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Image Compression

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h0(n) is scaling function, low pass filter (LPF) ... Synthesis filters: g0(n)= (-1)nh1(n) g1(n)= (-1)nh0(n) is up-sampling (zeroes inserting) ... – PowerPoint PPT presentation

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Title: Image Compression


1
DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF
JOENSUU JOENSUU, FINLAND
  • Image Compression
  • Lecture 18
  • JPEG 2000
  • Alexander Kolesnikov

2
Wavelet Transform and Filter Banks
3
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)
4
5/3 filter for lossless encoding
h0(n) - LPF scaling func.
h1(n) - HPF wavelet func.
5
5/3 filter for lossless encoding
6
9/7 filter for lossy encoding
h0(n) - LPF scaling func.
h1(n) - HPF wavelet func.
7
9/7 filter for lossy encoding
8
5-tab low pass filter (LPF)
2
Filtration
Subsampling
9
3-tab high pass filter (HPF)
2
Subsampling
Filtration
10
Filtration with Haar -filters
11
Filtration with 5/3-filters
Input x
Input x
LPF s
HPF d
12
Inverse wavelet transform
is up-sampling (zeroes inserting)
Synthesis filters g0(n)?(-1)nh1(n)
g1(n)?(-1)nh0(n)
13
Wavelet transform as Subband filtering
14
Complexity of discrete wavelet transform
Without scaling-function property
15
2-D Wavelet transform
Horizontal filtering
Vertical filtering
16
2-D wavelet transform
Transform Coeff. 4123, -12.4, -96.7, 4.5,
Original 128, 129, 125, 64, 65,
17
2-D wavelet transform
LL3
HH4
LH2
HH3
LH1
HH2
HL2
HH1
HL1
18
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.

19
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

20
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

21
Key components
  • Visual
  • Weighting
  • Masking
  • Region of interest (ROI)
  • Lossless color transform
  • Error resilience

22
2-D wavelet transform
Transform Coeff. 4123, -12.4, -96.7, 4.5,
Original 128, 129, 125, 64, 65,
23
Quantization of wavelet coefficients
Transform Coeff. 4123, -12.4, -96.7, 4.5,
Quantized Coeff.(Q64) 64, 0, -1, 0,
24
Quantizer with dead zone
Quantized Magnitude
Sign
25
Entropy coding
0 1 1 0 1 1 0 1 0 1 . . . Coded Bitstream
Quantized Coeff.(Q64) 64, 0, -1, 0,
26
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

27
Block structure in EBCOT
Encode each block separately record the
bitstream of each block. Block size is 64x64.
28
Progressive encoding
29
Quantizer with dead zone
Quantized Magnitude
Sign
30
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.
31
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

32
Tiling
  • Image ? Component ? Tile ? Subband ? Code-Block ?
    Bit-Planes

33
JPEG 2000 vs JPEG
DCT
WT
34
JPEG 2000 vs JPEG Quantization
JPEG
JPEG 2000
35
JPEG 2000 vs JPEG 0.3 bpp
JPEG
JPEG 2000
36
JPEG 2000 vs JPEG Bitrate0.3 bpp
MSE150
MSE73 PSNR26.2 db
PSNR29.5 db
37
JPEG 2000 vs JPEG Bitrate0.2 bpp
MSE320
MSE113 PSNR23.1 db
PSNR27.6 db
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