transform based watermarking

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Department of Informatics, Aristotle University of Thessaloniki 1

Transform Based

Watermarking

Solachidis Vassilios

Department of Informatics

Aristotle University of Thessaloniki


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Watermarking

Proof of ownership of digital data byembedding copyright statements

EmbedderDigital

data

Key

Watermarkeddigital

data

Detector

Digital data(possiblywatermarked)

Key

WatermarkedNot watermarked


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Basic idea

Spatial domain watermarking

not robust against compression and

filteringshould have lowpass characteristics


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Robustness against attacks (filtering,compression)

Advantages of Transform Based

WatermarkingWatermark construction having specific

frequency content

Watermark perceptibility

Transform properties accelerates thedetection (in geometrically distorted data)


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Watermarking in spatial /transform domain

Transform

Signal Perceptualanalysis

Watermark

InverseTransform

Watermarked Signal

Signal Perceptualanalysis

WatermarkWatermarked Signal


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Watermark construction

1-D sequence 2-D sequence

keyRandomgenerator

1-D sequence of

real numbers ~N(0,1)

or

1


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Watermark Embedding

Modifications in the low frequencies cause visible

changes in the spatial domain Compression and filtering affects the high frequencies

of the transform and destroys the watermark

The watermark is added in the middlefrequencies because

TransformSignal Perceptualanalysis

Watermark

InverseTransform

Watermarked Signal



Low

frequencies

Medium

frequencies

High

frequencies



Watermark Detection

Correlation is used in most of the methods.

Transform

Signal

Watermark

Correlation

Detectoroutput

0, not

watermarked1, watermarked



Transform Domains

Discrete cosine transform (DCT)

Discrete Fourier transform (DFT)

Fourier-Mellin transformDiscrete Wavelet transform (DWT)

Fourier descriptors



DCT (discrete cosine transform)

1 2

1 2

1 1

1 1 2 21 2 1 2

0 0 1 2

(2 1) (2 1)( , ) 4 ( , )cos cos2 2

N N

n n

n k n k X k k x n nN N

1 2 1 2( , ),x n n N N

1 2

1 2

1 1

1 1 2 21 2 1 1 2 2 1 2

0 01 2 1 2

1

1 1

1 1

2

2 2

2 2

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

2 2

1/2 0( )

1 1 1

1/2 0( )

1 1 1

N N

k k

n k n k x n n w k w k X k k

N N N N

kw k

k N

kw k

k N



Watermark embedded in DCT (discrete cosinetransform) domain

Advantages

Real output

Resistance against JPEG compression

Fast transform (especially when it is used incompressed images)

DisadvantagesNot robust against geometric attacks

DCT (discrete cosine transform)



DCT can be performed atentire image

t, t`, original and watermarked signal

W watermark, a embedding power

A pseudorandom sequence ofreal numbers is embedded inthe frequency domain

The coefficients of the NNDCT are reordered in a vectorusing a zig-zag scan.

Watermark is embeddedaccording to:

t`= t + a | t |wPivaet al.



}

88

Select a block (pseudorandomly)

Select a pair of midfrequency coefficientsModify the sign of their difference according to a

bit value

Select a block (Gaussiannetwork classifier decision)

Using a DCT constraint or acircular DCT detection regionmodify the middle frequencycoefficients

Kochet al.

DCT can be performed at each 88 block

Bors and Pitas



Watermark embedded in DFT (discrete Fourier transform)

domainAdvantages

Resistance against frequency attacks

Properties that accelerates the detection of geometricallydistorted image

Disadvantages

Complex outputCalculating complexity (when size is not power of 2)

DFT (discrete Fourier transform)



Rotation in spatial domain causes rotation of the

Fourier domain by the same angle

Circular shift in the spatial domain does not effect

the magnitude of DFT

Scaling in the spatial domain causes inverse scaling

in the frequency domain

Cropping in the spatial domain changes thefrequency sampling step

Discrete Fourier transform properties




Watermark: a ring that is separated in sectors and

homocentric circles. The same value 1 or 1 is assigned

in each watermark circular sector.

