A FRACTAL WATERMARKING SCHEME FOR IMAGE IN DWT DOMAIN

A FRACTAL WATERMARKING SCHEME FOR IMAGE IN DWT DOMAIN ABSTRACT A ne digital approach based on the fractal technolog in the Disperse Wavelet Transform domain is proposed in this paper. First e constructed the domain subtrees and the range subtrees in the avelet decomposed subbands. Second searched for the self-similar domain subtrees b the fractal transforms. The selected domain subtrees ere regarded as the embedded trees. Then, the ing signals ere embedded, detected or extracted according to the JND model. Final A large number of attacking experiments results test securit and robustness of the method. Ke ords: Disperse Wavelet Transform; the domain subtree; the Fractal Transform. I. INTRODUCTION With the rapid development of information technolog, Images are becoming more and more popular in the internet. There is an urgent need for copright protection of images against pirating. Therefore, image or signature algorithms represent a ne, fast emerging area in image processing. After researching on man images, e find that there exists a certain self-similarit among the different parts of an image or beteen the parts and the hole of an image. This self-similarit is an inherent attribute of the image. That is to sa, hich is hard to be changed and removed unless the qualit of the image isn t guaranteed [1]. The avelet transform coefficients of an image have good similarities hich represent the self-similarit of the image. Because one character of the discrete avelet decompose of an image is that it keeps the spatial local character of the image. Obvious this kind of self-similarit can combine ith the fractal method ver ell [2]. This paper presents a novel ing approach based on the fractal theor and the discrete avelet transform. In section II, e propose the embedding method based on the fractal transform in the DWT Domain. In section III, e discuss the detecting (or extracting) process of the proposed scheme. At last, man experimental results represent the excellence of the scheme in section IV. II. THE WATERMARK EMBEDDING METHOD BASED ON THE FRACTAL TRANSFORM The embedding scheme contains the folloing steps: Step 1. Processing the signals First e process the, then calculate the maximum capacit according to the character of the image so as to guarantee the energ of the embedded signals ithin the permitted range. Supposing the after preprocessing is W = { i i {,1}, i = 1,2, L, N}, taking the later embedding into account, e change the into: 1, if i = 1 T : i i = 1, if i = Final e get the information data hich are going to be embedded into the image: W = { i i { 1,1}, i = 1,2, L, N} (1) Step 2. Transforming the original image b the DWT and constructing the sets of domain subtrees and range subtrees hich e called in this paper, then searching the self-similar domain subtrees hich the data are embedded into. The DWT is identical to a hierarchical subband sstem, here the subbands are logarithmicall spaced in frequenc and represent an octave-band decomposition. B the DWT, e have three parts of multiresolution representation (MRR) and a part of multiresolution approximation (MRA),The subbands in the 1 st level labeled LH 1,HL 1 and HH 1 of the MRR represent the finest scale avelet coefficients. To obtain the next coarser scale of avelet coefficients, the subband LL 1 (that is, MRA) is further decomposed and criticall subsampled,and so on. An image is decomposed into 3L+1 subbands for L scales. As the construction approach of domain blocks and range blocks b the traditional fractal coding in the spatial domain, e select avelet transform coefficients from the L level suband to the 1st level suband to construct the domain subtree D and construct the range subtree R from the L-1 level suband to the 1 st level suband: Each avelet coefficient in the L level subband has the corresponding relation ith 2 2 coefficients in the L-1 level subband, 2 2 2 2 coefficients in the L-2 level subband and (2 L-1 ) (2 L-1 ) coefficients in 1st level subband. Therefore, ever coefficient of the L level subband on the vertica horizontal and diagonal directions ith its corresponding coefficient group can construct the domain tree D hose size is 4 L -1. In the same a, ever avelet coefficient in the L-1 level subband ith its corresponding coefficient group can construct the range tree R. For example, if the root joint of the avelet tree from the third level of the avelet decompose together ith its coefficient group can form a avelet tree R hose size is 63. Obvious if the size

