A blind robust watermarking method based on Arnold Cat map and amplified pseudo-noise strings with weak correlation
Seyyed Hossein Soleymani, Amir Hossein Taherinia, Amir Hossein Mohajerzadeh
AA blind robust watermarking method based on Arnold Cat map and amplifiedpseudo-noise strings with weak correlation
Seyyed Hossein Soleymani a , Amir Hossein Taherinia a, ∗ , Amir Hossein Mohajerzadeh a a Computer Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran
Abstract
In this paper, a robust and blind watermarking method is proposed, which is highly resistant to the common imagewatermarking attacks, such as noises, compression, and image quality enhancement processing. In this method, ArnoldCat map is used as a pre-processing on the host image, which increases the security and imperceptibility of embeddingwatermark bits with a strong gain factor. Moreover, two pseudo-noise strings with weak correlation are used as thesymbol of each 0 or 1 bit of the watermark, which increases the accuracy in detecting the state of watermark bits atextraction phase in comparison to using two random pseudo-noise strings. In this method, to increase the robustness andfurther imperceptibility of the embedding, the Arnold Cat mapped image is subjected to non-overlapping blocking, andthen the high frequency coefficients of the approximation sub-band of the FDCuT transform are used as the embeddinglocation for each block. Comparison of the proposed method with recent robust methods under the same experimentalconditions indicates the superiority of the proposed method.
Keywords:
Data hiding, Watermarking, Robustness, Curvelet transform, Arnold Cat map, Weak correlation noises.
1. Introduction
Hiding information in image has been widely used in re-cent years. The numerous applications of hiding informa-tion in today’s life have made this science be divided intosubcategories, based on the application. The two mainsubcategories of information hiding are watermarking andsteganography. A common important point in these sub-categories is the hiddenness of the message, watermark,data, or information. In steganography methods, the goalis to transfer the information through an image securelyand invisibly, so that embedding does not create tangiblechanges in the image and is not recognizable through ste-ganalysis methods that attempt to detect whether carryingthe message or not by an image [1–3].Today, with the growth of virtual communications andthe dramatic advance of the Internet, access to text, au-dio, image and video is provided to everyone, and pro-tecting these documents against the forgery, manipulation,and violation of property rights is a requirement of sucha space. Without losing the whole subject, using encryp-tion methods and digital signature, changes made in thedigital image can be found, however, this only works un-til the unintentional attacks, such as compression, imagequality processing, poor noise, etc., cause no change in theimage; since the digital signature accompanying the image ∗ Corresponding author
Email addresses: [email protected] (Seyyed Hossein Soleymani), [email protected] (Amir HosseinTaherinia), [email protected] (Amir Hossein Mohajerzadeh) will not be the same as what is extracted by the receiver.In this case, it can only be determined whether the imagehas changed or not, and the intentional or unintentionalattack cannot be determined.The watermarking can be divided based on the amountof information required to extract the watermark in thedestination into three blind, semi-blind, and non-blind cat-egories. In the blind watermarking, the main signal is notrequired during the extraction process, and only the keysare needed. In other words, in these methods, the unem-bedded original image is not needed to extract the water-mark, and only the watermarked image and a few sim-ple keys are needed [6, 11]. In semi-blind watermarking,in some cases, we need additional information to extractthe watermark. For example, in some SVD-based meth-ods, to extract the embedded watermark in the destina-tion additional information (such as eigenvectors of theoriginal image) is required [8, 12–14]. In the non-blindwatermarking, the original image is required to extractthe watermark. These methods are generally more robustthan blind watermarking methods, instead, are not verycommon and functional due to the need to send additionalinformation [15–17].In terms of embedding domain, the watermarking isdivided into two categories of spatial domain and trans-form domain. The spatial domain-based methods spreadthe watermark data in pixel values of the original imageand creates a very small change in image brightness. Thismethods have less computational complexity and do notrequire a specific transform. The spatial domain-based
Preprint submitted to Visual Communication Image Representation September 18, 2018 a r X i v : . [ c s . MM ] M a r ethods, although performs well in terms of impercep-tibility, operate poorly in terms of robustness to signalprocessing attacks such as image compression, low passfiltering and noises. The simplest method of this domainis embedding the watermark in the least significant bitsof image pixels [18, 19]. To provide simultaneous imper-ceptibility and robustness, the watermark is embedded inthe transform domain of cover image. In this method, co-efficients of transformed image are changed to embed thewatermark. The domain of the transform is also calledthe frequency domain; since the signal is changed from itsoriginal form and decomposed into frequency components.The most important and widely used methods in the fre-quency domain are the discrete cosine transform (DCT),the discrete wavelet transform (DWT), the integer wavelettransform (IWT) and other transforms of the X-Let fam-ily [20, 22, 23].In order to protect the property rights of an image, it isnecessary to insert the watermark in the image in a robustmanner that is resistant to unintentional attacks such asimage compression, adding noise, resizing, and even cut-ting some part of the image. In this paper, a blind water-marking based on Arnold Cat map method, a fast discretecurvelet transform (FDCuT), and a DCT transform is pro-posed which uses two random pseudo-noise with a low cor-relation as the symbol of the bits 0 and 1 of the watermark.This method has the high robustness to intentional andunintentional manipulation, such as intense noises, imagecompression, and image quality enhancements processing.The rest of the structure of this article is such that inSection 2, related works was investigated. In Section 3,the proposed method is described in detail. In sections 4and 5, the results of the experiments and conclusion arepresented, respectively.
