Joint Watermarking and Compression for Images in Transform Domain

Transcription

1 Vol.2, Issue.4, July-Aug pp ISSN: Join Waermarking and Compression for Images in Transform Domain Gamal Fahmy Elecrical Engineering Dep., Assiu Universiy, Egyp, Absrac: Image waermarking, auhenicaion and encrypion have gained an increased imporance during he las decade. This is due o he widespread use of visual media over he Inerne and in several digial media applicaions. Several waermarking echniques have been proposed, some in spaial domain, and more recenly in he ransform/frequency domain and have been repored o be robus agains differen aacks, namely compression. I is also well known he imporance and effeciveness of compression echniques o sore ransmi and rerieve visual informaion. However, he creaion or developmen of a join waermarking and compression framework for images has ye o be explored, where waermarking and compression could be pursued joinly on a rade-off manner. In oher words, waermarking embedding/exracion can be performed on compressed domain daa, while compression parameers could be used as waermarking keys. The primary focus of his paper is o explore his novel/unique idea. We propose a join waermarking and compression (JWC) echnique in he ransform domain. This ransform domain is based on he Naural Preserve Transform and can be uilized o achieve a balance beween waermarking and compression for visual informaion. Waermarking performance is evaluaed blindly for differen compressed domain daa scenarios, while compression performance is analyzed for oher waermarking cases. Exensive simulaion resuls ha demonsrae he efficiency of he proposed join waermarking and compression echnique are presened. Keywords: Image Waermarking, Naural Preserve Transform, Image Compression; Harley Transform I. Inroducion The rapid growh of visual media based applicaions necessiaes sophisicaed compression echniques in order o sore, ransmi and rerieve audio-visual informaion. The recen MPEG 4 and JPEG 2000 sandards address he need for conen based coding and manipulaion of visual media. Wih he widespread use of he Inerne and he rapid and massive developmen of mulimedia, here is an impending need for efficien and powerfully effecive copyrigh proecion echniques [1-3]. Digial waermarking schemes are ypically classified ino hree caegories. (1) Privae waermarking which requires he prior knowledge of he original informaion and secre keys, a he receiver, (2) Semi-privae or semi-blind waermarking where he waermark informaion and secre keys may be available a he receiver, and (3) public or blind waermarking where he receiver mus only know he secre keys [4]. The robusness of privae waermarking schemes is high o endure signal processing aacks. While privae waermarking is suiable for high securiy applicaions such as financial or defense daa, i is are no feasible in real applicaions, such as DVD copy proecion where he original informaion may no be available for waermark deecion. On he oher hand, semi-blind and blind waermarking schemes are more feasible in ha siuaion [5], bu hey have lower robusness han he privae waermarking schemes [6]. Hence, while privae waermarking is mainly uilized for auhenicaion and verificaion, blind or public waermarking is for copy proecion applicaions. In general, he requiremens of a waermarking sysem fall ino hree caegories: robusness, visibiliy, and capaciy [7] A variey of image waermarking mehods have been proposed mosly based on ransform domain [7-9]. In spie of he successful performance of mos waermarking echniques repored in he lieraure, hey sill suffer from being semifragile due o he energy concenraion of heir ransform domains (DCT and Waveles), which makes hem discard much of he mid and high frequency waermarked daa in compression [10-13]. Waermarking compressed domain daa will obviae he need for i o be decompressed for waermark exracion, while compressing waermarks would sore and ransmi visual daa efficienly. Hence, here is an impending need for sophisicaed join waermarking and compression echniques ha could compress, proec and waermark daa simulaneously. While compression aims a concenraing daa in he leas possible informaion, waermarking aims a disribuing and hiding logos and parameers. Hence, compression and waermarking are inversely relaed and hey have o be reaed on a rade-off manner. The amoun of exraced/rerieved waermarked daa is affeced by he compression degree of he hos daa, while he efficiency of compression is affeced by he amoun of daa ha needs o be embedded and exraced. In his paper we propose a ransform domain based echnique for daa waermarking ha has been previously repored in [14], and [15]. This ransform domain is based upon he Naural Preserve Transform (NPT) originally repored in [16]. We uilized his ransform domain o presen our main conribuion in his paper, which is o develop a join compression and waermarking sysem based on he NPT and wavele domains for visual daa. We ry o achieve a framework/equaion ha includes boh compression and waermarking joinly in our proposed sysem. The organizaion of his paper is as follows. Secion 2 conains necessary mahemaical background abou he NPT based waermarking approach. Secion 3 briefly explains he waermarking embedding and exracion process in he NPT domain. Secion 4 shows he robusness of he waermarking echnique agains several aacks. Secion 5 shows our proposed join 2341 Page

