1

SPIHT

2

SPIHT

• O(i,j) 為點 (i,j) 的兒子集合• D(i,j) 為點 (i,j) 的子嗣集合• L(i,j)=D(i,j) - O(i,j)• H: 所有空間指向樹的樹根 (最低子頻帶 )

3

Initialization

• Output • set the LSP as an empty list• add the coordinates to the LIP• those with descendants also to the LIS ,as type

A entries

jiji cn ,),(2 (maxlog

Hji ),(

4

Initialization

63

2

-2

2

-2

-1

9

4 23

4-430

6363

4

2

03 -2

64

-13

1049-34

23-31

15 14 3 -12

643

7-12137

5

-3 6 -4

3 0 -3

-5 9 -1 47

3

8-14-7-9

5

14

115 6

-7

Threshold = 32

LIP LIS LSP

63 -34(A)

-34 -31(A)

-31 23(A)

23

5

Sorting Pass

2.1 for each entry (i,j) in the LIP do:

2.1.1 output Sn(i,j);

2.1.2 if Sn(i,j) = 1 then move (i,j) to the

LSP and output the sign of (i,j) ;

otherwise

thresholdjijiSn

,0

),(,1),(

6

Sorting Pass

63

2

-2

2

-2

-1

9

4 23

4-430

6363

4

2

03 -2

64

-13

1049-34

23-31

15 14 3 -12

643

7-12137

5

-3 6 -4

3 0 -3

-5 9 -1 47

3

8-14-7-9

5

14

115 6

-7

Threshold = 32

LIP LIS LSP

-31 -34(A) 63

23 -31(A) -34

23(A)

output: : 111000

7

Sorting Pass

2.2 for each entry (i,j) in the LIS do:

2.2.1 if the entry is of type A then

output Sn(D(i,j));

if Sn(D(i,j)) = 1 then

for each do:

output Sn(k,l) ;

if Sn(k,l) = 1 then add (k,l) to the LSP and output

the sign of (k,l) ;

if Sn(k,l) = 0 then add (k,l) to the end of the LIP ;

),(),( jiOlk

O(i,j)={ (2i , 2j ) ,

(2i , 2j+1) ,

(2i+1 , 2j ) ,

(2i+1 , 2j+1) }

8

Sorting Pass

63

2

-2

2

-2

-1

9

4 23

4-430

6363

4

2

03 -2

64

-13

1049-34

23-31

15 14 3 -12

643

7-12137

5

-3 6 -4

3 0 -3

-5 9 -1 47

3

8-14-7-9

5

14

115 6

-7

Threshold = 32

LIP LIS LSP

-31 -34(A) 63

23 -31(A) -34

10 23(A) 49

14

-13

15

14

-9

-7

output: : 111000 111000 10000 0

9

Sorting Pass

If then move (i,j) to the end of the LIS as an entry of type B , and go to step2.2.2;

Otherwise, remove entry (i,j) from the LIS ;

2.2.2 if the entry is of type B then

output Sn(L(i,j));

if Sn(L(i,j)) = 1 then

add each to the end of the LIS as

an entry of type A ;

remove (i,j) from the LIS

),( jiL

),(),( jiOlk

10

Sorting Pass

63

2

-2

2

-2

-1

9

4 23

4-430

6363

4

2

03 -2

64

-13

1049-34

23-31

15 14 3 -12

643

7-12137

5

-3 6 -4

3 0 -3

-5 9 -1 47

3

8-14-7-9

5

14

115 6

-7

Threshold = 32

LIP LIS LSP

-31 -34(B) 63

23 -31(B) -34

10 49

14

-13

15

14

-9

-7

output: : 111000 111000 10000 0 0

11

Sorting Pass

63

2

-2

2

-2

-1

9

4 23

4-430

6363

4

2

03 -2

64

-13

1049-34

23-31

15 14 3 -12

643

7-12137

5

-3 6 -4

3 0 -3

-5 9 -1 47

3

8-14-7-9

5

14

115 6

-7

Threshold = 32

LIP LIS LSP

-31 -3 15(A) 63

23 2 14(A) -34

10 -9(A) 49

14 -7(A) 47

-13

15

14

-9

-7

-1

output: : 111000 111000 10000 0 0 0 101100 0 0

12

MSE

112.0301

122.4032

116.6248

105 110 115 120 125

FATHER

Intra

Combine

PSNR

28.36669

28.15783

27.92759

27.7 27.8 27.9 28 28.1 28.2 28.3 28.4

FATHER

Intra

Combine

13

Image Quality

Quality

0.9756

0.974063

0.973232

0.972 0.9725 0.973 0.9735 0.974 0.9745 0.975 0.9755 0.976

FATHER

Intra

Combine

y

])())[((

42222 yx

yxQ

yx

xy

N

iixN

x1

1

N

iiyN

y1

1

N

iix xx

N 1

22 )(1

1

N

iiy yy

N 1

22 )(1

1

N

iiixy yyxx

N 1

))((1

1

ii

ii

xxyif

xyifQ

2,1

,1

14

Image Quality

22

22

22222222

2

)()(

2

2

)()(

2

])())[((

4

yx

yx

yx

xy

yx

yx

yx

xy

yx

xy

yx

yx

yx

yx

yx

yxQ

表示 x y 的線性相關程度，當 y=ax+b 得到最大值 1

表示 x y 的平均亮度，當 x=y 得到最大值 1

表示 x y 的對比相似度，當 得到最大值1

yx

15Father PSNR=28.1872 Q=0.977938

16Combine PSNR=27.9566 Q=0.976747Intra PSNR=28.1552 Q=0.97779

17

Father

IntraCombine

18

Father

IntraCombine