chinese university of hong kong department of information engineering a capacity estimate technique...

Chinese University of Hong KongDepartment of Information Engineering

A Capacity Estimate Technique for JPEG-to-A Capacity Estimate Technique for JPEG-to-JPEG Image WatermarkingJPEG Image Watermarking

Peter Hon Wah WongPeter Hon Wah Wong

Department of Information EngineeringDepartment of Information Engineering

Chinese University of Hong KongChinese University of Hong Kong


OutlineOutline

JPEG-to-JPEG (J2J) image watermarkingJPEG-to-JPEG (J2J) image watermarking

Background of capacity estimation for image Background of capacity estimation for image

watermarkingwatermarking

Proposed J2J capacity estimate techniqueProposed J2J capacity estimate technique

Necessary condition to achieve maximum capacityNecessary condition to achieve maximum capacity

Experimental resultsExperimental results

ConclusionsConclusions


Background of capacity estimation for image Background of capacity estimation for image watermarkingwatermarking

There are some existing methods to estimate There are some existing methods to estimate the data hiding capacity of digital images the data hiding capacity of digital images

Ramkumar [1] et al. focused on comparing the Ramkumar [1] et al. focused on comparing the capacity among different transformscapacity among different transforms

Moulin et al. [2] estimated the capacity under Moulin et al. [2] estimated the capacity under different kind and degree of attacksdifferent kind and degree of attacks

Voloshynovskiy et al. [3] considered security Voloshynovskiy et al. [3] considered security issue of watermark to estimate the capacityissue of watermark to estimate the capacity



Shannon [4] showed Shannon [4] showed that for Gaussian that for Gaussian channelchannel

For watermarking, For watermarking, image is considered as image is considered as noisenoise

+X

N

Y

2

2

2 1log2

1Capacity

N

Y

+X

N

Y+

I

22

2

2 1log2

1Capacity

NI

Y



Costa [5] showed that if the distribution of the Costa [5] showed that if the distribution of the image is only known at the watermark image is only known at the watermark embedderembedder

2

2

2 1log2

1Capacity

N

Y


Most of the digital images are stored in JPEG format Most of the digital images are stored in JPEG format Both the input and output images need to be JPEG Both the input and output images need to be JPEG

compatiblecompatible It is called JPEG-to-JPEG (J2J) watermarkingIt is called JPEG-to-JPEG (J2J) watermarking All DCT coefficients need to be re-quantized after All DCT coefficients need to be re-quantized after

watermark insertionwatermark insertion

JPEG-to-JPEG (J2J) Image WatermarkingJPEG-to-JPEG (J2J) Image Watermarking


JPEG-to-JPEG Watermarking (J2J)JPEG-to-JPEG Watermarking (J2J)

JPEG File

Quantizationtable Qo

WatermarkEmbedding

QuantizedDCT

coefficients Dq JPEGEncoder

Quantizationtable Qn

WatermarkedJPEG File


Proposed J2J Capacity Estimate TechniqueProposed J2J Capacity Estimate Technique

Capacity of watermarking is defined as the maximum Capacity of watermarking is defined as the maximum number of bits that can be embedded in the image and number of bits that can be embedded in the image and invisible invisible

There are two assumptionsThere are two assumptions– the watermarked images will be JPEG-compressed using after the watermarked images will be JPEG-compressed using after

watermark insertionwatermark insertion– the dimensions of the images are not changed in the watermark the dimensions of the images are not changed in the watermark

embedding embedding Human Visual System (HVS) model is used to estimate Human Visual System (HVS) model is used to estimate

the Just Noticeable Difference (JND) of DCT coefficients the Just Noticeable Difference (JND) of DCT coefficients Does not assume any specific watermarking method and Does not assume any specific watermarking method and

embedding domain embedding domain


J2J - Capacity EstimationJ2J - Capacity Estimation

Denote the Denote the ijijthth quantized DCT coefficient of the quantized DCT coefficient of the kkthth block block as as DDqq((ii,,jj,,kk))

The dequantized DCT coefficient The dequantized DCT coefficient DDoo((ii,,jj,,kk) is given by) is given by

The quantized watermarked DCT coefficient The quantized watermarked DCT coefficient DDnn((ii,,jj,,kk) ) should satisfiesshould satisfies

Guarantees the invisibility of the watermarkGuarantees the invisibility of the watermark

81 jikjiDjiQkjiD qoo ,,,,,,

kjiJkjiDkjiD oon ,,,,,,



Only finite possible values of Only finite possible values of DDnn((ii,,jj,,kk) is allowed) is allowed

The no. of possible value isThe no. of possible value is

J2J data hiding capacity of the image is given J2J data hiding capacity of the image is given approximately by approximately by CCww

KK is the number of blocks in the image is the number of blocks in the image

K

k j iww kjiNC

1

8

1

8

12 ,,log

1

,

,,,,

,

,,,,,,

jiQ

kjiJkjiD

jiQ

kjiJkjiDkjiN

n

oo

n

oow



),,( kjiDo

),,( kjiJo),,( kjiJo

),( jiQn

NNww((ii,,jj,,k) = 5k) = 5 Capacity = logCapacity = log22(5) bits(5) bits



Agrees somewhat with the works of Costa Agrees somewhat with the works of Costa WW is assumed to be uniformly distributed is assumed to be uniformly distributed

power of the watermark ispower of the watermark is assuming the quantization noise is uniformly assuming the quantization noise is uniformly

distributed in distributed in the power of quantization noise is the power of quantization noise is

