Image Compression 2011

7/27/2019 Image Compression 2011

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Presenter:

Jin-Zuo L iu

Research Advisor:

Jian-Jiun Ding , Ph. D.Digital Image and Signal Processing Lab

Graduate Institute of Communication Engineering

National Taiwan University

Image Compression

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Outlines

Introduction to Image compression

JPEG Standard

JPEG2000 Standard

Shape-Adaptive Image Compression Modified JPEG Image Compression

Conclusions

Reference

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Image Storage System

Object

R-G-B

coordinate

Transform to

Y-Cb-Cr

coordinate

Downsample

ChrominanceEncoder

DecoderR-G-Bcoordinate

Transform toR-G-B

coordinate

UpsampleChrominance

Monitor

C

Camera

C

V

HDDPerformance

RMSE

PSNR

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Transform function:

Y: the luminance represents the brightness

Cb: the difference between the gray and blue Cr: the difference between the gray and red

0.299 0.587 0.114 0

0.169 0.334 0.500 128

0.500 0.419 0.081 128

Y R

Cb G

Cr B

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Downsampling formats of YCbCr

Y

Cb

Cr

W

W

W

H

H

H

Y

W

H Y

W

H

Cb

W/2

H

Cr

W/2

H

Cb

W/2

H/2

Cr

W/2

H/2

(a) 4 : 4 : 4 (b) 4 : 2 : 2 (c) 4 : 2 : 0

Y

W

H

C

bH

Cr

W/4

H

(d) 4 : 1 : 1

W/4

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Performance measures

n1 the data quantity of original

image

n2the data quantity of the

generated bitstream.

Wthe width

H

the height of the

original image

1

2

nCR

n

1 1 2

0 0

( , ) '( , )W H

x y

f x y f x y

RMSEWH

10

25520logPSNR

MSE

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Outlines


JPEG Standard

JPEG2000 Standard


Conclusions

Reference

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JPEG flowchart

Image

RG

B

YCbCr Color

Transform

Chrominance

Downsampling

(4:2:2 or 4:2:0)

8 8

FDCT

Quantizer

QuantizationTable

Zigzag &

Run Length

Coding

Differential

Coding

Huffman

Encoding

Huffman

Encoding

Bit-stream

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Why we apply DCT?

Reduce the correlation between the neighboringpixels in the image

coordinate rotation

the f2th pixel value Y

X

the f1th pixel value

f1-f2= 3 pixels in horizontal

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Covariance Matrix

Step1: Image partition

Step2: Re-aligned the pixels of a 2-D block into a

1-D vector

1 1 1

1

m m m m

N

xx

m m m m

N N N

E x x E x x

C

E x x E x x

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Karhunen-Loeve Transform (KLT)

Coordinate rotation

Normal orthogonal transformation

V = [ v1v2vN ]vithe eigenvector of the corrosponding

eigenvalue i ofCxx ( i1N )

m mty V x

t t

m m m mt t t t

yy xxC E E C

V x V x V x x V V V

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DCT V.S KLT KLT is the Optimal Orthogonal Transform with minimal MSE

but is difficult to implement

DCT is the limit situation of KLT

DCT advantages:

1. Eliminate the dependence on image data

2. Obtain the general transformation for every

image

3. Reduce the correlation between pixels just

like KLT

4. Smaller computation time

5. Real numbers

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Discrete Cosine Transform (DCT) Forward 2-D Discrete Cosine Transform

Inverse 2-D Discrete Cosine Transform

f(x,y) : the element in spatial domain

F(u,v) : the DCT coefficient in the frequency domain

7 7

0 0

1 (2 1) (2 1)( , ) ( ) ( ) ( , ) cos cos

4 16 16

for 0,...,7 and 0,...,7

1/ 2 for 0

where ( ) 1 otherwise

x y

x u y vF u v C u C v f x y

u v

k

C k

1 1

0 0

2 (2 1) (2 1)( , ) ( ) ( ) ( , )cos cos

2 2

for 0,..., 1 and 0,..., 1

N N

u v

x u y vf x y C u C v F u v

M NMN

x M y N

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Discrete Cosine Transform (DCT)

88 DCT

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JPEG Quantization

Qantization:

Qantization table

( , )( , )

( , )Quantization

F u vF u v round

Q u v

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DPCM for DC Components

large correlation still exists between the DCcomponents in the neighboring macroblocks

DCi-1 DCi

Blocki-1 Blocki

Diffi = DCi - DCi-116


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Grouping method for DC component

Values Bits for the valuegroup

0 0

-1,1 0,1 1

-3,-2,2,3 00,01,10,11 2

-7,-6,-5,-4,4,5,6,7 000,001,010,011,100,101,110,111 3

-15,...,-8,8,...,15 0000,...,0111,1000,...,1111 4

-31,...,-16,16,...31 00000,...,01111,10000,...,11111 5

-63,...,-32,32,...63 000000,...,011111,100000,...,111111 6

-127,...,-64,64,...,127 0000000,...,0111111,1000000,...,1111111 7

-255,..,-128,128,..,255 ... 8

-511,..,-256,256,..,511 ... 9

-1023,..,-512,512,..,1023 ... 10

-2047,...,-1024,1024,...,2047 ... 11

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Grouping method for DC component

