Digital VideoSolutions to Midterm Exam 2012

Edited by Yang-Ting ChouConfirmed by Prof. Jar-Ferr Yang

LAB: 92923 R, TEL: ext. 621E-mail: yangting115@gmail.com

Page of MPL: http://mediawww.ee.ncku.edu.tw

AVG: 120.806STDEV: 42.9794

MAX: 168MIN: 21

(a)

I

•These entropy encoders compress data by replacing each fixed-length input symbol by the corresponding variable-length prefix-free output codeword. The length of each codeword is approximately proportional to the negative logarithm of the probability. Therefore, the most common symbols use the shortest codes.•According to Shannon's source coding theorem, the optimal code length for a symbol is −logbP, where b is the number of symbols used to make output codes and P is the probability of the input symbol.•Two of the most common entropy encoding techniques are Huffman coding and arithmetic coding. If the approximate entropy characteristics of a data stream are known in advance, a simpler static code may be useful. These static codes include universal codes and Golomb codes.

(b)

(c)

(d)

(e)

(f)

II 2.1

Huffman code:A 0 (1) B 11 (00)C 100 (011)D 1011 (0100)E 10100 (01011)F 10101 (01010)

A 0.85B 0.05C 0.05D 0.02E 0.02

1

1

1

0

1

0

0

0

(a)

p(A) = 0.85, p(B) = 0.05, p(C) = 0.05, p(D) = 0.02, p(E) = 0.02p(F) = 1- p(A)- p(B)- p(C)- p(D)- p(E)=0.01

F 0.01

1

0

01

11

101100

1000

1001

10001

10000

10

10

Optimal symmetrical RVLCA 0B 11C 101 D 1001E 10001F 100001

(b)

100001

100000

01

11

101

001

0001

1001

10001

00001

01

01

Prefix conflict

Optimal asymmetrical RVLCA 0B 11C 101 D 1001E 10001F 100001

(c)

100001

000001

2.20 0

0

0

0 0 0

0 0

0 0

0

4

-1

3

1

RLC Skip SSSS Value Encoded

(1,4) 1 3 100 1111001 100

(0,-1) 0 1 0 00 0

(1,1) 1 1 1 1100 1

(3,3) 3 2 11 111110111 11

EOB 0 0 1010

(a) (b) (c)

題目沒給

2.3(a)

Entropy:

2ln

1*)1ln(*)1(log* H(p)i

2i

ii

i pppp

7219.0)8.01(log8.0)2.0

1(log2.0 22 H

(b)

64.08.08.0)p(A

16.02.08.0)p(A

16.08.02.0)p(A

04.02.02.0)p(A

22

12

21

11

A

A

A

A

Huffman code:A2A2 0 (1) A2A1 11 (00)A1A2 100 (011)A1A1 101 (010)

A2A2 0.64

A2A1 0.16A1A2 0.16A1A1 0.04 1

1

1

0

0

0

(c)

{A2A1A2A2}:{110} ({001})

Huffman code:A2A2 0 (1) A2A1 11 (00)A1A2 100 (011)A1A1 101 (010)

(d) Occurrence symbols: {A2A1A2A2}

0.0 1.00.2

0.20.36

1.0

0.2 0.36

0.232

0.360.2320.2576

0.2576<W<0.36

16

5

0101

2.4

]- 1 -[][],- -[][ 21

21

181

41

43

41

81

0 nhnh-2 -1 0 1 2

Synthesis Filter:

n

n

nhng

nhng

)1(][][

)1(][][

01

10

2~2

00 ]2[][]2[k

knxkhny

1~1

11 ]12[][]12[k

knxkhny

k

kngkynx ]2[]2[][ 000

k

kngkynx )]12([]12[][ 111

]- - - -[][], 1 [][ 81

41

43

41

81

121

21

0 ngng

n -3 -2 -1 0 1 2 3 4 5 6 7 8 9

x[n] 3 4 1 -3 1 4 3 2 -2 2 3 4 1

y0[2n] 0 -2.75 0 4.125 0 1 0 1

y1[2n+1] 0 0.5 0 0.5 0 0 0 -4 0 0

x0[n] -2.75 0.6875 4.125 2.5625 1 1

x1[n] -0.25 0.3125 -0.125 0.4375 1 -3

x’[n] -3 1 4 3 2 -2

The last row is the reconstructed synthesis data

2.5

1111

1111

1111

1111

T

0022

0220

0130

0012

X

(a)

1111

1111

1111

1111

TT T1-

(c) They are not unitary transforms.

