xsiz x Ysiz
• The image is aligned to the bottom-right corner
  of the grid
• XRsiz, YRsiz vertical and horizontal sampling
  periods of each component
• Size of the Image area (Xsiz-XOsiz)x(Ysiz-YOsiz)

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Preprocessing

• Source Image Model
• Reference Grid
• Image Tiling
• DC Level Shifting
• Intercomponent Transform

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Image Tiling

• Partitions image into one or more disjoint
  rectangular regions (tiles)
• Size of a tile XTsiz x YTsiz
• All further operations are performed on tiles

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Image Tiling (2)

• Original Image (b)-(d) after JPEG2000
  compression at 0.255 bpp
• Without Tiling
• With 128 x 128 Tiling
• With 64 x 64 Tiling

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Preprocessing

• Codec Structure
• Source Image Model
• Reference Grid
• Image Tiling
• DC Level Shifting
• Intercomponent Transform

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DC Level Shifting

• Input sample data should have a nominal dynamic
  range centered about zero
• Preprocessing
• Fixes the sample range to be centered around
  zero
• Postprocessing
• Undoes the effects

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Preprocessing

• Codec Structure
• Source Image Model
• Reference Grid
• Image Tiling
• DC Level Shifting
• Intercomponent Transform

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Intercomponent Transform

• Reduces the correlation between components
• Maps image data from RGB to YCrCb
• Advantages
• Improve coding efficiency
• Allow visually relevant quantization
• Two Transforms
• Irreversible color transform (ICT)
• Reversible color transform (RCT)

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Irreversible Component Transformation

• Used for Lossy coding

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Reversible Component Transformation

• Used for Lossless or Lossy coding
• Advantages
• Reasonable Color Space
• Ability of having lossless compression

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Agenda

• Introduction
• JPEG-2000 Coding Engine
• Codec Structure
• Preprocessing
• Core Processing
• Bit-Stream Formation
• Representation
• Remarkable Features
• Progression
• Region of Interest Coding

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Core Processing

• Wavelet Transform
• Quantization/Dequantization

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Wavelet Transform

• Basic idea of 1D wavelet transform

• di0(n) Lower-band signal in level i
• di1(n) Higher-band signal in level i

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Wavelet Transform (2)

• The result of a K-Level wavelet transform on
  input signal X(n)
• In reverse, composition of di0(n) by di1(n)
  results in d(i-1)0(n).

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Wavelet Transform (3)

• 2D wavelet transform
• 1st 1D wavelet transform to all rows
• 2nd 1D wavelet transform to all columns
• It is used for the analysis of
• different components
• into a number of decomposition levels

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Wavelet Transform (4)

• At each level the area is divided into 4
  sub-bands
• LLi down-sampled, low-resolution version of the
  original block
• HLi, LHi, HHi down-sampled residual version of
  the original block

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Wavelet Transform (5)
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Wavelet Transform (6)

• An example

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Wavelet Transform (7)

• 5/3 Transform reversible
• Integer to Integer transform
• Can be used both for lossless or lossy coding
• 9/7 Transform nonreversible
• Real to Real transform
• Can only be used for lossy coding

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Quantization

• A uniform scalar quantization with dead-zone
  about the origin

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Quantization (2)

• One quantization step size is allowed for each
  sub-band
• This operation is lossy unless for step size
  equal to 1
• i.e. when reversible wavelet transform is used
• When step sizes are gt 1
• The step sizes are chosen in conjunction with
  rate control
• They are transferred with the code stream

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Agenda

• Introduction
• JPEG-2000 Coding Engine
• Codec Structure
• Preprocessing
• Core Processing
• Bit-Stream Formation
• Representation
• Remarkable Features
• Progression
• Region of Interest Coding
• Scalability
• Error Resilience

32
Bit-Stream Formation

• Precincts and Code Blocks
• Tier-1 Coding
• Bit-Plane Coding
• Fractional Bit-Plane Scan
• MQ Coder
• Mode Variations
• Tier-2 Coding
• Packets and Layers
• Packet Header Coding
• Packet Body Coding

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Precincts and Code Blocks

• Each subband is divided into rectangular blocks
• Precinct
• 3 spatially consistent rectangle (from each
  subband at each resolution level)
• Code Block
• Each Precinct is partitioned into code blocks
• Each Code Block is encoded independently

Different from Zero-Tree!
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Tier-1 Coding

• Embedded Block Coding
• Every prefix of the encoded stream can be
  decoded to reconstruct the original code block
• Bit-plane Coding
• A technique for Embedded Block Coding
• Bit-plane
• Binary array of bits from all coefficients, at
  same significance level

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Bit-Plane Coding

• Stripe-oriented scans of samples
• Membership of coding passes is
• determined dynamically
• based on the significance of 8 immediate
  neighbors
• Significant bit
• A 1 has been coded for that coefficient in
  current or previous bitplanes

