A robust associative watermarking technique based on similarity diagrams

Source: Pattern Recognition, Vol. 40, No. 4, pp. 1355-1367, 2007

Authors: Jau-Ji Shen and Po-Wei Hsu

2

Background

Concept of Digital Watermarking

3

Framework

4

Introduction

Just Noticeable Distortion

Sobel Operator

Association Rules

Discrete Cosine

Transform

Original Image

Watermark

Embedded Image

5

Discrete Cosine Transform (DCT)

139 139 141 136 135 135 133 132

136 137 138 135 133 133 132 132

136 134 135 135 136 134 132 133

136 135 136 136 135 135 132 134

135 135 135 137 137 134 132 136

134 134 137 137 136 135 134 138

135 135 138 138 137 136 136 144

137 137 138 140 138 139 143 147

FDCT

IDCT

Spatial domain108 2 -1 -5 3 -1 3 0

-9 13 -3 4 -4 0 0 1

9 -2 3 -2 -2 1 0 1

-2 3 -2 -1 -1 -1 1 0

4 0 1 1 -1 0 -1 0

1 0 0 0 0 0 2 0

1 -1 -1 2 0 1 0 1

0 0 0 1 2 -1 0 0

Frequency domain

AC

DC

6

Just Noticeable Distortion (JND)

108 2 -1 -5 3 -1 3 0

-9 13 -3 4 -4 0 0 1

9 -2 3 -2 -2 1 0 1

-2 3 -2 -1 -1 -1 1 0

4 0 1 1 -1 0 -1 0

1 0 0 0 0 0 2 0

1 -1 -1 2 0 1 0 1

0 0 0 1 2 -1 0 0

Frequency domain (DCT)0 2 3 4 4 3 6 8

1 2 4 5 5 7 9 4

3 4 5 2 4 5 7 9

3 4 5 2 2 9 8 10

5 5 6 6 3 7 8 9

4 4 5 4 6 7 8 10

6 6 6 6 5 5 10 12

7 8 7 9 8 10 12 20

JND

7

Sobel Operator

1 2 1

0 0 0

-1 -2 -1

1 0 -1

2 0 -2

1 0 -1

1 2 1

0 0 0

-1 -2 -1

Mask 2

Mask 1

(x, y)

|2||1| EIEI Threshold

0 -1 -2

1 0 -1

2 1 0

-1 -2 -1

0 0 0

1 2 1

0 1 2

-1 0 1

-2 -1 0

1 0 -1

2 0 -2

1 0 -1

-1 0 1

-2 0 2

-1 0 1

2 1 0

1 0 -1

0 -1 -2

-2 -1 0

-1 0 1

0 1 2

(0) (1) (2) (3)

(4) (5) (6) (7)

8

Watermark-random sequence (1/2)

139 139 141 136 135 135 133 132

136 137 138 135 133 133 132 132

136 134 135 135 136 134 132 133

136 135 136 136 135 135 132 134

135 135 135 137 137 134 132 136

134 134 137 137 136 135 134 138

135 135 138 138 137 136 136 144

137 137 138 140 138 139 143 147

original image

108 2 -1 -5 3 -1 3 0

-9 13 -3 4 -4 0 0 1

9 -2 3 -2 -2 1 0 1

-2 3 -2 -1 -1 -1 1 0

4 0 1 1 -1 0 -1 0

1 0 0 0 0 0 2 0

1 -1 -1 2 0 1 0 1

0 0 0 1 2 -1 0 0

random sequence={-1,1,-1,-1,1,…,1,-1,1}

watermarking key

FDCT

108 2 -3 -5 3 -1 3 0

-9 39 -3 4 -4 0 0 1

-9 -2 -3 -2 -2 1 0 1

-2 3 -2 1 -1 -1 1 0

4 0 1 1 -1 0 -1 0

1 0 0 0 0 0 2 0

1 -1 -1 2 0 1 0 1

0 0 0 1 2 -1 0 0

selected coefficients={9,13,-1,3,-1}

modified coefficients={-9,39,-3,-3,1} 2for a

IDCT

9)1(|9|29'1 c

5for N

.,...,3,2,1,||' ** Niwcacc iiii

9

Watermark-random sequence (2/2)