以 quantization or scaling 來做補償 AA-1 = AAT ≠ I

(b)

1111

71159

1313

9315

TTXY T

003232

032320

016480

001632

YTTX T'

2.6p(A) = 0.7, p(B) =0.2, p(C) = 0.05, p(D)=p(E)=0.02, p(F)=0.01

Huffman code:A 0 (1) B 10 (01)C 110 (001)D 1111 (0000)E 11100 (00011)F 11101 (00010)

A 0.7B 0.2C 0.05D 0.02E 0.02F 0.01 1

1

1

1

1

0

0

0

0

0

(a)

RVL code:A 0 (1) B 101 (010)C 11011 (00100)D 1111111 (0000000)E 111000111 (000111000)F 111010111 (000101000)

(b)

01

11

101100

1000

1001

10001

10000

10

10

100001100000

Optimal symmetrical RVLCA 0B 11C 101 D 1001E 10001 F 100001

optimal symmetrical RVLC : 從後面長

(c)

01

11

101

001

0001

1001

10001

00001

01

01

Prefix conflict

Optimal asymmetrical RVLCA 0B 11C 101 D 1001E 10001 F 100001

100001 000001

optimal asymmetrical RVLC : 從前面長

2.7

Initialization:LIP: { (0,0)42, (0,1)17, (1,0)-19, (1,1)13 }LIS: { D(0,1), D(1,0), D(1,1) }LSP: {}

Significant Pass: 10 0 0 0 000Refinement Pass:LIP: { (0,0)42, (0,1)17, (1,0)-19, (1,1)13 }LIS: {D(0,1), D(1,0), D(1,1) }LSP: { (0,0)42 }

(a)

(b)

SPIHT

48

42 17

-19

6 -7

7 8

4 5

-4 -5

3 -4

0 0

13

322 42log0

2 T

485132 00 T.T

16MSB5:1

16MSB5:05

th

th

加減

n

Significant Pass: 10 11 0 000 Refinement Pass: 0LIP: { (0,1)17, (1,0)-19, (1,1) 13}LIS: {D(0,1), D(1,0), D(1,1) }LSP: {(0,0)42, (0,1)17, (1,0)-19}

Significant Pass: 10 0 1 0 0 0 10 0Refinement Pass: 1 0 0 up to 25 bits

Generated bitstream: 10 0 0 0 000 10 11 0 000 0 10 0 1 0 0 0 1

40

42 17

-19

6 -7

7 8

4 5

-4 -5

3 -4

0 0

13

245116 11 T.T

8MSB4:1

8MSB4:04

th

th

加減

n

12518 22 T.T

4MSB3:1

4MSB3:03

th

th

加減

n

(c)Generated bitstream: 10 0 0 0 000 10 11 0 000 0 10 0 1 0 0 0 1

48 0

0

0 0

0 0

0 0

0 0

0 0

0 0

0

40 24

-24

0 0

0 0

0 0

0 0

0 0

0 0

0

(1)

(2)

(3)

40 24

-24

0 0

0 0

0 0

0 0

0 0

0 0

12

Generated bitstream: 10 0 0 0 000 10 11 0 000 0 10 0 1 0 0 0 1

Generated bitstream: 10 0 0 0 000 10 11 0 000 0 10 0 1 0 0 0 1

4851

32

0

0

T.

T

16MSB5:1

16MSB5:05

th

th

加減

n

8MSB4:1

8MSB4:04

th

th

加減

n2451

16

1

1

T.

T

1251

8

2

2

T.

T

2.8

JPEG-LS Block Diagram(a)

(b)Fixed Predictor

sc zc

zc

zc

sc

zc zc

zc

zc sc

zc

zc

zc

zc

zc

zc

zc

zc

sc zc

zc

zc

zc

zc

zc

zc

zc

zc

sc

Significance Propagation Pass (Pass 1)

: Coefficient which is already significant

: Significance Propagation Pass (Pass 1)

ZC: Zero CodingSC: Sign Coding

(a)

zc

zc

zc

00

00

01

00

10

00

01

01

00

00

00

00

00

00

00

00

00

00

00

00

00

00

01

00

01

00

00

10

00

00

01

00

2.9

Magnitude Refinement Pass (Pass 2)

: Significance Propagation Pass (Pass 1)