Example: diff=17

(17)10 = (10001)2

group 5 codeword: (110)2

code: (11010001)2

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Zigzag Scanning of the AC

Coefficients

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Run Length Coding of the AC

Coefficients

The RLC step replaces the quantized values by

Example:

the zig-zag scaned 63 AC coefficients:

Perform RLC :

( , )RUNLENGTH VALUE

the number ofzeros

the nonzerocoefficients

57, 45, 0, 0, 0, 0, 23, 0, 30, 16, 0, 0, 1, 0, 0, 0,0, 0, 0, 0, ..., 0

0,57 0,45 4,23 1, 30 0, 16 2,1 EOB 20


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The Run/Size Huffman table for the

luminance AC coefficients

Run/Size code length code word

0/0 (EOB) 4 1010

15/0 (ZRL) 11 11111111001

0/1 2 00

...

0/6 7 1111000

...

0/10 16 1111111110000011

1/1 4 1100

1/2 5 11011

...

1/10 16 11111111100010002/1 5 11100

...

4/5 16 1111111110011000

...

15/10 16 1111111111111110

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Outlines


JPEG Standard

JPEG2000 Standard


Conclusions

Reference

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The JPEG 2000 Standard

JPEG2000 fundamental building blocks

Image

RG

B

Forward

ComponentTransform

2D DWT Quantization EBCOT

ContextModeling

ArithmeticCoding

Rate-Distortion

Control

Tier-2Tier-1

JPEG 2000

Bit-stream

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Discrete Wavelet Transform

The analysis filter bank of the 2-D DWT

2

2

( 1, , )W j m n

( )h n

( )h n

2

2

( )h m

2

2

( )h m

( , , )DW j m n

( , , )VW j m n

( , , )HW j m n

( , , )W j m n

Columns

Rows

( )h m

( )h m

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Wavelet Transforms in Two Dimension

Two-scale of 2-D decomposition

( , , )DW j m n( , , )VW j m n

( , , )HW j m n( , , )W j m n

( 1, , )W j m n

LL2

LH2

LH1 HH1

HL1

HL2

HH2

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Discrete Wavelet Transform

One-scale of 2-D DWT

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Outlines


JPEG Standard

JPEG2000 Standard


Conclusions

Reference

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Shape-Adaptive Image Compression

Block-based transformation disadvantages:

1.block effect

2. no take advantage of the local

characteristics in an image segment

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Algorithm structure

Image

Segmentation

Boundary

TransformCoding

Arbitrary Shape

TransformCoding

Quantization

AndEntropy Coding

Quantization

AndEntropy Coding

Bit-stream

Boundary

Interal texture

Boundary Descriptor

Coefficients of Transform Bases

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Shape-Adaptive

Transformation(1)

Padding Algorithm

Padding zeros into the pixel positions out of the

image segment

0 0 0 0 75 96 0 0

105 98 99 101 73 85 66 60

100 970 89 94 87 64 55

0 0 84

0 0 0

0 0 93

0 0 0 105 104 0 0 0

0 0 0

94 90 81 71 66

86 86 81 72 0

86 94 81 70 0

98 97 78 0 0

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Shape-Adaptive Transformation(2)

Arbitrarily-Shaped DCT Bases

For and , where

W: the width of the image segment

H: the height of the image segment

1 1

0 0

2 ( ) ( ) (2 1) (2 1)( , ) ( , ) cos cos

2 2*

W H

x y

C u C v x u y vF u v f x y

W HH W

0,..., 1u W 0,..., 1v H

1 / 2 for 0( )

1 otherwise

kC k

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Arbitrarily-Shaped DCT Bases

0 0 0 0 1 1 0 0

1 1 1 1 1 1 1 1

1 10 1 1 1 1 1

0 0 1

0 0 0

0 0 1

0 0 0 1 1 0 0 0

0 0 0

1 1 1 1 1

1 1 1 1 0

1 1 1 1 0

1 1 1 0 0

0 1 2 3 4 5 6 70

1

23

4

5

6

7The shape matrix

The 8x8 DCT bases with the shape

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Gram-Schmidt algorithm

The 37 arbitrarily-shape orthogonal DCT bases

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37

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Shape-Adaptive DCT Algorithm ( SADCT )x

y

x x

y' u

x

u

x' v

u u

DCT-1

DCT-2

DCT-3

DCT-4

DCT-3

DCT-6

DCT-6DCT-5DCT-4DCT-2

DCT-1DCT-1

(a) (b) (c)

(d) (e) (f)