140 141 141 138 136 134 132 131

140 138 136 135 133 134 132 131

137 138 135 135 136 134 132 133

136 135 136 136 135 135 132 134

135 135 135 137 137 134 132 136

134 134 138 138 137 136 135 139

136 136 138 139 136 135 134 143

139 139 140 141 137 138 142 146

test image

108 2 -3 -5 3 -1 3 0

-9 39 -3 4 -4 0 0 1

-9 -2 -3 -2 -2 1 0 1

-2 3 -2 1 -1 -1 1 0

4 0 1 1 -1 0 -1 0

1 0 0 0 0 0 2 0

1 -1 -1 2 0 1 0 1

0 0 0 1 2 -1 0 0

FDCT

random sequence={-1,1,-1,-1,1,…,1,-1,1}

test key

selected coefficients={-9,39,-3,-3,1}

N

iiicw

N1

'1

valuesimlarity

11

)11)3()1()3()1(391)9()1((5

1

ed watermarkis imagetest

thresholdpredefined a valuesimilarity if

5for N

10

Association Rules (K-itemset)

Transaction Database

TID Items

T1 A,B,E,F

T2 A,B,C,E,F

T3 B,D,E

}EB,A,{X

}F{Y

YXKYX ||||

rulen associatioitemset 4: YX

{F}E}B,{A,

TDYX

11

Key Concept

Just Noticeable Distortion

Sobel Operator

Association Rules[b1I(k), b2I(k), b3I(k), b4I(k)]

[b1W(k), b2W(k), b3W(k), b4W(k)]

Discrete Cosine

Transform

Original Image

Watermark

Embedded Image

12

Position alignment items

120 80 90 95 100 100 100 120

115 75 85 90 105 105 105 115

100 80 65 80 80 90 70 100

120 90 80 75 75 80 75 85

110 100 60 80 130 110 120 110

100 115 95 80 125 120 120 115

90 95 100 105 120 135 105 110

95 100 105 120 120 130 125 120

Block mean value

1 2 10 0 0-1 -2 -1

0 -1 -21 0 -12 1 0

-1 -2 -10 0 01 2 1

0 1 2-1 0 1-2 -1 0

1 0 -12 0 -21 0 -1

-1 0 1-2 0 2-1 0 1

2 1 01 0 -10 -1 -2

-2 -1 0-1 0 10 1 2

(0)

(1)

(2)

(3)

(4)

(5)

(6)

(7)

1 2 3 8…9 …

k

…57 646362I

75)(1b kI

125}35 ,75 ,125 ,45 ,35 ,75 ,125 ,45max{)(2b kI

1)(3b kI

(-1)*65+(-2)*80+(-1)*80+0*80+0*75+0*75+1*60+2*80+1*130=45

random sequence={1,1,-1,…,1,-1,-1…,-1,-1,1} watermark Wwatermarking key

13

Value alignment item

108 2 -1 -5 3 -1 3 0

-9 13 -3 4 -4 0 0 1

9 -2 3 -2 -2 1 0 1

-2 3 -2 -1 -1 -1 1 0

4 0 1 1 -1 0 -1 0

1 0 0 0 0 0 2 0

1 -1 -1 2 0 1 0 1

0 0 0 1 2 -1 0 0

1 2 3 8…9 …

k

…57 646362I

DCT transform

AC={0, -1, 2, 77, 9, 13, -3,…, -9, 20, 3,…, 33, 5, 0}

sort(abs(AC))={77,33,20,…,13,9,9,5,…,1,0,0}

select first C elements

0 0 0 0 0 0 0 0-9 13 0 0 0 0 0 09 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

)(4B kI )(4B kW

0 1 -1 -1 1 -1 1 1

-1 1 -1 1 -1 1 1 1

1 -1 1 -1 -1 1 1 1

-1 1 -1 -1 -1 -1 1 1

1 1 1 1 -1 1 -1 1

1 1 1 1 1 1 1 1

1 -1 -1 1 1 1 1 1

1 1 1 1 1 -1 1 1

13-99

)(DCT kI

14

Quantization and sieve

)3(4B)7,200,100(

)2(4B)6,250,120(

)1(4B)1,125,75(

I

I

I

Quantization

)3(4B)7,6,3(

)2(4B)6,7,3(

)1(4B)1,4,2(

I

I

I

(M1=8, M2=7)

