Basic Image Compression Concepts Presenter: Guan-Chen Pan Research Advisor: Jian-Jiun Ding , Ph. D. Assistant professor Digital Image and Signal Processing Lab Graduate Institute of Communication Engineering National Taiwan University

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Basic Image Compression ConceptsPresenterGuan-
Chen PanResearch AdvisorJian-Jiun Ding , Ph.
D.Assistant professorDigital Image and Signal
Processing LabGraduate Institute of
Communication EngineeringNational Taiwan
University
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Outlines

• Introductions
• Basic concept of image compression
• Proposed method for arbitrary-shapeimage segment
  compression
• Improvement of the boundary region by morphology
• JPEG2000
• Triangular and trapezoid regions and modified
  JPEG image compression

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Introduction

• Lossless or lossy(widely used)

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YCbCr

• Ythe luminance of the image which represents
  the brightness
• Cbthe chrominance of the image which
  represents the difference between the
  gray and blue
• Crthe chrominance of the image which
  represents the difference between the
  gray and red

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Chrominance Subsampling

• The name of the format is not always related to
  the subsampling ratio.

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Reduce the Correlation between Pixels

• Transform coding
• Coordinate rotation
• Karhunen-Loeve transform
• Discrete cosine transform
• Discrete wavelet transform
• Predictive coding

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Coordinate rotation

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Weight
Height
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• do the inverse transform to get the data and
  reduce the correlation

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Karhunen-Loeve transform(KLT)

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Discrete cosine transform

• The DCT is an approximation of the KLT and more
  widely used in image and video compression.
• The DCT can concentrate more energy in the low
  frequency bands than the DFT.

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Discrete wavelet transform

• Wavelet transform is very similar to the
  conventional Fourier transform, but it is based
  on small waves, called wavelet, which is composed
  of time varying and limited duration waves.
• We use 2-D discrete wavelet transform in image
  compression.

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Predictive Coding

• Predictive coding means that we transmit only the
  difference between the current pixel and the
  previous pixel.
• The difference may be close to zero.
• However, the predictive coding algorithm is more
  widely used in video.
• EX. Delta modulation (DM), Adaptive DM. DPCM
  ,Adaptive DPCM (ADPCM)

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Quantization

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• Luminance quantization matrix
• Chrominance quantization matrix
• Removes the high frequencies

16 11 10 16 24 40 51 61
12 12 14 19 26 58 60 55
14 13 16 24 40 57 69 56
14 17 22 29 51 87 80 62
18 22 37 56 68 109 103 77
24 35 55 64 81 104 113 92
49 64 78 87 103 121 120 101
72 92 95 98 112 100 103 99
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Entropy Coding Algorithms

• Huffman Coding
• Difference Coding (DC)
• Zero Run Length Coding (AC)
• Arithmetic Coding
• Golomb Coding

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Huffman Coding

• Huffman coding is the most popular technique for
  removing coding redundancy.
• Unique prefix property
• Instantaneous decoding property
• Optimality
• JPEG(fixed, not optimal)

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Difference Coding

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Zero Run Length Coding

• Encode each value which is not 0, than add the
  number of consecutive zeroes in front of it
• EOB (End of Block) (0,0)
• Only 4-bit value
• 57,45,0,0,0,0,23,0,-30,-16,0,,0
• ?(0,57)(0,45)(4,23)(1,-30)(0,16)EOB
• Eighteen zeroes, 3 ?(15,0) (2,3)
• where (15,0) is 16 consecutive zeroes

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Arithmetic Coding

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Symbol Probability Sub-interval
k 0.05 0.00,0.05)
l 0.2 0.05,0.25)
u 0.1 0.25,0.35)
w 0.05 0.35,0.40)
e 0.3 0.40,0.70)
r 0.2 0.70,0.90)
? 0.1 0.90,1.00)

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Symbol Probability Sub-interval
k 0.05 0.00,0.05)
l 0.2 0.05,0.25)
u 0.1 0.20,0.35)
w 0.05 0.35,0.40)
e 0.3 0.40,0.70)
r 0.2 0.70,0.90)
? 0.1 0.90,1.00)

• 0.071334 ? L

• For interval 0.050.25

Symbol Probability Sub-interval
k 0.05 0.05,0.06)
l 0.2 0.06,0.1)
u 0.1 0.1,0.12)
w 0.05 0.12,0.13)
e 0.3 0.13,0.19)
r 0.2 0.19,0.23)
? 0.1 0.23,0.25)

• 0.071334 ? L

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Golomb Coding

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• Decode 101111
• q 1, r 9
• ? a 1019 19

