VIEWS: 62 PAGES: 19 CATEGORY: Technology POSTED ON: 11/9/2009 Public Domain
A Stochastic Approach to Content Adaptive Digital Image Watermarking S. Voloshynovskiy*#, A. Herrigel#, N. Baumgaertner#, T. Pun* *Computer Science Department (CUI) University of Geneva, Switzerland Contact: http://cuiwww.unige.ch/~vision # Digital Copyright Technologies (DCT) Stauffacher-Strasse 149 CH-8004 Zurich, Switzerland 1 Content 1. Introduction 1.1. Why deal with content adaptive watermarking 1.2. Empirical perceptual models used in watermarking applications 2. Image watermarking – MAP formulation 2.1. Stochastic models of watermark and cover image 2.2. Generalized solution of MAP – image denoising 2.3. Image denoising and lossy compression 3. Adaptive image watermarking 3.1. Noise visibility function (NVF) 3.2. NVF based on non-stationary Gaussian model 3.3. NVF based on stationary GG model 3.4. Content adaptive watermarking 4. Results of computer simulation 5. Conclusions 2 1. Introduction 1.1. Why deal with content adaptive watermarking 3 linked criteria for watermarking Visibility V Capacity C Robustness R Why stochastic approach Perceptual mask Stochastic Image modeling Image Detector As a model of channel noise robustness Capacity 3 1.2. Empirical perceptual models used in watermarking applications Transfer modulation function of HVS J. Ruanaidh, T. Pun (Signal Processing, No3, 1998) - CUI Luminance sensitivity M. Kutter (Proc. SPIE, 1998) - EPFL Luminance and texture masking - L&T M. Kankanhalli, R. Ramakrishman (ACM Multimedia, 1998) F. Bartolini, M. Barni, V. Cappelini, A. Piva (ICIP, 1998) use results of perceptual image compression (N. Jayant, J. Johnton, R. Safranek, Proc. IEEE, 1993) CUI EPFL L&T Basic Idea: Basic Idea: Basic Idea: Embed in middle band Embed according to Embed according to as trade-off between Luminance Function Lumainance and visibility & distortions Texture masking (as (lossy compression) edge detection) Basic drawbacks: It does not take into Watermark strengh is -A set of empirically account spatial different only for darker adjusted parameters anisotropy of image and lighter regions. is required spectra and as the Pattern masking -No closed form result is not adaptive to properties are not taken expression for optimal image content into account detector design and capacity estimation 4 Complete content adaptive model should include: Luminance masking Contrast sensitivity Texture masking including spatial anisotropy (and MTF) Color masking We concentrate on texture masking function in coordinate domain with further extension to wavelet transform and steerable pyramids to incorporate spatial anisotropy The main advantages of the proposed approach: - closed form solution - automatically adjusted to wide set of images - simple computation in comparison with the theoretical models of HVS - a few model parameters needed to be estimated - criterion is stochastically based - takes into account statistics of cover image and distribution of watermark - makes possible to design optimal watermark detector and resolve 3 contradicting requirements: Visibility-Robustness- Capacity - opens new opportunities to perceptual image quality criterion development 5 2. Image watermarking – MAP formulation Two problems: - watermark estimation/detection - watermark removal Generalized model Notations: y: stego image; x: original (cover) image; n: watermark (considered as noise-like signal) y = x+n Maximum A Posteriori (MAP) estimation Watermark estimation n = argmax{ln p X ( y ¦ n ) + ln pn (n )} ˆ ~ ~ ~ n ∈ℜ N Watermark removal (or ≡ image estimation/denoising) x = arg max{ln pn ( y ¦ ~ ) + ln p X (~ )} ˆ x x ~ ∈ℜ N x 6 y ˆ x ˆ n Robust Message - Estimator ⊕ detector and demodulator Key 2.1. Stochastic models of watermark and cover image 2.1.1. Watermark models: r.v. ind. ident. distributed samples - p n (n ) ∝ i.i.d . N (0, Iσ n ) for spread spectrum wm 2 - pn (n ) ∝ i.i.d . GGD for binary wm + Masking 2.1.2. Cover image models: r.v. ind. ident. distributed samples AR formulation x = Ax + ε = x + ε ε = x − x = (I − A)x ≡ Cx A - neighborhod set; x - predicted value; ε - residual (i.i.d.) A – LP operator; C – HP operator (Homogeneous) (Inhomogeneous) Globally i.i.d. GGD Locally i.i.d. Gaussian σ x2 0 L 0 σ x1 2 0 L 0 0 σ 2 0 M 0 σ x22 0 M Rx = x Rx = M 0 O 0 M 0 O 0 2 0 0 0 σ x2 0 0 0 σ xN 9 2.2. Generalized solution of MAP – image denoising Consider problem of image estimation in AWGN. ( p n (n ) ∝ i.i.d . N 0, Iσ n 2 ) p X (x ) ∝ i.i.d . GG (x , R x ) or p X (x ) ∝ i.i.d . N (x , R x ) Known solutions Globally i.i.d. GGD Locally i.i.d. Gaussian (non-convex function) (convex function) General close form solution does not exist!!! Close form solution Iterative solutions Adaptive Wiener (Lee filter) ICM Reweighted Stoch.