ring middle frequencies sectors resistant in slight rotation (3 degrees)

full search only for degrees 6k, k=1,2,,29

Correlation for many

frequency steps can detect

the watermark in a cropped image

Solachidis

and Pitas




Watermark embedded in FMT (Fourier-Mellin

transform)

Advantages

Properties that accelerates the detection of

geometrically distorted image

Disadvantages

Complex output

Very big calculating complexity (2 fourier transforms

logpolar tranform)

Not very accurate

Fourier Mellin transform



Cartesian

coordinates

Log polar

coordinates




DFT

Amplitude resistant in

translation

Cartesian Log polar

(x,y)

(,), x=e

cos(), y=e

sin()Scaling and rotation equals translation

Rotation by an angle (x,y)(,+)

Scaling by a factor (x, y)(+log(),)DFT

Amplitude resistant in translation,rotation, scaling

3 steps

Ruanaidh etal.




Watermark embedded in wavelet domain

Spatial localization

Frequency spreading

Average values from eachcorrelator from all thesub bands and levels

Tsekeridouand Pitas

DWT Discrete wavelet transform


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Let L be such a closed polygonal line that consistsofN vertices, each of them represented as a pair ofcoordinates (xi,yi).

We construct the complex signal:

1 1

2 2

n n

x iy

x iyz

x iy

Watermark embedded in the Fourier descriptors of apolygonal line

Solachidiset al.


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A watermarkW is added in the magnitude |Z| of theFourier coefficients of z

|Z |=|Z| pW ,p power of the watermarkTranslation affects only the DC term Z(0). By not addingwatermark to the DC term we obtain watermark immunity totranslation.

Rotation by an angle results in phase shift of the Fourier

descriptors. The magnitude of the FD remains invariant.Scaling by a factor a results in the scaling of the FDmagnitude by the same factor. Normalized correlationovercomes this effect.

Fourier descriptors


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Inversion of the traversal direction results in the sameindexing reversal in the FD:

Zinvertion(k)=Z(N-1-k)

Solutions:

Construct a symmetrical watermark

Always embed the watermark in the same direction(e.g. clockwise). During detection determine the traversaldirection and invert it, if needed.

Change of the polygonal line starting point affects only thephase of the FD.

Reflection (mirroring) causes FD magnitude indexingreversal:

|Zreflection(k)|=|Z(N-1-k)|

Solution: Construct a symmetrical watermark.

Fourier descriptors


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References A.Piva, M.Barni, E.Bartolini, and V.Cappellini DCT-based watermarking recovering

without resorting to the uncorrupted original imagein Proc. IEEE Int.Conf.ImageProcessing (ICIP), vol 1, Santa Barbara, CA, 1997, p.520

E.Koch, J.Rindfrey, and J.Zhao, Copyright protection for multimedia data,Digital mediaand electronic publishing, 1996

A.Bors and I.Pitas, Image watermarking using DCT domain constraints inProc.Int.Conf.Image Processing (ICIP), Lausanne, Switzerland, Sept.1996

V. Solachidis and I. Pitas, Circularly symmetric watermark embedding in 2-D DFTdomain, IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP'99),

Phoenix, Arizona, USA, Vol.6, pages 3469-3472, 15-19 March 1999 J.J.K. Ruanaidh, F.M.Boland, and O.Sinnen, Rotation, scale and translation invariant

spread spectrum digital image watermarking, Signal Processing (Special Issue onwatermarking), vol.66, no.3, pp.303-318, May 1998

S. Tsekeridou, I. Pitas, Embedding Self-Similar Watermarks in the Wavelet Domain , 2000IEEE Int. Conf. on Acoustics, Systems and Signal Processing (ICASSP'00), vol. IV, pp.

1967-1970, Istanbul, Turkey, 5-9 June 2000 V. Solachidis, N. Nikolaidis and I. Pitas, Watermarking Polygonal Lines Using Fourier

Descriptors, IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP'2000),Istanbul, Turkey, vol. IV, pp 1955-1958, 5-9 June 2000

S.Katzenbeisser, F.Petitcolas, Information hiding techniques for steganography and digitalwatermarking,Artech house

transform based watermarking

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