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Bit-plane Coding (2)

• Four Primitives
• Significance Coding
• The sample is not yet significant
• Sign Coding
• When the sample become significant
• Refinement
• The sample is already significant
• Run-length Coding
• When the sample and all neighbors are
  insignificant
• Uses a context-based arithmetic coder

37
Bit-Stream Formation

• Precincts and Code Blocks
• Tier-1 Coding
• Bit-Plane Coding
• Fractional Bit-Plane Scan
• MQ Coder
• Mode Variations
• Tier-2 Coding
• Packets and Layers
• Packet Header Coding
• Packet Body Coding

38
Fractional Bit-Plane Scan

• Each bit-plane is encoded in 3 passes
• Significance Propagation,
• Magnitude Refinement,
• Cleanup,
• Each coefficient bit is coded once (in one of the
  three passes)

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Significance Propagation

• Includes samples that
• are currently insignificant
• have at least one significant neighbor
• Sign bit is coded after the first 1 bit
• Propagation
• Context is dependent on
• The significance of the neighbors
• The subband in which the block is

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Magnitude Refinement/Cleanup

• Magnitude Refinement
• Includes samples that became significant in a
  previous pass
• Context is dependent on
• the significance of the neighbors
• Whether this is the first refinement bit
• Cleanup
• Includes samples that are skipped in Pass 1 and
  Pass 2
• Context is dependent on
• The significance of the neighbors
• Run-length

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Example of Bit-Plane Coding
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Bit-Stream Formation

• Precincts and Code Blocks
• Tier-1 Coding
• Bit-Plane Coding
• Fractional Bit-Plane Scan
• MQ Coder
• Mode Variations
• Tier-2 Coding
• Packets and Layers
• Packet Header Coding
• Packet Body Coding

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Binary Arithmetic Coder

• A message is represented by an interval between 0
  and 1
• MPS More Probable Symbol
• LPS Less Probable Symbol
• With the probability of Qe
• An interval is represented by two real values
• A Size of the interval
• C bottom of the interval

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Binary Arithmetic Coder (2)

• After coding an MPS
• C Qe
• A - Qe
• After coding an LPS
• A Qe
• If A lt ¾, renormalize A and C
• Double the value of A and C
• Overflow of the C register is put in the encoded
  stream

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Binary Arithmetic Coder (3)

• An Example Coding 911

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MQ Coder

• An Adaptive Binary Context-based Arithmetic Coder
• Accepts binary symbols along with their
  probability estimates
• Separate probability estimates are maintained for
  each context
• Probability estimates are updated by a
  finite-state machine

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Bit-Stream Formation

• Precincts and Code Blocks
• Tier-1 Coding
• Bit-Plane Coding
• Fractional Bit-Plane Scan
• MQ Coder
• Mode Variations
• Tier-2 Coding
• Packets and Layers
• Packet Header Coding
• Packet Body Coding

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Mode Variations

• Parallel Execution of Coding Passes
• Parallel processing in each block
• Parallel processing of samples in each coding
  pass
• Lazy Coding
• Less Significant bits have less skewed
  probability distribution
• Bypassing MQ coder in First and Second pass when
  p lt P-4

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Bit-Stream Formation

• Precincts and Code Blocks
• Tier-1 Coding
• Bit-Plane Coding
• Fractional Bit-Plane Scan
• MQ Coder
• Mode Variations
• Tier-2 Coding
• Packets and Layers
• Packet Header Coding
• Packet Body Coding

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Tier-2 Coding

• Input
• The set of bit-plane coding passes, generated in
  Tier-1
• Operation
• Packaging the coding pass information
• Organizing the coding passes
• Output
• Packets

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Packets and Layers

• Packet
• Includes compressed bit streams from each block
  in a precinct
• Layer
• A collection of packets
• Final Bit-Stream
• A succession of Layers

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Packets and Layers (2)
One quality increment for the entire full
resolution tile
One quality increment for one resolution level at
one spatial location
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Packet Header Coding

• For each block in the packet body specifies
• Block inclusion information
• The number of zero bit-planes
• The number of sub-bit-planes included
• The number of bytes for storing encoded
  sub-bit-planes
• Packet header is encoded in an efficient
  embedded manner

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Packet Header Coding (2)
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Packet Body Coding
Different number of sub-bitplanes in for each
code block
Empty Packet Bodies are allowed
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Agenda

• Introduction
• JPEG-2000 Coding Engine
• Codec Structure
• Preprocessing
• Core Processing
• Bit-Stream Formation
• Representation
• Remarkable Features
• Progression
• Region of Interest Coding
• Scalability
• Error Resilience

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Representation

• Two different level of syntax
• Code Stream
• File Format

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Code Stream

• Marker Segment
• Basic building block
• Code Stream
• A sequence of marker segments and data

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File Format

• Specifies additional information
• Color Space, Ownership,
• Box Basic building block
• File A sequence of Boxes