& determ. anneling Least Graduated nonconvexity Squares (RLS) ARTUR Particular close form solution in wavelet domain Shrinkage methods 10 Generalized solution 1 x = arg min 2 y − ~ + ρ (r ) 2 ˆ x ~∈ℜ N x 2σ n RLS solution 1 2 2 x k +1 = arg min 2 y − ~ k ˆ x + w k +1 r k ~∈ℜ N x 2σ n Iterative solution: x k → w k +1 → x k +1 ˆ ˆ Notations for k-iteration: ρ (r ) = [η (γ ) ⋅ r ] γ - GGD energy function x−x r= - residual σx ′ ρ (r ) = γ [η (γ )] γ r 2 −γ - derivative from GGD energy function r ′ ρ (r ) 1 w= - weighting function r with γ estimated using moment matching method w is constant for k-iteration: RLS solution in the form of the adaptive Wiener filter wσ n2 σx2 x= ˆ x+ y wσ n + σ x 2 2 wσ n + σ x 2 2 RLS solution in the form of Lee filter σx2 x=x+ ˆ (y − x ) wσ n + σ x 2 2 11 Comparative analysis of different distributions in RLS estimate Estimated, Gaussian and Corresponding energy functions Laplacian pdfs Derivatives from energy functions Weighting functions 12 2.3. Image denoising and lossy compression y = x+n Assumptions: ( p n (n ) ∝ i.i.d . N 0, Iσ n 2 ) p X (x ) ∝ i.i.d . GG (x , R x ) RLS solution for fixed iteration: σx2 x=x+ ˆ (y − x ) wσ n + σ x 2 2 Shrinkage solution (known in wavelet domain) x = x + max (0, y − x − T )sign( y − x ) ˆ σn 2 T= 2 - for Laplacian image prior σx 13 Denoising – shrinkage function ˆ x HF ˆ x HF x−x x−x r= r= σx σx Hard-thresholding Soft-thresholding ˆ x HF γ =1 γ = 0.7 x−x r= σx GGD prior 14 Denoising – Lossy compression As watermark estimation and corresponding attacks Denoising – shrinkage Quantization x−x r= x−x σx r= σx Laplacian image prior 15 3. Adaptive image watermarking 3.1. Noise visibility function (NVF) Consider term from RLS solution (plays the role of texture masking) σx 2 b := wσ n + σ x 2 2 In our approach we define NVF function as wσ n2 NVF = 1 − b = wσ n + σ x 2 2 ( n ∝ N 0, Iσn 2 ) NVF Perceptual model σn = 1 Behavior: - flat regions: NVF → 1 - edges and textured regions: NVF → 0 17 (Homogeneous) (Inhomogeneous) Advantages Only two parameters of the model should be estimated Convex energy function Disadvantages Concave energy function - Local variance is estimated as ML (NVF is ‚noisy‘, under locally i.i.d assumption that is but with good resolution) not true for large windows, but small windows – bias in estimate - NVF is oversmooth Original image NVF 20 4. Results of computer simulation Classical PSNR 2 255 PSNR = 10 log 10 x− y 2 Weighted PSNR 2 255 wPSNR = 10 log 10 2 x− y NVF Barbara image: Gaussian distributed watermark Method of embedding Watermark strength Non-adaptive 5.0 10.0 15.0 Adaptive non-stationary Gaussian NVF 6.5 15.0 23.0 Adaptive stationary GG NVF 8.0 20.0 31.0 Adaptive Kankanhalli 9.8 19.6 30.4 PSNR, dB 34.1 28.3 24.7 Examples of embedding of binary watermark for the fixed PSNR=24.7dB (in adaptive case Sf=3 for all embedding) wPSNR,dB: 26.45 27.87 29.28 Strength: 15.0 Se: 23.0 31 21 Examples of embedding of binary watermark for the fixed PSNR (in adaptive case Sf=3 for all embedding) Non-adaptive adaptive nG adaptive sGG PSNR, dB: 34.10 5.0 6.5 8.0 28.30 10.0 15.0 20.0 24.7 15.0 23.0 31.0 22 Examples of Gaussian watermark embedding for the fixed PSNR (in adaptive case Sf=3) Kankanhalli’s method Adaptive sGG PSNR: 28.3 dB Strength: 19.6 20.0 PSNR: 28.67 dB Strength: 21.7 21.0 23 4. Conclusions - stochastic approach to content adaptive watermarking is developed - developed models require small amount of parameters to be estimated - results show superior performance in comparison with the other known empirical adaptive approaches with respect to both visual quality and watermark strength - the similarity between denoising and compression as the watermark removal attacks is shown - models make possible to develop the optimal detector for the watermark and to estimate capacity of the images Future work: - new ML and MAP solutions for local image variance estimation - design of the optimized robust watermark detector for the stationary non- Gaussian and non-stationary Gaussian channels (considered image models) and corresponded distribution of errors in watermark estimation - unified approach to the compression/denoising attack analysis