2 Vol.2, Issue.4, July-Aug pp ISSN: waermarking and compression framework, analysis and resuls. Discussion is in secion 6, followed by conclusions in secion Mahemaical Background for NPT based Waermarking The NPT was firs used as a new orhogonal ransform ha holds some unusual properies ha can be used for encoding and reconsrucing los daa from images. The NPT ransform of an image S of size N x N is given by: S r ( ) S ( ) (1) As ( ) is he ransformaion kernel defined as in [17-18]. ( ) I N (1 ) H N I N is N h order ideniy marix, 0 1 (2), and H N is any orhogonal ransform, like Hadamard, DCT, Harley, ec. Throughou his paper, we use he 2-D Harley ransform, defined by 1 2( k 1) 2( j 1) H ( k, j) cos sin (3) N N N N We noe here ha he Harley ransform was uilized due o is circular symmery performance, as i evenly disribues he energy of he original image in he 4 corners of he orhogonally projeced ransform image, Fig. 1(a). Hence he Harley ransform achieves a rade-off poin beween he energy concenraion feaure (which is crucial for any ransform domain for compression purposes) and he even disribuion and spreading feaure (which is crucial for waermarking and daa hiding applicaions). Afer he ransformaion kernel is calculaed in eq. 2, i is muliplied by he inpu image as a separable 2-D kernel, eq.1. The value of in eq. 2, gives a balance beween he original domain (ha would be muliplied by he ideniy marix) and he ransform domain (ha would be muliplied by he Harley basis). Clearly, when 1, he ransformed image is he original image, whereas when 0, i is is orhogonal projecion (which is he Harley ransform as in his paper). Hence he NPT ransform is capable of concenraing energy of he image while sill preserving is original sample values on a rade-off basis. This makes he NPT ransform domain image has boh almos original pixel values (ha can no be visually disinguished from he original image) and a capabiliy feaure of rerieving he logo waermark image from a small par of he ransformed image (provided ha his small par has enough energy concenraion in i). The original image can be rerieved from he ransformed image S r, using 1 1 S ( ) Sr ( ) (4) If H is symmeric, as in Harley marices, he marix 1 ( ) can be compued as follows: ( ) I H H H... (5) Fig. 1(b-c) shows he Lena image and is NPT ransformed image. is adjused o a value of 0.994, which yields a nominal PSNR of around 45 db. The high similariy beween he original and ransformed images, suggess ha NPT is very convenien for waermarking and daa hiding Page

3 Vol.2, Issue.4, July-Aug pp ISSN: Hos Image NPT Transformed Image PSNR =44.17 db (a) (b) (c) NPT WaerMarked image A w Waermarked Image A w m (d) (e) Fig. 1. (a) Transform basis of he Harely. (b-c) Original image and is NPT image, compued wih (d) NPT waermarked image wih logo in las r rows. (e) NPT waermarked image wih las r rows replace wih las r rows of original image 3.1 Waermark Embedding Le he hos image S, (size N x N) be waermarked by a waermarking logo (image) w, of size (m x n). In he boom embedding echnique [14-15], he logo is embedded o S as he las r boom lines. Hence, he logo marix is reshaped o be a mn marix w 1 (of size r x N, r ). Then, he las r rows of S are replaced by he reshaped logo w 1, as in Fig. 1(d). This would N S1 yield a waermarked image S wm, S wm, S1 S(1: N r, :) w 1 A0 w ( N r) Aw ( ) Swm ( ) z r N. Then he NPT of S wm is obained as: This sep in eq. 6, would regiser he waermark (disribue is energy) over he enire hos image. In order o make he waermarking logo invisible, we replace he las r rows z of A w wih he las r of he original image S, Fig 1(e). A0 w Awm (7) S( N r 1: N,:) 3.2 Waermark Exracion The waermarking exracion process is divided ino a non-blind case, and a blind case. In he non blind case he original hos image is known a he receiver side and we only ry o exrac he logo from he waermarked image. In he blind case he hos image is no known a he receiver side, and we ry o exrac boh he hos and logo images from he waermark image, A wm The Non Blind Case Assuming ha he original image S, he parameer of eq. 1 and he ype of he orhogonal ransformaion H N, are known a he receiver, he exracion of he waermark from he received A wm proceeds as follows: (6) 2343 Page