DC values

DC coefficients

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Sh Ad ti DCT Al ith


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Shape-Adaptive DCT Algorithm

( SADCT )

The variable length (N-point) 1-D DCT transform

matrix DCT-N

: thepth DCT basis vector

Transform function:

(2 / ) DCT-Nj jc N x

0

1DCT-N( , ) cos , , 0 1

2

p k c p k k p N

N

1 / 2 for 0( )

1 otherwise

pC p

p

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Morphological Erosion

Input ImageImage

Segmentation

Morphological

Operation (Erosion)

Shape

Adaptive DCT

QuantizationEntropy CodingOutput

Bitstream

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Contour sub-region

Interior sub-region

The overall

object

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Algorithm structure

Interior sub -regions

Contour sub-regions

Shape-

adaptive

DCT

Shape-

adaptive

DCT

Segmentation+

boundaries extraction

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1010101011011111

Image segments

100111101010

101010111111111001

111000111000101011111

Quantizing & encoding

EOB

EOB

EOB

DCT coefficients

boundary

encoding

bit stream of

boundaries

100111101010 1010101111111110

111000111000101011111

EOB

EOB EOB01

M1

M2

M3

S.A.DCT

Bit-stream of image

segments

combine

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Simulation Results

0.4 0.5 0.6 0.7 0.8 0.9 1 1.138

38.5

39

39.5

40

40.5

41

41.5

42

42.5

43

Bitrate(104) [Bits]

PSNR

[dB]

SADCT

SADCT with erosion

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Outlines

Introduction to Image compression JPEG Standard

JPEG2000 Standard


Conclusions

Reference

41

o e mage


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o e mageCompression

2-D Orthogonal DCT Expansion inTriangular and Trapezoid Regions

p

All 8X8 rectangular blocks

Triangular, trapezoid or rectangular

blocks

(b)(a)

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Trapezoid Definition

Define the trapezoid :

(M-1)th row

(M-2)th row

1st row

0th row

.

.

.

.

.

.

1 is a constant.K m K M m

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Trapezoid Definition

Shearing a region that satisfies into the trapezoidregion whose first pixels in each row are aligned

at the same column.

A triangular region can be viewed as a specialcase of the trapezoid region where

Shearing

(b)(a)

(M-1)th

row

1st row

0th

row

.

.

.

.

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C l t d O th l DCT


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Complete and Orthogonal DCT

Basis in the Trapezoid Region

m=M-1

m = M-2

m= 1m= 0

.

.

.

.

.

.

n= 0 1 2

Region A

Region B

Rotation by 180Region A

Region B

Rectangular Region

(a)

(b)

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Basis in the Trapezoid Region

2 4 6 8 10

2

4

2 4 6 8 10

2

4

2 4 6 8 10

2

4

2 4 6 8 10

2

4

2 4 6 8 10

2

4

2 4 6 8 10

2

4

2 4 6 8 10

2

4

2 4 6 8 10

2

4

2 4 6 8 10

2

4

2 4 6 8 10

2

4

2 4 6 8 10

2

4

2 4 6 8 10

2

4

2 4 6 8 10

2

4

2 4 6 8 10

2

4

2 4 6 8 10

2

4

2 4 6 8 10

2

4

(b)

(a)

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Fi di i t t id


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Finding an approximate trapezoid

region in an arbitrary shape

(a) (b)

approximate

(a) (b)

47

M difi d JPEG I C i


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Modified JPEG Image Compression

Divide Images into three regions:

Trapezoid and triangularregions

Traditional 8X8 image

blocks

8X8 SADCT image blocks

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Simulation Results

50 100

50

100 50 100

50

100

(a) JPEG 692 Bytes (b) Proposed scheme 165 Bytes

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Simulation Results

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Reference [1] R. C. Gonzalea and R. E. Woods, "Digital Image

Processing", 2nd Ed., Prentice Hall, 2004. [2] Liu Chien-Chih, Hang Hsueh-Ming, "Acceleration and

Implementation of JPEG 2000 Encoder on TI DSPplatform" Image Processing, 2007. ICIP 2007. IEEEInternational Conference on, Vo1. 3, pp. III-329-339,2005.

[3] ISO/IEC 15444-1:2000(E), "Information technology-

JPEG 2000 image coding system-Part 1: Core codingsystem", 2000. [4] Jian-Jiun Ding and Jiun-De Huang, "Image

Compression by Segmentation and BoundaryDescription", Masters Thesis, National Taiwan University,Taipei, 2007.

[5] Jian-Jiun Ding and Tzu-Heng Lee, "Shape-AdaptiveImage Compression", Masters Thesis, National TaiwanUniversity, Taipei, 2008.

[6] G. K. Wallace, "The JPEG Still Picture CompressionStandard", Communications of the ACM, Vol. 34, Issue 4,pp.30-44, 1991.

[7]JPEG 2000

() IC 2003.8.51


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Thank you forl is ten ing ~

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Image Compression 2011