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File Format (2)

• JP2 file format
• Allows storing application specific data with
  JPEG 2000 code stream
• Specifies image properties
• Color-Space of the image
• Intellectual Property Rights
• Metadata can be accessed without decoding the
  image

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Agenda

• Introduction
• JPEG-2000 Coding Engine
• Codec Structure
• Preprocessing
• Core Processing
• Bit-Stream Formation
• Representation
• Remarkable Features
• Progression
• Region of Interest Coding
• Scalability
• Error Resilience

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Progression

• Different ordering of the packets in the code
  stream
• 4 Types of Progression
• Resolution
• Quality
• Spatial Location
• Component
• Progression Type can be changed during coding

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Progression (2)

• Progression by Resolution

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Progression (3)

• Progression by Quality

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Agenda

• Introduction
• JPEG-2000 Coding Engine
• Codec Structure
• Preprocessing
• Core Processing
• Bit-Stream Formation
• Representation
• Remarkable Features
• Progression
• Region of Interest Coding
• Scalability
• Error Resilience

66
Region of Interest

• Coding different regions of the image with
  different quality
• Used when certain parts of the image are of
  higher importance
• ROI coding
• General Scaling-Based method
• MAXSHIFT method

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General Scaling-Based

• Idea
• Scale (shift) coefficients s.t. the bits
  associated with ROI are in higher bit-planes
• Some bits of ROI might be encoded together with
  nonROI bits

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General Scaling-Based (2)

• Steps
• Wavelet Transform
• ROI Mask is derived
• Quantization
• nonROI coefficients are downscaled
• Entropy coding
• Scaling Value and ROI coordinates are included

69
MAXSHIFT Method

• Scaling value S is chosen such that
• The minimum ROI coefficient is larger than the
  maximum nonROI coefficient
• Advantages
• Allows arbitrary shaped ROIs
• No ROI mask is needed

70
Agenda

• Introduction
• JPEG-2000 Coding Engine
• Codec Structure
• Preprocessing
• Core Processing
• Bit-Stream Formation
• Representation
• Remarkable Features
• Progression
• Region of Interest Coding
• Scalability
• Error Resilience

71
Scalability

• The ability to achieve coding of more than one
  qualities and/or resolution simultaneously
• Two important types
• SNR Scalability
• Spatial or Resolution Scalability
• Advantages
• No need to know target bit rate/resolution
• No need for multiple compressions
• Resilience to transmission errors

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SNR Scalability

• The bit stream can be decompressed at different
  quality levels (SNR)

Decompressed image bike at (a) 0.125 b/p, (b)
0.25 b/p, (c) 0.5 b/p
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Spatial Scalability

• The bit stream can be decompressed at different
  resolution level

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Scalability (2)

• Combination of Spatial and SNR
• Changing the progression type

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Agenda

• Introduction
• JPEG-2000 Coding Engine
• Codec Structure
• Preprocessing
• Core Processing
• Bit-Stream Formation
• Representation
• Remarkable Features
• Progression
• Region of Interest Coding
• Scalability
• Error Resilience

76
Error Resilience

• Desirable in mobile and Internet applications
• Tools for Error Resilience

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JPEG-2000 V.S. JPEG
(a)
(b)
Compression at 0.25 b/p by means of (a) JPEG (b)
JPEG-2000
78
JPEG-2000 V.S. JPEG
(a)
(b)
Compression at 0.2 b/p by means of (a) JPEG (b)
JPEG-2000
79
References

• M.D. Adams, The JPEG-2000 Still Image
  Compression Standard, ISO/IEC JTC1/SC29/WG1
  (ITU-T SG8), 2001
• D. Taubman, E. Ordentlcih, I. Ueno, Embedded
  Block Coding, Proc. Int. Conf. on Image
  Processing (ICIP '2000), Vol. II, 33-36, 2000
• M.W. Marcellin, M.J. Gormish, A. Bilgin, M.P.
  Boliek, An Overview of JPEG-2000, Proc. Of IEEE
  Data Compression Conference, pp. 523-541, 2000
• A. Skodras, C. Christopulos, T. Ebrahimi, The
  JPEG 2000 Still Image Compression Standard, IEEE
  Signal Processing Magazine, pp. 36-60, September
  2001
• D.S. Taubman, and M.W. Marcellin, "Jpeg2000
  Image Compression Fundamentals, Standards, and
  Practice", Kluwer Academic Pulishers, 2001.
• G. Cena, P. Montuschi, L. Ciminiera, A. Sanna, A
  Q-Coder Algorithm with Carry Free Addition,
  Proc. 13th IEEE Symposium on Computer Arithmetic,
  pp. 282-290, July 1997
• S.Y. Choo, G. Chew, JPEG 2000 and Wavelet
  Compression,
• http//www-ise.stanford.edu/class/psych221/00/shu
  oyen/