(a)

: Magnitude Refinement Pass (Pass 2)

sc zc

zc

zc

sc

zc zc

zc

zc sc

zc

zc

zc

zc

zc

zc

zc

zc

sc zc

zc

zc

zc

zc

zc

zc

zc

zc

sc

zc

zc

zc

00

00

01

00

10

00

01

01

00

00

00

00

00

00

00

00

00

00

00

00

00

00

01

00

01

00

00

10

00

00

01

00

sc

zc zc

zc zc zc zc zc

zc

Clean-up Pass (Pass 3)(a)

: Pass 1

: Pass 2

: Pass 3 (ZC & SC)

: Pass 3 (RLC)

sc zc

zc

zc

sc

zc zc

zc

zc sc

zc

zc

zc

zc

zc

zc

zc

zc

sc zc

zc

zc

zc

zc

zc

zc

zc

zc

sc

zc

zc

zc

00

00

01

00

10

00

01

01

00

00

00

00

00

00

00

00

00

00

00

00

00

00

01

00

01

00

00

10

00

00

01

00

a: ZC, LL bandkh[j] = 1, kv[j] = 1, kd[j] = 0, ksig[j]=7

b: SCh[j] = 0, v[j] = 0, ksign[j] = 9

c: ZC, LL bandkh[j] = 1, kv[j] = 0, kd[j] = 0, ksig[j]=5

d: SC h[j] = 1, v[j] = 0, ksign[j] = 12

(b)

sc

zc zc

zc zc zc zc zc

zc

sc zc

zc

zc

sc

zc zc

zc

zc sc

zc

zc

zc

zc

zc

zc

zc

zc

sc zc

zc

zc

zc

zc

zc

zc

zc

zc

sc

zc

zc

zc

00

00

01

00

10

00

01

01

00

00

00

00

00

00

00

00

00

00

00

00

00

00

01

00

01

00

00

10

00

00

01

00

(a) (b)

(c)

(d)

(b)

sig[j]LL and LH blocks HL blocks HH blocks

h[j] v[j] d[j] h[j] v[j] d[j] d[j] h[j]+v[j]

8 2 x x x 2 x ≥3 x

7 1 ≥1 x ≥1 1 x 2 ≥1

6 1 0 ≥1 0 1 ≥1 2 0

5 1 0 0 0 0 0 1 ≥2

4 0 2 x 2 0 x 1 1

3 0 1 x 1 0 x 1 0

2 0 0 ≥2 0 0 ≥2 0 ≥2

1 0 0 1 0 0 1 0 1

0 0 0 0 0 0 0 0 0

Assignment of context labels for significant coding

“x” means “don’t care.”

(b)

h[j] v[j] sign flip

1 1 13 1

1 0 12 1

1 -1 11 1

0 1 10 1

0 0 9 1

0 -1 10 -1

-1 1 11 -1

-1 0 12 -1

-1 -1 13 -1

Assignment of context labels and flipping factor for sign coding

h[j] , v[j]: neighborhood sign status

-1: one or both negative.0: both insignificant or both significant but opposite sign.1: one or both positive.

][h j

Current sample

][v j

(b)

[j] sig [j] mag

0 0 14

0 >0 15

1 X 16

Assignment of context labels and flipping factor for magnitude refinement coding

[j]: remains zero until after the first magnitude refinement bit has been coded. For subsequent

refinement bits, [j] = 1.

sig[j]: context label for significant coding of sample j

2.10(a) Diamond Search

-2 -1 0 1 2 3 4 5 6 7

0-1-2-3

123456789

(-2, 3): 9+6+4 = 19 points

(2, -7): 9+6+5+5+4 = 29 points

-2 -1 0 1 2 3 4 5 6 7

0-1-2-3

123456789

(b) Four Step Search

-2 -1 0 1 2 3 4 5 6 7

0-1-2-3

123456789

(-2, 3): 9+5+8 = 22 points

-2 -1 0 1 2 3 4 5 6 7

0-1-2-3

123456789

(2, -7): 9+5+3+3+8 = 28 points

(c) Enhanced Hexagon Search

(-2, 3): 7+3+2 = 12 points

-2 -1 0 1 2 3 4 5 6 7

0-1-2-3

123456789

(2, -7): 7+3+3+3+2 = 18 points

-2 -1 0 1 2 3 4 5 6 7

0-1-2-3

123456789

2.11