Sieve

)3(4B)7,6,3(

)1(4B)1,4,2(

I

I

)3(4B)6,100,100(

)2(4B)0,200,80(

)1(4B)5,150,60(

W

W

W

Quantization

)3(4B)6,4,3(

)2(4B)0,7,2(

)1(4B)5,6,1(

W

W

W

0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

smooth block

21 }200,250,125max{

125 ,

256

75MM

15

Coupling and alignment

)3(4B)7,6,3(

)1(4B)1,4,2(

I

I

)3(4B)6,4,3(

)2(4B)0,7,2(

)1(4B)5,6,1(

W

W

W

7|51||64||12| 4|01||74||22|

6|61||44||32|

Coupling

)2(4B)0,7,2(

)1(4B)1,4,2(

W

I

)3(4B)6,4,3(

)3(4B)7,6,3(

W

I

0 0 0 0 0 0 0 0

-9 13 0 0 0 0 0 0

9 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

)1(4B I )2(4B W0 1 -1 -1 1 -1 1 1

-1 1 -1 1 -1 1 1 11 -1 1 -1 -1 1 1 1

-1 1 -1 -1 -1 -1 1 1

1 1 1 1 -1 1 -1 1

1 1 1 1 1 1 1 1

1 -1 -1 1 1 1 1 1

1 1 1 1 1 -1 1 1

0 2 3 4 4 3 6 8

1 2 4 5 5 7 9 4

3 4 5 2 4 5 7 9

3 4 5 2 2 9 8 10

5 5 6 6 3 7 8 9

4 4 5 4 6 7 8 10

6 6 6 6 5 5 10 12

7 8 7 9 8 10 12 20

108 2 -1 -5 3 -1 3 0

-9 13 -3 4 -4 0 0 1

9 -2 3 -2 -2 1 0 1

-2 3 -2 -1 -1 -1 1 0

4 0 1 1 -1 0 -1 0

1 0 0 0 0 0 2 0

1 -1 -1 2 0 1 0 1

0 0 0 1 2 -1 0 0

)1(JND I

)1(DCTI108 2 -1 -5 3 -1 3 0

-9 13 -3 4 -4 0 0 1

9 -2 3 -2 -2 1 0 1

-2 3 -2 -1 -1 -1 1 0

4 0 1 1 -1 0 -1 0

1 0 0 0 0 0 2 0

1 -1 -1 2 0 1 0 1

0 0 0 1 2 -1 0 0

IDCT

-10 1512

pair

)1(DCTI

Alignment

16

Detection scheme

108 2 -1 -5 3 -1 3 0

-9 13 -3 4 -4 0 0 1

9 -2 3 -2 -2 1 0 1

-2 3 -2 -1 -1 -1 1 0

4 0 1 1 -1 0 -1 0

1 0 0 0 0 0 2 0

1 -1 -1 2 0 1 0 1

0 0 0 1 2 -1 0 0

0 0 0 0 0 0 0 0-9 13 0 0 0 0 0 09 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