Encoding of quotient part q output
bits 0 0 1 10 2 110 3 1110 4 11110 5 111110 6 1111
110 N ltN repetitions of 1gt0
Encoding of remainder part r offset binary output
bits 0 0 0000 000 1 1 0001 001 2 2 0010 010 3 3 00
11 011 4 4 0100 100 5 5 0101 101 6 12 1100 1100 7
13 1101 1101 8 14 1110 1110 9 15 1111 1111
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  Without codeword table Flexibility and adaptation
Huffman NO GOOD
Golomb YES MIDDLE
Adaptive Golomb YES GOOD
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Proposed Method for Arbitrary-Shape Image Segment
Compression

• An arbitrary-shape image segment f and its shape
  matrix.

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• Standard 8x8 DCT bases with the shape of f

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• The 37 arbitrary-shape orthonormal DCT bases by
  Gram-Schmidt process

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Quantization

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Improvement of the Boundary Region by Morphology
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JPEG2000

• JPEG 2000 is a new standard and it can achieve
  better performance in image compression.
• Advantages
• Efficient lossy and lossless compression
• Superior image quality
• Additional features such as spatial scalability
  and region of interest.
• Complexity

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• JPEG 2000 encoder

• Embedded Block Coding with Optimized
  Truncation(EBCOT) Tier-1Tier-2

• JPEG 2000 decoder

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Irreversible component transform (ICT)

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Reversible component transform (RCT)

• Reversible and integer-to-integer

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• Irreversible , Daubechies 9/7 filter

  Analysis Filter Coefficients Analysis Filter Coefficients Synthesis Filter Coefficients Synthesis Filter Coefficients
n Lowpass Filter Highpass Filter Lowpass Filter Highpass Filter
0 0.602949018236 1.115087052456 1.115087052456 0.6029490182363
1 0.266864118442 -0.059127176311 0.591271763114 -0.2668641184428
2 -0.078223266528 -0.057543526228 -0.057543526228 -0.0782232665289
3 -0.0168641184428 0.091271763114 -0.0912717631142 0.0168641184428
4 0.026748757410     0.0267487574108
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Tier-1 Encoder

• Each Fractional Bit-plane coding will generate
  the Context (CX) and the Decision (D), which are
  used for arithmetic coding.
• zero coding
• sign coding
• magnitude refinement coding
• run length coding

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Bit-plane Conversion

• Converts the quantized wavelet coefficients into
  several bit-planes
• First bit-plane is the sign plane
• The other planes are the magnitude plane, from
  MSB to LSB

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17 22 33 48 64 80 96 112
22 28 38 52 67 81 96 112
33 38 48 62 75 86 100 116
48 52 62 70 83 96 110 125
64 67 75 83 96 108 118 132
80 81 86 96 108 117 128 142
96 96 100 110 118 128 140 150
112 112 116 125 132 142 150 160

• 17 000100012
• 160 101000002

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Stripe and Scan Order
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Zero Coding
d v d
h D h
d v d

• D current encode data, binary 0 or 1
• h 02 v 02 d 04

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Sign Coding
v
h D h
v

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Magnitude Refinement Coding

• s'x,y is initialized to 0, and it will become 1
  after the first time of the magnitude refinement
  coding is met at x,y

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Run-Length Coding

• For four zeros (CX,D) is (0,0)
• Else is (0,1), and use 2 uniform(CX18) to
  record the 1s position
• (0110)
• The first nonzero position is (01)2
• ?(0,1), (18,0), (18,1)

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D (0,1)
Arithmetic encoder
Compressed data
CX (total 19)
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Why Called Fractional?
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Tier-2 Encoder

• Rate/Distortion optimized truncation

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Triangular and Trapezoid Regions and Modified
JPEG Image Compression

• Divide an image into 3 parts
• Lower frequency regions
• Traditional image blocks and
• The arbitrarily-shaped image blocks

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• 1 sections
• 1 sections
• 1 sections
• 1 sections
• 2 sections
• 2 sections
• 1 sections
• 1 sections

1 1 1 1 1 1 1 1 1 0
0 1 1 1 1 1 1 1 1 1
0 1 1 1 1 1 1 1 1 0
0 1 1 1 1 1 1 1 0 0
0 0 1 1 0 1 1 1 1 0
0 0 1 0 0 1 1 1 0 0
0 0 0 0 0 0 1 1 0 0
0 0 0 0 0 0 1 1 0 0

• Zone 1

• Zone 2

• Zone 3

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• a-distance lt threshold

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• Corner too close
• Trapezoid inside the zone

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N 10

• N K(m) K(M-1-m)

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