2. Related Work
In this section, a number of robust watermarking methodscompared in the evaluation section of the proposed methodare briefly described and their main ideas are expressed.In [9], an LWT-based blind robust watermarking methodwas proposed that uses the quantization method of theLH3 sub-band coefficients for embedding. In this method,the coefficients in the LH3 sub-band are subjected to dis-turbance and then grouped into blocks. The coefficientsin each block are arranged, and then two values as thedifference between the two maximum and the difference ofthe two minimum coefficients are obtained. If the differ-ence between the two minimum coefficients is lower thanthe threshold, then the block is considered as an em-beddable block. Moreover, to embed in each embeddableblock, quantization of the maximum value of that block isused.In [10], a blind robust watermarking based on quantiza-tion through dither modulation has been proposed which,in addition to optimal robustness, maintains the visual quality of the image. In this method, three levels of dis-crete wavelet transform are performed on the host image,and then the LH3 and HL3 coefficients are selected andgrouped. In this method, the difference between the twominimum and maximum values in each group is calculatedand used in the quantization process.In [6], a robust blind watermarking method based onBCH error correction coding and the Spread spectrummethod is proposed. In this method, the second level ap-proximation sub-band of the discrete wavelet transformwas used as the embedding location of the watermark.In this method, the LL2 sub-band are divided into non-overlapping blocks and the high frequency coefficients ofeach block are selected for embedding the watermark. Inthis method, Spread Spectrum technique is used as embed-ding method. Moreover, the watermark bits are encodedby BCH error correction codding before embedding. Therobustness of this method against attacks, especially com-pression, is significant.In [8], a semi-blind watermarking method is proposedbased on the DWT transform and singular values decom-position (SVD). In this way, in order to increase security,the watermark is first encrypted with a public key andRSA algorithm. Then a DWT transform level is calcu-lated from the host image and the approximate sub-bandis selected for embedding. The encoded watermark infor-mation is embedded in the eigen-values of LL1 approxi-mation sub-band of cover image. The robustness and theimage quality of this watermarking method are high, how-ever, there is the point that it is a semi-blind method, andin order to extract the watermark, the right and left matri-ces (U, V) obtained from SVD decomposition of the hostimage are required, which is a weakness for this method.
3. Proposed method
The proposed algorithm involves the advantages of sev-eral methods such as Arnold Cat map, FDCuT transform,DCT transform, and two weak correlated noises. Eachmethod and using trend in the proposed method are pre-sented in sub-sections 3.1, 3.2, 3.3 and 3.4, respectively.The embedding and extraction way will be expressed insub-sections 3.5 and 3.6, respectively. The flowchart of theembedding operation of the proposed method is shown inFig. 1.
Arnold Cat map is a two-dimensional mapping, and whenapplied to a digital image, it changes the original loca-tion of the pixels randomly. Arnold Cat map is one ofthe widely used image processing transforms in the fieldof encryption and watermarking. This map is a simple,periodic, and reversible transform. The periodicy and re-versibility of a transform mean that if we apply a transformsuccessively to a given matrix, then the initial data will beobtain after a complete period. This map is defined as theequation 12 pproximation subband of FDCuT for each 64*64 block (One 21*21 pixel block) 64×64 Pixel .. Do reverse of DCT, FDCuT and Arnold Cat MapOriginal image (512×512) Arnold Cat Map with a Key 1 Divide the encrypted image into 64 blocks
High frequency coefficients of DCT selected for embedding Two groups of random bits with low correlation for representing zero(0) and one(1) bits of watermark
55 bits
Watermarked image (512×512) EmbeddingGenerate two groups of random bits with low correlation
55 bits
Key 2 DC0
Fig. 1.
