Image Compression

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DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF
JOENSUU JOENSUU, FINLAND

• Image Compression
• Lecture 18
• JPEG 2000
• Alexander Kolesnikov

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Wavelet Transform and Filter Banks
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Wavelet Transform and Filter Banks
h0(n) is scaling function, low pass filter
(LPF) h1(n) is wavelet function, high pass filter
(HPF)
is subsampling (decimation)
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5/3 filter for lossless encoding
h0(n) - LPF scaling func.
h1(n) - HPF wavelet func.
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5/3 filter for lossless encoding
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9/7 filter for lossy encoding
h0(n) - LPF scaling func.
h1(n) - HPF wavelet func.
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9/7 filter for lossy encoding
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5-tab low pass filter (LPF)
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Filtration
Subsampling
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3-tab high pass filter (HPF)
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Subsampling
Filtration
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Filtration with Haar -filters
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Filtration with 5/3-filters
Input x
Input x
LPF s
HPF d
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Inverse wavelet transform
is up-sampling (zeroes inserting)
Synthesis filters g0(n)?(-1)nh1(n)
g1(n)?(-1)nh0(n)
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Wavelet transform as Subband filtering
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Complexity of discrete wavelet transform
Without scaling-function property
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2-D Wavelet transform
Horizontal filtering
Vertical filtering
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2-D wavelet transform
Transform Coeff. 4123, -12.4, -96.7, 4.5,
Original 128, 129, 125, 64, 65,
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2-D wavelet transform
LL3
HH4
LH2
HH3
LH1
HH2
HL2
HH1
HL1
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JPEG 2000

• JPEG 2000 is a new still image compression
  standard
• One-for-all image codec
• Different image types binary, grey-scale,
  color,
• multi-component
• Different applications natural images,
  scientific,
• medical remote sensing text, rendered
  graphics
• Different imaging models client/server,
  consumer
• electronics, image library archival,
  limited buffer
• and resources.

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History

• Call for Contributions in 1996
• The 1st Committee Draft (CD) Dec. 1999
• Final Committee Draft (FCD) in March 2000
• Accepted as Draft International Standard in Aug.
  2000
• Published as ISO Standard in Jan. 2002

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Key components

• Transform
• Wavelet
• Wavelet packet
• Wavelet in tiles
• Quantization
• Scalar
• Entropy coding
• (EBCOT) code once, truncate anywhere
• Rate-distortion optimization
• Context modeling
• Optimized coding order

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Key components

• Visual
• Weighting
• Masking
• Region of interest (ROI)
• Lossless color transform
• Error resilience

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2-D wavelet transform
Transform Coeff. 4123, -12.4, -96.7, 4.5,
Original 128, 129, 125, 64, 65,
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Quantization of wavelet coefficients
Transform Coeff. 4123, -12.4, -96.7, 4.5,
Quantized Coeff.(Q64) 64, 0, -1, 0,
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Quantizer with dead zone
Quantized Magnitude
Sign
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Entropy coding
0 1 1 0 1 1 0 1 0 1 . . . Coded Bitstream
Quantized Coeff.(Q64) 64, 0, -1, 0,
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EBCOT

• Key features of EBCOT Embedded Block Coding with
  Optimized Truncation
• Low memory requirement in coding and decoding
• Easy rate control
• High compression performance
• Region of interest (ROI) access
• Error resilience
• Modest complexity

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Block structure in EBCOT
Encode each block separately record the
bitstream of each block. Block size is 64x64.
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Progressive encoding
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Quantizer with dead zone
Quantized Magnitude
Sign
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ROI Region of interest
Scale-down the coefficients outside the ROI so
those are in lowerer bit-planes. Decoded or
refined ROI bits before the rest of the image.
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ROI Region of interest

• Sequence based code
• ROI coefficients are coded as independent
  sequences
• Allows random access to ROI without fully
  decoding
• Can specify exact quality/bitrate for ROI and the
  BG
• Scaling based mode
• Scale ROI mask coefficients up (decoder scales
  down)
• During encoding the ROI mask coefficients are
  found significant at early stages of the coding
• ROI always coded with better quality than BG
• Can't specify rate for BG and ROI

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Tiling

• Image ? Component ? Tile ? Subband ? Code-Block ?
  Bit-Planes

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JPEG 2000 vs JPEG
DCT
WT
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JPEG 2000 vs JPEG Quantization
JPEG
JPEG 2000
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JPEG 2000 vs JPEG 0.3 bpp
JPEG
JPEG 2000
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JPEG 2000 vs JPEG Bitrate0.3 bpp
MSE150
MSE73 PSNR26.2 db
PSNR29.5 db
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JPEG 2000 vs JPEG Bitrate0.2 bpp
MSE320
MSE113 PSNR23.1 db
PSNR27.6 db