108 2 -1 -5 3 -1 3 0

-10 15 -3 4 -4 0 0 1

12 -2 3 -2 -2 1 0 1

-2 3 -2 -1 -1 -1 1 0

4 0 1 1 -1 0 -1 0

1 0 0 0 0 0 2 0

1 -1 -1 2 0 1 0 1

0 0 0 1 2 -1 0 0

)1(DCTI

)1(DCTD

)1(4B I

0 1 -1 -1 1 -1 1 1

-1 1 -1 1 -1 1 1 1

1 -1 1 -1 -1 1 1 1

-1 1 -1 -1 -1 -1 1 1

1 1 1 1 -1 1 -1 1

1 1 1 1 1 1 1 1

1 -1 -1 1 1 1 1 1

1 1 1 1 1 -1 1 1

)2(4B W

1)910(&)01( Similarity1)912(&)01( Similarity1)1315(&)01( Similarity

4.05

01111 valueSimilarity

pair

JND

2-3-778-577108

10-10-10-10

-10-11-11-11

-1-10-10020

0-1-101221

0-121-25-11

001-362-6-1

0010-5-6-89

00000000000000000000000000000000000000000000000900000009000000770

132-67860106

-11100000

-20010000

012-2-1101

1011-1210

01-22010-1

010112-22

23-51-2-869

)3(DCTI

)3(DCTD

)3(4B I

1-111-111-1

1-11-111-11

-111-111-1-1

1-111-11-11

1-1-11-11111-1-11-1-111

1-1-1111-11

1-1-111110

)3(4B W

1)7760(&)01( Similarity

0)99( Similarity

pair

JND

17

Experiments (1/4)

850,8,8 21 CMM

256x256 image, 208x208 watermark

PSNR=36.062 PSNR=37.222 PSNR=35.563

18

Experiments (2/4)

200 test keys (100th key)

0 20 40 60 80 100 120 140 160 180 200-0.2

0

0.2

0.4

0.6

0.8

1

Test key

Sim

ilarit

y va

lue

more blurring

0 20 40 60 80 100 120 140 160 180 200-0.2

0

0.2

0.4

0.6

0.8

1

Test key

Sim

ilarit

y va

lue

more sharpening

0 20 40 60 80 100 120 140 160 180 200-0.2

0

0.2

0.4

0.6

0.8

1

Test key

Sim

ilarit

y va

lue

brightness adjustment(+40)

0 20 40 60 80 100 120 140 160 180 200-0.2

0

0.2

0.4

0.6

0.8

1

Test key

Sim

ilarit

y va

lue

Gaussion noise (σ2=20)

0 20 40 60 80 100 120 140 160 180 200-0.2

0

0.2

0.4

0.6

0.8

1

Test key

Sim

ilarit

y va

lue

cutting (50%)

0 20 40 60 80 100 120 140 160 180 200-0.2

0

0.2

0.4

0.6

0.8

1

Test key

Sim

ilarit

y va

lue

JPEG compression (1%)

19

0 20 40 60 80 100 120 140 160 180 200-0.2

0

0.2

0.4

0.6

0.8

1

Test key

Sim

ilarit

y va

lue

Experiments (3/4)

18.0T

False-negative errors: an embedding image while watermark not being detected

False-positive errors: a non-watermarked image but extracted result is yes

S

200 test keys (100th key)

20

Experiments (4/4)

Comparisons of the proposed method and Fotopoulos’s method.

Image processing attack type

Our method Fotopoulos’s method

False-negative

errors

False-positive errors

False-negative

errors

False-positive errors

Attack-Free 0 / 600 0 / 600 0 / 600 0 / 600

Blurring 0 / 600 0 / 600 0 / 600 0 / 600

Sharpening 0 / 600 0 / 600 0 / 600 0 / 600

Brightness adjustment (+40) 0 / 600 0 / 600 0 / 600 0 / 600

Gaussion noise (σ2=10, 15, 20) 0,0,0 / 600 0,0,0 / 600 0,0,0 / 600 0,0,1 / 600

Cut (70%, 60%, 50%) 0,0,10 / 600 0,0,0 / 600 0,0,0 / 600 0,0,0 / 600

JPEG compression (20%, 10%, 1%)

0,0,0 / 600 0,0,0 / 6000,138,597 /

6000,0,0 / 600

Total 10 / 7800 0 / 7800 735 / 7800 1 / 7800

21

Conclusions

A novel associative watermarking concept is proposed

Robust against different attacks Original image is needed while detecting

watermark

24

DCT version of JND formula

Takij

kij cctt )/( 00},max{

1 ijwij kij

wkij

kij

kij tctJND

Ta is a constant whose value is 0.649,

kc0 stands for the DC coefficient value of the kth block in the image,

0c is the average value of the DC coefficients from all the image blocks,

ijt is the value of the element in position (i, j) of the JPEG quantization matrix,

ijw is a constant set to be 0.7, and finally

kijc is the coefficient value of the kth block of the image.

A. B. Watson, “DCT quantization matrices visually optimized for individual images,” Proc. SPIE, Vol. 1913 (1993) 202-216.

25

Peak Signal-to-Noise Ratio - PSNR