Embedding diagram (cid:20) x (cid:48) y (cid:48) (cid:21) = (cid:20) ab ab + 1 (cid:21) (cid:20) xy (cid:21) mod N. (1)In equation 1, x, y ∈ { , , ..., N − } , and N is the size ofhost image. a and b are control parameters and increasethe security in determining the mapping periodicity. (cid:20) xy (cid:21) is the main location of image pixels and (cid:20) x (cid:48) y (cid:48) (cid:21) is the locationof the mapped pixels. This mapping does not change theintensity of the image and only image data are disturbed.After several repetitions, the relationship between adja-cent pixels is completely disturbed and the image looksdistorted and meaningless [4]. Using this mapping as apre-process in watermarking increases the security and re-duces the possibility of targeted attacks. In the proposedmethod, the original image is Arnold mapped by Key1(number of repetitions), and keys, and after disturbanceof the pixels are subjected to the other algorithm phases.In addition to the security advantage that Arnold mappingprovides, this mapping distributes the changes caused byembedding the watermark with a strong gain factor pa-rameter in the entire image, which is not visually recog-nizable. However, using a strong power parameter withoutusing Arnold mapping, the changes will be noticeable vi-sually. One of the multi-scale transforms is the curvelet transform,which works better in distinguishing edges and curves com-pared to the other transform, and is more accurate toapproximate and describe the dispersion and direction.Curvelet transform was first introduced on the basis of fil-tering the sub-bands and Ridgelet transform and is knownas the first type curvelet. Due to defects in the first typecurvelet, the second generation curvelet was presented basedon the filtering the bypass in the Fourier domain. Inthe second generation curvelet, it initially takes a two-dimensional Fourier transform from the image, and thenthe image is fragmented into a series of discrete regions bya window in the frequency domain [5]. Then, the data arewrapped around the origin, finally the two-dimensional in-verse Fourier transform is calculated on the wrapped datain order to calculate the curvelet coefficients.Two types of fast discrete curvelet implementations arethe Unequally Spaced Fast Fourier Transform USFFT-based curvelet and Wrapping-based curvelet. The firststep in curvelet transform is decomposition of the signalinto the sub-bands. These discrete transforms receive theCartesian arrays (two-dimensional image) as X [ k , k , ≤ k , k ≤ k as the input and create the coefficients as theequation 2. C D ( p, q, r ) = (cid:88) ≤ k ,k ≤ k X [ k , k ϕ Dp,q,r ( k , k . (2)3 ) b) Fig. 2. a) The host image. b) decomposed image through FDCuTmethod.
LF MF HF
Fig. 3.
LF, low frequency. MF, moderate frequency. HF, highfrequency. Left and top corner, DC0 coefficient.
Where ϕ Dp,q,r is the wave-form digital curvelet, and D rep-resents the Digital word. The steps of discrete Wrappingcurvelet transform briefly is as the following steps:1) Obtain Fourier coefficients ˆ X ( k , k
2) by applying FFT.2) Perform the following sub-steps for each j scale and i direction: • Obtain the multiplication of ˆ V p,q ˆ X ( k , k V p,q is the parabolic window. • Wrap the multiplication around the origin andobtain ˜
Xp, q ( k , k
2) = W ( ˆ V p,q ˆ X )( k , k ≤ k < p and 0 ≤ k < p . • Calculate the discrete coefficients by applyingthe inverse FFT transform on the wrapped date,where, C D ( p, q, r ) is obtained. Algorithm 1: function GetPseudoNoisesFunc: Gen-erate two pseudo random noise with low correlation
Data:
Seed , HF − count // Random generator seedand High Frequency coefficients count Result:
SequenceOne , SequenceZero // TwoPseudo Random Noise corresponding to 0and 1 bits of watermark using alphabet { -1, 0, 1 } . Set random generator seed to Seed ; SequenceOne = round (2 × ( rand (1 , HF − count ) − . SequenceZero = round (2 × ( rand (1 , HF − count ) − . while (( corr SequenceOne, SequenceZero ) > . && (( corr SequenceOne, SequenceZero ) < − . do SequenceOne = round (2 × ( rand (1 , HF − count ) − . SequenceZero = round (2 × ( rand (1 , HF − count ) − . Return
SequenceOne , SequenceZero ;In Fig. 2, the result of applying a wrap-based FD-CuT is provided for a 512 ×
512 image. The FDCut trans-form divides the input image into a 21 ×
21 approxima-tion sub-band, 4 moderate frequency sub-band with a 16-orientation parameter, and finally, a detail sub-band withthe same size of the original image. The approximationsub-band ( 21 ×
21 pixels) of image is presented in the cen-tral part of the Fig. 2-b. Medium frequency sub-bands anddetail sub-band are presented respectively in black andgray. In the proposed method, the result of Arnold Catmat is divided into 64 ×
64 non-overlapping blocks. Then,the FDCuT transform is applied on each block in order toget approximation sub-band. In the proposed method, ap-proximation sub-band of each block is used for embeddingjust one bits of watermark. The reason for choosing theapproximation sub-band for embedding the watermark isit’s robustness against watermarking attacks and its ap-propriate distribution of information in the whole image.
