Department of Informatics, Aristotle University of Thessaloniki1 Transform Based Watermarking Solachidis Vassilios Department of Informatics Aristotle

Department of Informatics, Aristotle University of Thessaloniki 1

Transform Based Watermarking

Solachidis Vassilios

Department of Informatics

Aristotle University of Thessaloniki


WatermarkingProof of ownership of digital data by embedding copyright statements

Embedder

Digital data

Key

Watermarkeddigital

data

Detector

Digital data (possibly

watermarked)Key

•Watermarked•Not watermarked


Basic idea

Spatial domain watermarking not robust against compression and filteringshould have lowpass characteristics


–Robustness against attacks (filtering, compression)

Advantages of Transform Based Watermarking

Watermark construction having specific frequency content

–Watermark perceptibility

Transform properties accelerates the detection (in geometrically distorted data)


Watermarking in spatial / transform domain

TransformSignal Perceptual

analysis

Watermark

Inverse Transform

Watermarked Signal

Signal Perceptual analysis

Watermark

Watermarked Signal


Watermark construction

1-D sequence 2-D sequence

keyRandomgenerator

1-D sequence of real numbers ~N(0,1)

or

±1


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 middle frequencies because

TransformSignal Perceptual

analysis

Watermark

Inverse Transform

Watermarked Signal


Low Low frequenciesfrequencies

Medium Medium frequenciesfrequencies

High High frequenciesfrequencies


Watermark Detection

Correlation is used in most of the methods.

TransformSignal

Watermark

CorrelationDetectoroutput0, not

watermarked1, watermarked


Transform Domains

Discrete cosine transform (DCT) Discrete Fourier transform (DFT) Fourier-Mellin transform Discrete Wavelet transform (DWT) Fourier descriptors


DCT (discrete cosine transform)DCT (discrete cosine transform)

1 2

1 2

1 11 1 2 2

1 2 1 20 0 1 2

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

2 2

N N

n n

n k n kX k k x n n

N N

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

1 2

1 2

1 11 1 2 2

1 2 1 1 2 2 1 20 01 2 1 2

11 1

1 1

22 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 kx 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 cosine DCT (discrete cosine transform)transform) domain

Advantages

•Real output

•Resistance against JPEG compression

•Fast transform (especially when it is used in compressed images)

Disadvantages

•Not robust against geometric attacks

DCT (discrete cosine transform)DCT (discrete cosine transform)


DCT can be performed at entire image

t, t`, original and watermarked signal

W watermark, a embedding power

•A pseudorandom sequence of real numbers is embedded in the frequency domain

•The coefficients of the NN DCT are reordered in a vector using a zig-zag scan.

•Watermark is embedded according to:

t`= t + a | t |wPiva et al.


}

88

•Select a block (pseudorandomly)

•Select a pair of midfrequency coefficients

•Modify the sign of their difference according to a bit value

•Select a block (Gaussian network classifier decision)

•Using a DCT constraint or a circular DCT detection region modify the middle frequency coefficients

Kochet al.

DCT can be performed at each 88 block

Bors and Pitas


Watermark embedded in DFT (discrete Fourier transform)DFT (discrete Fourier transform) domain

AdvantagesAdvantages

•Resistance against frequency attacks

•Properties that accelerates the detection of geometrically distorted image

DisadvantagesDisadvantages

•Complex output

•Calculating complexity (when size is not power of 2)

DFT (discrete Fourier transform)DFT (discrete Fourier transform)


RotationRotation in spatial domain causes rotation of the Fourier domain by the same angle

CircularCircular shift in the spatial domain does not effect the magnitude of DFT

ScalingScaling in the spatial domain causes inverse scaling in the frequency domain

CroppingCropping in the spatial domain changes the frequency sampling step

Discrete Fourier transform properties



WatermarkWatermark: 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 FMT (Fourier-Mellin transform)transform)

AdvantagesAdvantages

•Properties that accelerates the detection of geometrically distorted image

DisadvantagesDisadvantages

•Complex output

• Very big calculating complexity (2 fourier transforms – logpolar tranform)

•Not very accurate

Fourier Mellin transformFourier Mellin transform


Cartesian coordinates

Log polarcoordinates



•DFT

Amplitude resistant in

translation

•Cartesian Log polar

(x,y) (μ,θ), x=eμcos(θ), y=eμsin(θ)

Scaling and rotation equals translation

Rotation by an angle θ’ (x,y) (μ,θ+θ’)

Scaling by a factor ρ (ρx, ρy) (μ+log(ρ),θ)

•DFT

Amplitude resistant in translation,rotation, scaling

3 steps3 steps

Ruanaidh et al.



Watermark embedded in waveletwavelet domain

•Spatial localization

•Frequency spreading

•Average values from each correlator from all the sub bands and levels

Tsekeridou and Pitas

DWT Discrete wavelet transformDWT Discrete wavelet transform


Let LL be such a closed polygonal line that consists of NN vertices, each of them represented as a pair of coordinates (x(xii,y,yii).

We construct the complex signal:

1 1

2 2

n n

x iy

x iyz

x iy

Watermark embedded in the Fourier descriptorsFourier descriptors of a polygonal line

Solachidis et al.


A watermark WW is added in the magnitude |Z||Z| of the Fourier coefficients of z

|Z΄ |=|Z| pW , p power of the watermark

TranslationTranslation affects only the DC term Z(0).Z(0). By not adding watermark to the DC term we obtain watermark immunity to translation.

RotationRotation by an angle θθ results in phase shift of the Fourier descriptors. The magnitude of the FD remains invariant.

ScalingScaling by a factor aa results in the scaling of the FD magnitude by the same factor. Normalized correlation overcomes this effect.

Fourier descriptorsFourier descriptors


Inversion of the traversal directionInversion of the traversal direction results in the same indexing reversal in the FD:

Zinvertion(k)=Z(N-1-k)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 traversal direction and invert it, if needed.

Change of the polygonal line starting pointChange of the polygonal line starting point affects only the phase of the FD.

Reflection (mirroring)Reflection (mirroring) causes FD magnitude indexing reversal:

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

Solution: Construct a symmetrical watermark.

Fourier descriptorsFourier descriptors


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

without resorting to the uncorrupted original image”in Proc. IEEE Int.Conf.Image Processing (ICIP), vol 1, Santa Barbara, CA, 1997, p.520

• E.Koch, J.Rindfrey, and J.Zhao, “Copyright protection for multimedia data”, Digital media and electronic publishing, 1996

• A.Bors and I.Pitas, “Image watermarking using DCT domain constraints ” in Proc.Int.Conf.Image Processing (ICIP), Lausanne, Switzerland, Sept.1996

• V. Solachidis and I. Pitas, “Circularly symmetric watermark embedding in 2-D DFT domain”, 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.Ó Ruanaidh, F.M.Boland, and O.Sinnen, “Rotation, scale and translation invariant spread spectrum digital image watermarking”, Signal Processing (Special Issue on watermarking), vol.66, no.3, pp.303-318, May 1998

• S. Tsekeridou, I. Pitas, “Embedding Self-Similar Watermarks in the Wavelet Domain” , 2000 IEEE 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 digital watermarking”, Artech house

Documents

Department of Informatics, Aristotle University of Thessaloniki1 Transform Based Watermarking Solachidis Vassilios Department of Informatics Aristotle