of the original image is 512 512, then there ill be 124 domain subtrees D and 496 range subtrees R after the 4 levels decomposition. These orks are similar to construct non-overlapping image blocks of the fractal transform in the spatial domain[3]. According to this approach, the image block matching problem b the fractal transform in the spatial domain has been changed into the domain subtree matching problem in the avelet domain. That is to sa, e search those avelet domain subtrees hich are best-matched to their range subtrees R after the proper fractal transform, and then e call them self-similar domain subtrees. Here, the correspondent spatial blocks of the domain subtrees are no overlapping. Step 3. determining the position and the quantit of the embedding tree. In step 2, e constructed the domain subtrees D and the range subtrees R, e can use the fractal transform in the DWT domain to search for the domain subtree D hich is self-similar, and regard it as the embedding tree that e can embed the into. The calculation method of the self-similarit in the DWT domain is different from the affine transform in the spatial domain, the fractal affine transforms of the DWT domain isτ(d) R, hich are composed of the geometr transform, the combination transform and the coefficient transform[4]. When e search for the best-matched subtree D, ever D has a similar error hich is the minimum beteen it and its corresponding range R b the affine transform. Definition: Let the error threshold beε, and for the domain subtree D i, if there is a range subtree R j hich can make min( d ( R j, τ ( D i ))) ε (2) then e call D i the self-similar domain subtree hich can be embedding the into. Obvious the error threshold ε is ver important here, it determines the attribute and classification of the domain subtree D. e can divide the domain subtrees into to kind of the embedding subtree and the non-embedding subtree, and each D onl belongs to one of them. Step 4. Embedding the into the embedding subtree using the JND model in the DWT domain. After step 3, e can get the embedded domain subtree D i (i=1,2,,m), e ill embed the in the formula (1) into these domain subtrees. According to the JND model [5]: JND ( = T ( s, = frequenc( s) lu min ance(.34 texture( (3) e can calculate JND( of ever point in the embedding tree D, then embed the into it: f ( + JND( if f ( > JND( f ( = f ( otherise (4) Where JND( is the JND value of the point ( in the embedding subtree D, f( is the coefficient of dsubtree D, is the hich is embedded into the coefficient x, f(, and f( is the coefficient of the domain subtree D after embedding. x, Step 5. e transform the IDWT to the image, then e get the ed image. III. THE WATERMARK DETECTING (OR EXTRACTING) METHOD BASED ON THE FRACTAL TRANSFORM The detecting (extracting) process of the is the reverse process of the above embedding process, the steps are as follos: Step 1. Take the avelet transform on the original image, construct the domain subtrees and the range subtrees according to the method in section II, and then according to the threshold (secret keε to determine the positions and the quantities of the embedded subtrees, and calculate the avelet coefficient f( and the JND( of the corresponding point (; Step 2. We decompose the authentication image ith the same avelet transform, e can construct the domain subtrees and the range subtrees according to the method in step 1, e also can get the same position and quantit of the domain subtrees as ell as the coefficient f( in the authentication image. Step 3. The formula that the is extracted from the domain subtree is as follos: = f ( f ( = JND( Step 4. Processing the We can take the different process according to the different kind of the embedded. If the embedded is no-meaning as to-value stochastic sequence, e can judge it b the correlative detection method, that is depending on the folloing formula: ρ = (5), E E Calculating the ρ and comparing it ith the pre-set ' threshold ρ e can confirm hether there is the in the authentication image.