4 Vol.2, Issue.4, July-Aug pp ISSN: Since he size of he waermark m x n is known a he receiver side, as well as he number of rows of w. Form Y A wm 2. Pariion Y1 S1 Swm Y2 w ( N r) r N r. (8). (9) Then, as long as N-r r, he waermark w is he leas squares soluion of he sysem Y1 11S1 12 w1 (10) The qualiy of exracion is judged by compuing he normalized correlaion NCORR beween he original and exraced m n wij wexij i 1 j 1 logo, i.e. NCORR (11) w. wex w ex is he exraced waermark. The non-blind exraced logo, in our experimens achieved a NCORR = 1 performance facor The Quasi Blind Case When he prior knowledge of he hos image S is no available, he following quasi blind echnique is proposed for waermarking exracion of an NPT-based waermarked image. The proposed echnique can be described as follows: 1. Pariion ( N r) r (12) N r As A w S from eq. (6, 7, and 8), we can show ha wm A 0 w 11 12S1 i.e. A0 w 11 S1 12 w1 (13) S( N r 1: N,:) 21 22w1 2. To cancel he effec of S 1 in eq. 13, consruc an (N-r) square marix V such ha V This marix can be easily consruced by expressing is k h vecor V k as follows : V k I N r r, k jk 12 (:, j), and I N r, k I N r (:, k), 1 k N r (14) j1 The jk are obained by solving a se of r linear equaions saisfying he following condiion: V (:, ) j j r Since 12 is an (N-r) x r marix, k hen is maximum rank is r. Consequenly, he rank of he marix V is (N-2r), [19]. 3. Pre-muliply Equaion (13) by V o yield V A0 V w 11S1 (15) As he rank of 11 is (N-r), he rank of V 11 is (N-2r). So, o have a unique soluion of eq.15, r arbirary parameers of every column of S 1 have o be known a he receiver/exracor. This can be achieved if in he waermarked image A w, we choose he marix z (eq. 6), o be S(N-2r+1:N-r,:) insead of S(N-r+1:N,:).(i basically means replicaing he r las rows of he image as in Fig. 2 (a)) Page

5 Vol.2, Issue.4, July-Aug pp ISSN: LLLL HL Las r rows replicaed LH HH (a) (b) Fig.2. (a) Example of hos images wih las r rows replicaed, N=256, r=8 (b) LLLL is he lowes band in a 2 layer wavele decomposiion Having obained S 1 as he unique soluion of eq.15, w 1 (he logo) is exraced as in he non-blind case, and subsequenly reshaped o regain he original waermark w. We used he erminology quasi blind, as a minor amoun of informaion has o be known (r parameers of every column) a he receiver side. We noe here ha having r rows of he hos image known a he receiver side as a mandaory condiion for our blind echnique is a sligh draw back. However if we replicae he r rows of our hos image, S(N-2r+1:N-r,:), as he las r rows, our hos image would be like fig.4(a) wih negligible effec for his replicaion process, especially if he hos image has a large size compared o r, as N>>>r. 4. Robusness agains aacks (compression, noise and cropping) The proposed waermarking echniques has been repored o be robus agains compression (which is mainly shown in he nex secion), cropping and noise aacks [14-15]. Alhough his paper is primarily aimed a inroducing a join compression and waermarking sysem, we repor here he performance agains differen aacks and compare i wih oher lieraure performances. Regarding he cropping aack [14], if we crop he hos waermarked image up o 50% of is original size, full exracion of he waermarked logo is shown o be possible, as in he non blind case, provided ha he remaining waermarked size is a leas he logo size. This raio ouperforms mos of he oher waermarking echniques agains his kind of aack. Regarding he noise aack, as repored in [15], we mixed he waermarked image wih differen amouns of noise such as he sal and pepper noise and he AWGN noise, so ha he PSNR value of he original image wen as low as db. The waermarking logo was correcly exraced wih a correlaion rae higher han 90%, which is very compeiive wih he recen lieraure [8]. We noe here ha sudying he compression aack s impac on he proposed waermarking scheme is horoughly examined in he nex secion, as i is par of he proposed join compression and waermarking sysem, bu we briefly sae ha he proposed waermarking approach can fully exrac he hidden logo (more han 90% NCORR value) wih up 1.0 bpp compression using he SPIHT compression approach. 5. NPT based join waermarking and Compression In our proposed sysem, we waermark our hos image wih a logo image o obain a waermarked image. Then we compress he waermarked image hrough any ransform based image compression sandard. In our case we seleced he SPIHT wavele based image codec [20], o compress and hen decompress (a he receiver side) he waermarked image, and hen he exracion process akes place for he hos and logo images. In our sysem we measure he compression performance by he PSNR qualiy of he reconsruced image (wih respec o he original image) for a specific bi rae, while we measure he waermarking performance by he PSNR qualiy of he exraced image (hos and logo) for a specific bi rae wih a specific logo size. I can also be easily proven ha he arge compression bi rae would significanly affec he waermarking exracion qualiy, as shown nex. We also waermark compressed domain daa, by waermarking he LL band image in he wavele ransform of any compression process, Fig. 2(b). I can also be shown ha he amoun of waermarked daa (wih is arge exracion qualiy) would significanly affec he compression reconsrucion performance; i is also dependen on which wavele level (number of layers) is LL band is being waermarked as also shown in he nex secion. We noe here ha he higher he LL band (more layers) ha is being waermarked, he less he qualiy of he reconsruced image from wavele based compression heories. This is due o he fac ha more daa would be concenraed in LL band of he highes layer; herefore any manipulaion o he band coefficiens, as wha happens by NPT, would more deeriorae he reconsruced image, also as a larger number of high band frequencies are dependen on i as in SPIHT or EBCOT [20-21]. We noe here ha if he here is no waermark, zero number of embedded boom lines, hen increasing he number of wavele layers would definiely enhance he PSNR of reconsruced image from enhanced resoluion, bu if here is a waermark, even if i is small (5 rows), i will affec (negaively) he reconsruced hos image, and hence increasing he number of wavele decomposiion layers would furher deeriorae he PSNR of he reconsruced hos image. Increasing he number of wavele layers would also 2345 Page

