Digital Watermarking of Still Images using the Discrete Wavelet Transform

Transcription

1 Buletinul Ştiinţific al Universităţii "Politehnica" din Timişoara Seria ELECTROICĂ şi TELECOMUICAŢII TRASACTIOS on ELECTROICS and COMMUICATIOS Tom 48(62) Fascicola Digital Watermarking of Still Images using the Discrete Wavelet Transform Corina afornita 1 Aleandru Isar 2 Abstract We present a technique for the digital atermarking using a discrete avelet transform The proposed scheme is robust to a variety of signal distortions When embedding the atermark e make use of the image properties To achieve imperceptibility the loest band of the image is left unmodified To select the perceptually significant coefficients for each subband e generate a atermarking key using an adaptive threshold We compare our approach ith another transform domain method Simulation results sho the robustness and validity of the atermarking process proposed herein Keyords: copyright protection digital atermarking discrete avelet transform I ITRODUCTIO Transmission manipulation and storage of multimedia data are becoming an everyday practice The rapid evolution of digital technology has led to the need of copyright protection tools [1] One approach in this matter is cryptography Hoever cryptography can protect content in transit but once decrypted the content has no further protection [2] The alternative or complement to this approach is digital atermarking Digital atermarking is the process of embedding information called a atermark in media signals ithout making perceptible changes [3] The atermark should be imperceptible undeletable statistically undetectable robust to lossy compression and various signal distortions and unambiguous [4] Common types of signals to atermark are images audio and video In this paper e concentrate on the application of digital atermarking of still images Current techniques described in literature for the atermarking of images are spatial domain methods [8] and frequency domain methods [ ] The spatial domain-atermarking scheme is generally fast and simple but it doesn t guarantee robustness against common signal distortions like JPEG compression or noise In this paper e propose a frequency domain method based on a multiresolution avelet decomposition hich shos greater robustness against such common attacks This paper is organized as follos In Section II e introduce the proposed method for the digital atermarking In Section III e present the simulations results and in Section IV e provide some concluding remarks 12 Politehnica University of Timisoara Communications Dept For correspondence please mail to corina@etcuttro II THE PROPOSED WATERMARKIG TECHIQUE In this section e eplain the chosen method for embedding the atermark Enhancing the perceptual invisibility hinges on considering the characteristics of the original image eg modifications of high frequencies or of the high luminance regions are less perceptible Similar to the human eye the discrete avelet transform decomposes an image in subbands having a bandidth approimately equal on a logarithmic scale Therefore it is probable that small changes in some of the coefficients localized in the subbands that represent the detail images ill make the mark imperceptible to human eyes To achieve imperceptibility the loest band of the image is left unmodified To select the perceptually significant coefficients for each subband e generate a atermarking key using an adaptive threshold We present to versions of the same atermarking method A Architecture We assume that the binary atermark is of length and consists of elements from the set { 11 } Let OI be the original image We embed the atermark into the detail avelet coefficients using a atermarking key only in the first level of the decomposed image The folloing steps are to be performed: 1 Compute the first level avelet decomposition of the original image We obtain one approimation image and three detail images corresponding to the horizontal vertical and diagonal details of the image We denote the

2 th detail image of the original by d ( m here { h v (h v d stands for horizontal vertical and diagonal respectively) The approimation image is a ( m 2 For each detail image e consider the coefficient location ( m and e compute a k m n here atermarking key ( ) { h v : ( m 1 if d > qm k ( m = (1) 0 otherise here q is a user-defined variable and M is the maimum of the coefficients from the detail image d ( m For the given detail image d ( m if the associated value of the key is zero e do not embed a mark To embed a atermark bit ( m e increase or decrease the detail image coefficient ith a given quantity: ( m = d ( m + α( m d (2) and α is a user-defined positive variable 3 The atermarked image WI is computed from the approimation image a ( m and from the detail images d ( m here here { h v { h v The method is presented in Fig1 The parameters q and α are user-defined It is easy to notice that a larger value for α and and a smaller value for q ill increase the robustness of the method but ill make the marking process more visible B Watermark Detection and Etraction In order to etract the atermark e use an informed detector since the original image is knon The received image is a possibly distorted version of the atermarked image The objective of the etraction process is to obtain a reliable estimate of the original atermark For the detection process e make use of the original image and of the atermark ( m In order to detect if the received image RI is atermarked e perform the folloing operations: 1 Compute the first level discrete avelet decomposition of the received image RI and of the original image OI We obtain to decomposed images r( m and o ( m We denote the th detail image of the received image by rd ( m here { h v (h v d stands for horizontal vertical and diagonal respectively) The approimation image is ra ( m 2 Compute the atermarking key k ( m here { h v as described in the atermarking process of the original image We make use of the key to locate the coefficients here the mark as embedded We etract the atermark as follos: r ( m [ rd( m d( m ]/ [ rd ( m d ( m ]/ 1 if = 1 if rand( 11) otherise here ( m α > 0 α < 0 r is the recovered atermark bit We make a random guess for the recovered d m n = rd m n atermark bit if ( ) ( ) 3 If the atermark had been embedded in different locations several times then the most common bit value etracted is assigned for the recovered bit Otherise a random guess is made for its value After etracting the atermark e compare the original and the etracted atermarks using the correlation coefficient: c ( r) n= 1 ( ) r( n= 1 = (4) 2 n 2 ( r ( n= 1 here is the given atermark and r is the recovered atermark If the correlation coefficient is equal or higher than a pre-specified threshold the given atermark is positively detected in the received image When the received image is the atermarked image RI=WI the correlation coefficient c ( r) = 1 When the received image is a modified version of the atermarked image and the changes are not perceptually visible c ( r) ill be large value The etraction of the atermark is presented in Fig 2 (3)