If the embedded like image or ords has some meaning, e can process it on the reverse pre-process, so e can get the image or the ords information. IV. THE EXPERIMENTAL RESULTS A. The stochastic sequence tests The that e used is binar stochastic sequence, i.e. -1 or 1, its length is 15, and e have done the test ith the 512 512 8 standard test image(figure 1). We transformed the image b the 4 levels DWT, and constructed corresponding 496 range subtrees R and 124 domain subtrees D, the size of R is 63, the size of D is 255. Here the method e searched for D like the method in section II. For ever D, e embedded the into the 15 coefficients, and the number of the embedding D is 1. Then e embedded the into these domain subtrees D, and got the ed image(fig 2). Here e let ρ be.5 and consequentl calculated the detection results of the image b the method in section III. Figure 1. Standard test image We used (Qualit Factor) to indicate the effect of JPRE compression. The bigger the is, the better the compression qualit ill be. JPEG compression considers of the characteristic of Human Visual Sstem. This is as the same as hat e think hile e embedded. Therefore our method is robust. Test 2. We cropped the ed image above on the different s. Starting from the left up corner, and the cropping zone is square (cropping = the idth of cropping zone/the idth of the embedded image), finall e got corresponding test results: Table 2. The results after cropping Watermark or Correlative rate ρ no 1/32.9 YES 1/16.82 YES 1/8.69 YES 1/4.47 NO From table 2 above e can see, hen the cropping is smaller than 25%, the correlative rate of the is ver high. Of course, ith the cropping graduall increasing, the correlative rate is declining quickl. This is mainl because that the cropping destros the local similarit of an image. But at this time, the visual effect of the image also declined much. To attacker, the attack has little significance. Test 3. ing We filtered the ed image b different median filters, then detectded it, and the results are as follos: Test 1. JPEG compression Figure 2.Watermarked image We carried out JPEG compression to the ed image above (Fig 2), then detected the according to the method in section III, and correspondingl received the folloing test results. Table 1. The results after JPEG compressing Correlative rate ρ Watermark or no 8.95 YES 6.87 YES 4.76 YES 2.44 NO Table 3. The results after median filters Correlative Watermark or rate ρ no 3 1.92 YES 3 3.8 YES 5 1.74 YES 5 5.61 YES ing brings man losses of the details of the image, but hat it destros most is the high frequenc coefficients. The coefficients e chose hile embedding ere mostl in the lo frequenc zone, so this method is robust to median filter.

Test 4. Adding noises We added Gauss noises of the four different intensit levels to the embedded image, and calculated the correlative rate, the results are as follos: Table 4. The results after adding Gauss noise Noise Correlative variance rate ρ Watermark or no 2.91 YES 4.83 YES 6.66 YES 8.45 NO The destruction of noise to the image is hole. With the noise intensit adding, the correlative rate decline graduall. The ke reason is that the image similarit is destroed and the avelet coefficients are changed, but no the image visual qualit declined obviousl. B. Image tests We used 256 256 8 standard test image Lena.bmp(Fig 3) as the original image, and the e used is the to-value image of 32 32 S.bmp (Fig 4). To ensure the safet after embedding, e did the chaos processing before embedding and embedded the according to the method in section II and got the ed image (Fig 5). To imitate the damage condition of the image attacking, e used the common image processing like tests above to attack the embedded image and then extracted the according to the method in section III, the results are as follos: Test 1. JPEG compression Figure 5. Watermarked image We carried out JPEG compression to the ed image above (Fig 5), then extracted according to the method in section III. The results are shon in the folloing table: Test 2. cropping Table 5. The results after JPEG compressing We cropped the ed image above on the different s as Test 2 in section IV.A, then extracted. The results are shon in the folloing table: Table 6. the results after cropping 8 4 6 2 1/32 1/8 1/16 1/4 Test 3. ing Figure 3. Standard test image We filtered the ed image in different median filters, then extracted the. the results are as follos : Table 7. The results after median filters Figure 4. Image 3 1 5 1 3 3 5 5

Test 4. Adding noise We did the similar tests as the same as the test 4 in section IV.A. The results are shon in the folloing table: Table 8. The results after adding Gauss noise Noise variance Extracted Noise variance Extracted 2 6 4 8 V. CONCLUSIONS The scheme combines the fractal transform and the DWT, and adopted the image similarit propert to search the domain subtree that the is embedded into. The simulation results sho that the proposed method can actuall survive the general image processing attacks and can be presented to claim the invisibilit and robustness. References 1. A.Jacquin. Fractal image coding based on a theor of iterated contractive image transformations.in Proc.SPIE Visual Co-mmand Image Proc.199:227-239P. 2. D.Kundur and D.Hatzinakos. A robust digital image ing method using avelet-based fusion. Proc.of ICIP 97. Vol.1, 1997: 544-547P. 3. Zhang Zhong nian, Ma Yide, Yu Yinglin. A ne kind of Fractal Image Encoding In Wavelet Domain Journal of Institute of Technolog of South China. Vol.27 No.8 1999: 43-51P. 4. JIBing,ZHANGDe,JIXiaoon.A novel audio ing scheme using multiscale avelet modulation. Progress in Natural Science.24,14(8): 664-669 5. XUANJian-hui, WANGLi-na,ZHANGHuan-guo. Wavelet -Based Denoising Attack on Image Watermarking. Wuhan Universit Journal of Natural Sciences.25, 1(1): 279-283P.