6 Vol.2, Issue.4, July-Aug pp ISSN: double he number of r rows in he boom embedding process, as he logo (waermark) has a fixed size and he las LL band would be half he number of rows and columns of he previous case for every decomposiion level. This would provide us wih one more jusificaion for he deerioraed PSNR reconsrucion qualiy of he hos image for increasing he number of wavele layers from his join waermarking and compression process. For a waermarking sysem ha is based on secion 3, Fig.3 shows he PSNR values of he waermarked image for differen values of alpha ( ), along wih he corresponding NCORR values of he exraced image, when he waermarked image is compressed using SPIHT wih bpp (bis per pixel) =2.5, and no wavele decomposiion layers. I can be seen in he figure, ha he smaller he value of alpha, he less conribuion of he original image in eq.2, and he lower he PSNR, bu he more conribuion of he Harley basis, which means more energy disribuion, which will yield beer exracion, beer NCORR, and vice versa. A value of alpha in he range , is he opimal rade-off poin beween he 2 curves for his waermarking case, as in Fig. 3. Fig. 4, shows a block diagram for our proposed join waermarking and compression sysem. There are primarily hree parameers ha can significanly affec he performance of boh waermarking and compression. The alpha parameer ( ) as in eq.2, he number of wavele layers and he arge bi-rae in compression in he adoped SPIHT. While i can be easily proven ha he higher he bi-rae, he beer is he PSNR of he exraced image (boh hos and logo) and he lower is he compression performance from basic rae-disorion heories [20-22]. The higher he value of he more weigh of he original image would be in eq.2, which would imply less conribuion of he Harley basis, which means lower amoun of energy disribuion, which means less waermarking performance. On he oher hand, more wavele decomposiion layers, which would imply more resoluions levels, and would lead o beer compression performance as well known from successful wavele based coders [20, 21]. Since in our sysem we waermark he LL band in he las wavele layer, increasing he number of layers would deeriorae he compression reconsrucion qualiy of waermarking exraced images, as higher band frequencies are added o i in reconsrucion, as in Fig. 6. Therefore increasing he number of wavele layers in our sysem would imply less PSNR for he reconsruced image (ha has been waermarked and exraced). Hence, while increasing he bi rae would enhance he reconsrucion qualiy of waermarking an exraced image, increasing he number of wavele decomposiion layers would deeriorae i in our join waermarking and compression sysem, and he lower he value of alpha, he beer he waermarking exracion as he NCORR curve in Fig. 3. Since he number of wavele decomposiion layers and he bi rae are wo compression parameers and hey have an inverse impac on he waermarking performance, hey could be joinly combined in a single variable C, according o his relaion, C=K 1 * bpp +( 1/K 2 * No. of wavele layers ) 2346 Page