3 Original Image OI DWT Watermarking Key k h (m Key generation k v (m k d (m Watermark Watermarked Image WI IDWT Fig 1: Embedding steps of the proposed method

4 Original Image OI Received Image RI DWT DWT Key Generation k h (m Recovered atermark Original atermark k v (m k d (m Watermarking Key Correlation Measurement Fig 2: Etracting steps of the proposed method

5 III SIMULATIO RESULTS For all eperiments e used the ell-knon Lena image and a 256 length binary atermark The Daubechies avelet ith 4 vanishing moments is used to produce the coefficients We set the to parameters α = 10 and q = 0 06 We present to approaches for the same method In the first approach e embed the atermark in the diagonal detail image of the first level d d ( m The atermarked image has a peak signal-to-noise ratio PSR = 4376 db In the second approach e embed the atermark in all the detail images of the original image The atermarked image has a PSR = 3914 db The second image is perceptually more affected than the first hoever the etracted atermark from the second image is more robust in face of attacks than the etracted atermark from the first image The atermarked images as ell as the original image are shon in Fig 3 (a) (b) (c) Fig3: (a) Original image Lena (b) Watermarked version of Lena using the first approach (c) Watermarked version of Lena using the second approach We investigate the effects of common signal distortions (JPEG compression median filtering and additive Gaussian noise) on the correlation coefficient beteen the given and the etracted atermark We compare the performance of the proposed method ith a technique based on the multiresolution avelet decomposition proposed by Kundur and Hatzinakos [7] For comparison e embed the same atermark into the Lena image using the method described in [7] We use a atermarking key generated in our first approach k d ( m The user-defined parameter as set to Q = 4 In this particular case the atermarked image has a PSR = 5733 db All atermarked images ere distorted in turn by median filtering JPEG compression and additive Gaussian noise The results of the correlation coefficient c ( r) as a function of the filter size M M for median filtering as a function of the compression ratio for JPEG compression and as a function of signal-tonoise ratio ( SR ) are shon in Fig 4 The plots ith o symbols are the results from our first approach; the plots ith symbols are the results from our second approach and the remaining plots sho the performance of the technique described in [7] It is obvious that the correlation coefficient for the proposed method is higher than for the method from [7] in the case of JPEG compression and additive Gaussian noise IV COCLUSIOS We proposed a avelet-based atermarking method We only change the coefficients that e believe ill not have a visual impact on a human observer The coefficients ere selected using subband-adaptive thresholding The proposed technique shos a higher performance against JPEG compression and additive Gaussian noise than the method proposed in [7] Hoever the method proposed by Kundur and Hatzinakos shos a higher performance against median filtering ACKOLEDGEMETS We ish to thank to Mr Steart Fraser (University of Aberdeen UK) and especially to Prof Deepa Kundur (Teas A&M University USA) for their help hich alloed us to finish this ork

6 Correlation Coefficient Correlation Coefficient Detector Response to JPEG Compression Compression Ratio Detector Response to Median Filtering Filter Size M REFERECES [1] GVoyatzis I Pitas Problems and Challenges in Multimedia etorking and Content Protection TICSP Series o 3 editor Iaakko Astola March 1999 [2] I Co M Miller J Bloom Digital Watermarking Morgan Kaufmann Publishers 2002 [3] A Sequeira D Kundur Communications and Information Theory in Watermarking: A Survey Multimedia Systems and Applications IV A G Tescher B Vasudev and V M Bove eds Proc SPIE (vol 4518) pp Denver Colorado August 2001 [4] C Hsu J Wu Image Watermarking by Wavelet Decomposition Academy of Information and Management Sciences Journal Vol 3 o1 pp [5] I Co J Killian T Leighton T Shamoon Secure Spread Spectrum Watermarking for Multimedia IEEE Transaction On Image Processing 6 12 pp [6] S Craver Memon B Yeo M Yeung Resolving Rightful Onerships ith Invisible Watermarking Techniques: Limitations Attacks and Implications IEEE Journal On Selected Areas In Communications Vol 16 o 4 May 1998 [7] D Kundur D Hatzinakos Digital Watermarking using Multiresolution Wavelet Decomposition Proc IEEE Int Conf On Acoustics Speech and Signal Processing Seattle Washington Vol 5 pp May 1998 [8] ikolaidis I Pitas Robust Image Watermarking in the Spatial Domain Signal Processing Vol 66 o 3 pp [9] JR Kim and YS Moon A Robust Wavelet-Based Digital Watermarking Using Level-Adaptive Thresholding Proc of IEEE ICIP Vol 2 Kobe Japan Oct 1999 pp Detector Response to Additive Gaussian oise Correlation Coefficient SR (db) Fig4: Results for JPEG compression median filtering and additive noise The plots ith o and symbols are the correlation results for the proposed method (first and second approach respectively) The remaining plots are for the method in [7]