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

Department of Informatics, Aristotle University of Thessaloniki2 Watermarking Proof of ownership of digital data by embedding copyright statements Embedder Digital data Key Watermarked digital data Detector Digital data (possibly watermarked) Key Watermarked Not watermarked

Department of Informatics, Aristotle University of Thessaloniki3 Basic idea Spatial domain watermarking  not robust against compression and filtering  should have lowpass characteristics

Department of Informatics, Aristotle University of Thessaloniki4 –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)

Department of Informatics, Aristotle University of Thessaloniki5 Watermarking in spatial / transform domain Transform Signal Perceptual analysis  Watermark Inverse Transform Watermarked Signal Signal Perceptual analysis  Watermark Watermarked Signal

Department of Informatics, Aristotle University of Thessaloniki6 Watermark construction 1-D sequence  2-D sequence key Random generator 1-D sequence of  real numbers ~N(0,1) or  ±1

Department of Informatics, Aristotle University of Thessaloniki7 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 Transform Signal Perceptual analysis  Watermark Inverse Transform Watermarked Signal

Department of Informatics, Aristotle University of Thessaloniki8 Low frequencies Medium frequencies High frequencies

Department of Informatics, Aristotle University of Thessaloniki9 Watermark Detection Correlation is used in most of the methods. Transform Signal Watermark Correlation Detector output 0, not watermarked 1, watermarked

Department of Informatics, Aristotle University of Thessaloniki10 Transform Domains  Discrete cosine transform (DCT)  Discrete Fourier transform (DFT)  Fourier-Mellin transform  Discrete Wavelet transform (DWT)  Fourier descriptors

Department of Informatics, Aristotle University of Thessaloniki11 DCT (discrete cosine transform)

Department of Informatics, Aristotle University of Thessaloniki12 DCT (discrete cosine transform) Watermark embedded in DCT (discrete cosine 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)

Department of Informatics, Aristotle University of Thessaloniki13 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 N  N DCT are reordered in a vector using a zig-zag scan. Watermark is embedded according to: t`= t + a | t |w Piva et al.

Department of Informatics, Aristotle University of Thessaloniki14 } 8888 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 Koch et al. DCT can be performed at each 8  8 block Bors and Pitas

Department of Informatics, Aristotle University of Thessaloniki15 DFT (discrete Fourier transform) Watermark embedded in DFT (discrete Fourier transform) domain Advantages Resistance against frequency attacks Properties that accelerates the detection of geometrically distorted imageDisadvantages Complex output Calculating complexity (when size is not power of 2) DFT (discrete Fourier transform)

Department of Informatics, Aristotle University of Thessaloniki16 Rotation Rotation in spatial domain causes rotation of the Fourier domain by the same angle Circular Circular shift in the spatial domain does not effect the magnitude of DFT Scaling Scaling in the spatial domain causes inverse scaling in the frequency domain Cropping Cropping in the spatial domain changes the frequency sampling step Discrete Fourier transform properties DFT (discrete Fourier transform)

Department of Informatics, Aristotle University of Thessaloniki17 Watermark 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 DFT (discrete Fourier transform)

Department of Informatics, Aristotle University of Thessaloniki18 FMT (Fourier-Mellin transform) Watermark embedded in FMT (Fourier-Mellin transform) Advantages Properties that accelerates the detection of geometrically distorted imageDisadvantages Complex output Very big calculating complexity (2 fourier transforms – logpolar tranform) Not very accurate Fourier Mellin transform

Department of Informatics, Aristotle University of Thessaloniki19 Cartesian coordinates Log polar coordinates Fourier Mellin transform

Department of Informatics, Aristotle University of Thessaloniki20 DFT Amplitude resistant in translation Cartesian  Log polar (x,y)  (μ,θ), x=e μ cos(θ), y=e μ sin(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 steps Ruanaidh et al. Fourier Mellin transform

Department of Informatics, Aristotle University of Thessaloniki21 wavelet Watermark embedded in wavelet domain Spatial localization Frequency spreading Average values from each correlator from all the sub bands and levels Tsekeridou and Pitas DWT Discrete wavelet transform

Department of Informatics, Aristotle University of Thessaloniki22 L N (x i,y i Let L be such a closed polygonal line that consists of N vertices, each of them represented as a pair of coordinates (x i,y i ). We construct the complex signal: Fourier descriptors Watermark embedded in the Fourier descriptors of a polygonal line Solachidis et al.

Department of Informatics, Aristotle University of Thessaloniki23 W|Z| A watermark W is added in the magnitude |Z| of the Fourier coefficients of z |Z΄ |=|Z|  pW, p power of the watermark  TranslationZ(0).  Translation affects only the DC term Z(0). By not adding watermark to the DC term we obtain watermark immunity to translation.  Rotationθ  Rotation by an angle θ results in phase shift of the Fourier descriptors. The magnitude of the FD remains invariant.  Scalinga  Scaling by a factor a results in the scaling of the FD magnitude by the same factor. Normalized correlation overcomes this effect. Fourier descriptors

Department of Informatics, Aristotle University of Thessaloniki24  Inversion of the traversal direction  Inversion of the traversal direction results in the same indexing 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 traversal direction and invert it, if needed.  Change of the polygonal line starting point  Change 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)|  Solution: Construct a symmetrical watermark. Fourier descriptors

Department of Informatics, Aristotle University of Thessaloniki25 References 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 , 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 , 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 , 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 , 5-9 June 2000 S.Katzenbeisser, F.Petitcolas, “Information hiding techniques for steganography and digital watermarking”, Artech house