),,(),,,( kjiJkjiJ oo

2

w 3/,, 2kjiJ o

2/),(,2/),( jiQjiQ nn2

n 12/, 2jiQn



2

2

2

2

2

2

2

2

22

2

2

2

22

2

1log2

1

12/,

3/,,1log

2

1

,

,,41log

2

1

,

,,4log

2

1

,

,,2log

2

1

,

,,2log

1,

,,,,

,

,,,,log,,

n

w

n

o

n

o

n

o

n

o

n

o

n

oo

n

oo

jiQ

kjiJ

jiQ

kjiJ

jiQ

kjiJ

jiQ

kjiJ

jiQ

kjiJ

jiQ

kjiJkjiD

jiQ

kjiJkjiDkjiC


Necessary Conditions to Achieve CapacityNecessary Conditions to Achieve Capacity

Consider a DCT coefficientConsider a DCT coefficient The capacity of a communication channel with The capacity of a communication channel with

side information is given by side information is given by

where where UU is a finite alphabet auxiliary random is a finite alphabet auxiliary random variable, by setting variable, by setting UU = = DDnn

onW DUIDUIC ,,max

on

onnnonnW

DDH

DDHDHDHDDIDHC

|max

|max,max


Necessary Conditions to Achieve Necessary Conditions to Achieve CapacityCapacity

The maximum of is achieved when is equally The maximum of is achieved when is equally probable in when is known probable in when is known

the corresponding capacity is the corresponding capacity is

nD

oooo JDJD ,oD

otherwise ,0

,1

oonoo

wn

JDDJDNDp

w

QNm

QNm

Qm

Qm

Qm

Qm Ndwwfdwwfdwwf

nw

nw

n

n

n

n

1)(...)()(

2/1

2/3

2/3

2/1

2/1

2/1

wW NC 2log


Experimental ResultsExperimental Results

Two common test images 512x512 Two common test images 512x512 gray-scale images are estimated and gray-scale images are estimated and reportedreported

Only the luminance component is used Only the luminance component is used Scaling factor (SF) is used to scale the Scaling factor (SF) is used to scale the

default quantization table in JPEG to default quantization table in JPEG to control the compression ratiocontrol the compression ratio


Experimental ResultsExperimental Results

Lena Pepper


Experimental Results – Block CapacityExperimental Results – Block Capacity

Lena,SFbefore=1, SFafter=0.5,

Est. capacity=3507 bits

Pepper,SFbefore=1, SFafter=0.5,

Est. capacity=3663 bits


Experimental Results - HistogramExperimental Results - Histogram

Lena Pepper


ConclusionsConclusions

A method to estimate the watermarking A method to estimate the watermarking capacity of digital images in the JPEG-to-JPEG capacity of digital images in the JPEG-to-JPEG watermarking framework is proposed watermarking framework is proposed

The estimation does not assume any specific The estimation does not assume any specific watermarking method and embedding domain, watermarking method and embedding domain, it should apply to any watermarking method in it should apply to any watermarking method in the J2J frameworkthe J2J framework

More details can be founded from:More details can be founded from:P.H.W. Wong, Oscar C. Au, "P.H.W. Wong, Oscar C. Au, "A Capacity Estimation Technique for JPEG-To-JPEG Image WateA Capacity Estimation Technique for JPEG-To-JPEG Image Watermarkingrmarking," ," IEEE Transactions on Circuits and Systems for Video IEEE Transactions on Circuits and Systems for Video Technology: Special Issue on Authentication, Copyright Technology: Special Issue on Authentication, Copyright Protection and Information HidingProtection and Information Hiding, pp. 746-752, Aug. 2003. , pp. 746-752, Aug. 2003.


ReferencesReferences

1.1. M. Ramkumar and A.N. Akansu, “Capacity Estimates for Data M. Ramkumar and A.N. Akansu, “Capacity Estimates for Data Hiding in Compressed Images,” Hiding in Compressed Images,” IEEE Trans. Image IEEE Trans. Image ProcessingProcessing, vol. 10, no. 8, pp. 1252-1263, Aug. 2001., vol. 10, no. 8, pp. 1252-1263, Aug. 2001.

2.2. P. Moulin and M.K. Mıhçak, “A Framework for Evaluating the P. Moulin and M.K. Mıhçak, “A Framework for Evaluating the Data-Hiding Capacity of Image Sources”, Data-Hiding Capacity of Image Sources”, IEEE Trans. Image IEEE Trans. Image ProcessingProcessing, vol. 9, no. 8, pp. 1450-1455, Aug. 2000. , vol. 9, no. 8, pp. 1450-1455, Aug. 2000.

3.3. S. Voloshynovskiy and T. Pun, “Capacity-Security Analysis of S. Voloshynovskiy and T. Pun, “Capacity-Security Analysis of Data Hiding Technologies,” in Data Hiding Technologies,” in Proc. of IEEE Int. Conf. on Proc. of IEEE Int. Conf. on Multimedia and ExpoMultimedia and Expo, vol. 2, pp. 477-480, Aug. 2002., vol. 2, pp. 477-480, Aug. 2002.

4.4. C.E. Shannon, “A Mathematical Theory of Communication,” C.E. Shannon, “A Mathematical Theory of Communication,” Bell Systems Technical JournalBell Systems Technical Journal, vol. 27, pp.373-423, 623-656, , vol. 27, pp.373-423, 623-656, 1948.1948.

5.5. M. Costa, “Writing on Dirty Paper,” M. Costa, “Writing on Dirty Paper,” IEEE Trans. Inform. IEEE Trans. Inform. TheoryTheory, vol. 29, no. 3, pp. 439-441, May 1983., vol. 29, no. 3, pp. 439-441, May 1983.

chinese university of hong kong department of information engineering a capacity estimate technique...

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jpeg j2j watermarking

invisible n

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jpeg compatible n

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