7 Vol.2, Issue.4, July-Aug pp ISSN: From all above, we can idenify he wo variables of alpha and C as he parameers ha affec he performance of our proposed join waermarking and compression sysem. As shown above, each of hem can significanly affec he performance of boh waermarking and compression (JWC) on an inverse manner. Hence hese wo parameers can be combined ino a single equaion wih a Lagrange muliplier as in eq. 16. The Lagrange muliplier can be adjused o conrol boh alpha ( ) and C on a rade-off manner. JWC sand for performance of our join sysem. JWC *C (16) Fig.4 shows a block diagram of he proposed join waermarking and compression sysem wih a Lagrange muliplier as an adjusor ha conrols he rade-off beween boh. Fig. 5 shows he PSNR and he NCORR values for differen alpha values on he same curve, i can be shown ha an alpha value of is opimal on ha curve s rade-off. Fig.6 shows he reconsruced PSNR qualiy of hos images from waermarking he LL band for differen number of layers, wih an alpha ( ) value of and 2.5 arge bpp. Fig. 7 shows he reconsruced PSNR qualiy of hos images for differen bi raes from one wavele decomposiion layer wih an alpha value of Inpu Daa Fig. 3 PSNR and NCORR values for differenial alpha values for differen Wavele Decomposiion No. of layers C bpp NPT based Waermarking Exracion Oupu Daa NPT based Waermarking in LL band SPIHT compression SPIHT de-coding and de-compression Fig. 4 Block diagram of a join waermarking and compression sysem 2347 Page

8 Vol.2, Issue.4, July-Aug pp ISSN: We noe here he variables of K 1, K 2 and are image dependen, and can be adjused according o he needed poin on he compression and waermarking rade-off. Fig. 8 shows he PSNR of he reconsruced and exraced hos image wih a bpp 2.5 wih differen numbers of boom embedding rows, which imply differen logo sizes. I is obvious ha he increased number of boom rows of he logo image, would deeriorae he PSNR of he reconsruced hos image. Fig. 9 shows he compression performance (PSNR reconsrucion qualiy of waermarked hos image) and he waermarking performance (NCORR correlaion of he exraced logo), boh agains differen alpha ( ) values as well as differen C values, a higher C value would imply high bi rae and less number of wavele decomposiion layers. I can be shown ha he compression and waermarking performances are inversely affeced by changing he value of eiher alpha or C; hence hey have o be reaed on a rade-off manner. 5. Discussion In his paper we presened a join waermarking and compression sysem ha can boh compress and waermark a hos image on a rade-off manner. We noe here ha our primary objecive was o presen he idea of join compression and waermarking, raher han a regular single waermarking or compression echnique like he recen lieraure, or our work in [14-15]. Fig. 5 Join graph for PSNR and NCORR values for differen alpha values 2348 Page

9 Vol.2, Issue.4, July-Aug pp ISSN: Fig. 6 PSNR reconsruced qualiy of hos for differen number of wavele layers Fig. 7 PSNR reconsruced qualiy for differen bpp for one wavele decomposiion layer 2349 Page

10 Vol.2, Issue.4, July-Aug pp ISSN: Fig. 8 PSNR reconsruced qualiy for hos for differen logo sizes Fig. 9 Join waermarking and Compression for differen alpha values for Lena and Cameraman images 2350 Page

11 Vol.2, Issue.4, July-Aug pp ISSN: When reaing compression and waermarking joinly, compression parameers can be reaed as securiy keys, while waermarking daa or keys can be considered as compression indices. Our proposed simulaion resuls showed ha here were hree variables ha could significanly affec he performance of boh waermarking and compression. Bi rae, number of wavele decomposiion layers and he alpha value, which conrols he balance beween energy concenraion (compression) and energy disribuion (waermarking). The number of wavele decomposiion layers and he bi rae are wo compression parameers ha are ypically defined in any wavele-based compression process and hey were combined in a single compression parameer C. Since boh he alpha value and he C compression parameer had inverse impac on he performance of boh compression and waermarking, a Lagrange muliplier equaion was inroduced ha conrols he balance beween alpha and C on a rade-off manner. We noe here he Lagrange muliplier value would depend on boh he image class/ype/conen in addiion o he desired poin beween compression and waermarking performances. 7. Conclusions Our proposed sysem can be uilized in join waermarking and compression applicaions ha explois compression parameers as waermarking variables, while compression indices could be used as waermarking acuaors/adjusors. Our illusraed simulaion resuls suppor our hypoheses and analogies in join waermarking and compression, ha hey are inversely relaed and here is a rade-off relaion beween hem, hence hey should be reaed joinly o achieve he opimal poin of hem. This work is funded by he minisry of Communicaion and Informaion Technology, Egyp, ITIDA. I has also been funded parly by he Alexander von Humbold foundaion, Germany. References 1. C. Y. Lin and S. F. Chang, A robus image auhenicaion mehod disinguishing JPEG compression from malicious manipulaion, IEEE Trans. Circuis Sys. Video Technol., vol. 11, no. 2, pp , Feb N. 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