Discrete cosine transform (DCT) is a method that trans-forms the spatial domain signal to frequency coefficients.DCT is one of the most prominent linear transforms, whichis applicable in energy compression. The equation of dis-crete cosine transform is as the equation 3: C ( u, v ) = α ( u ) × α ( v ) × N − (cid:88) x =0 N − (cid:88) y =0 f ( x, y ) cos (cid:18) (2 x + 1) uπ N (cid:19) cos (cid:18) (2 y + 1) uπ N (cid:19) ;(3)4 lgorithm 2: Embedding algorithm
Input:
W atermark (64 bit),
Img (original image with size 512 × ey , K ey , a , b , Gain
Output: W − img (watermarked image) [ SequenceOne , SequenceZero ] = GetPseudoNoisesFunc(
Key );// Generate two pseudo random sequence withlow correlation using Alg. 1. ImgM apped = ArnoldFunc(
Img , Key , a , b );//Apply Arnold Cat Map on the Img with key
Key , a and b . ImgDivided = DivideFunc(
ImgM apped );//Divide
ImgM apped into 64 non-overlapping blocks of size 64 × counter =1; while counter ≤ do BlkApprox = FDCuTFunc(
ImgDivided ( counter ));// Applying FDCuT transform on each block of ImgDivided ( counter ) and get it’s approximation sub-band (21 ×
21 pixel for each block). BlkDCT = DCT2Func(
BlkApprox );// Apply 2D-DCT transform on each
BlkApprox . if W atermark ( counter ) == 0 then AugmenteN oiseZero = Gain ∗ SequenceZero ; BlkDCT = ReplaceNoiseFunc(
AugmentedN oiseZero );// Replace HF coefficients of
BlkDCT with
AugmentedN oiseZero . if W atermark ( counter ) == 1 then AugmentedN oiseOne = Gain ∗ P equenceOne ; BlkDCT = ReplaceNoiseFunc(
AugmentedN oiseOne );// Replace HF coefficients (Fig. 3) of
BlkDCT with
AugmentedN oiseOne . BlkApprox = InverseDCT2Func(
BlkDCT ); ImgDivided ( counter ) = InverseFDCuTFunc( BlkApprox ); counter = counter + 1; ImgM apped = AccumulateBlocksFunc(
ImgDivided );// Accumulation of embedded blocks to get a 512 × W − img = ArnoldFunc( ImgM apped , period - Key , a , b );// Apply Arnold Cat Map with key ( period - Key ). return W − img ;where α ( u ) , α ( v ) = (cid:113) N , u, v = 0; (cid:113) N , u, v = 1 , , · · · , N − . (4)The low, moderate, and high frequencies are shown inFig. 3, respectively, with LF, MF, and HF. Embeddinginformation in LF coefficients provides the highest robust-ness against attacks such as JPEG compression. However,this will create the most destructive effect on the image.The embedding at the HF frequency has a relatively lowrobustness, but instead has a slight damage to the im-age. In this paper, robustness is provided because of thefact that the watermark information is embedded into theapproximation sub-band calculated by FDCuT transform.However, in order to reduce the degradation effect of theembedding, the HF frequency coefficients of approximatesub-band is used to embed a bit of the watermark in eachblock. In the proposed method, two random pseudo-noise stringsusing the alphabet 1, 0, -1 and to the number of coefficientsin the HF frequency of each block (Fig. 3), are constructedas the symbol of the bit 0 and 1. Correlation of this two strings must be weak. The advantage of a weak corre-lation between the two randomly generated pseudo-noisestrings shows itself at the extraction stage, since if thecorrelation not be weak, then due to the damage causedby the watermarking attacks on the image, the correlationof the two randomly embedded pseudo-noise strings maybe close together and may disturb detection of 0 or 1 ofthe watermark. Therefore, as far as possible, correlationof two randomly generated pseudo-noise strings should beweak. The algorithm for producing two random pseudo-noise strings is as the Alg. 1. In the Alg. 1, the Seed inputis used to generate the same random values at the embed-ding and extraction stage. HF − count input representsthe number of high-frequency coefficients of each block,to which two random pseudo-noise strings must be gen-erated. Corr A and ¯ B are the mean of the two A and B matrices. corr ( A, B ) = (cid:80) m (cid:80) n ( A mn − ¯ A )( B mn − ¯ B ) (cid:113)(cid:0)(cid:80) m (cid:80) n ( A mn − ¯ A ) (cid:1) (cid:0)(cid:80) m (cid:80) n ( B mn − ¯ B ) (cid:1) . (5)5 lgorithm 3: Extracting algorithm
Input: W − Img (watermarked image ( Or attacked image) with size 512 × ey , K ey , a , b , Gain
Output:
W atermark [ SequenceOne , SequenceZero ] = GetPseudoNoisesFunc(
Key );// Generate two pseudo random sequence withlow correlation using Alg. 1. W − ImgM apped = ArnoldFunc( W − Img , Key , a , b );//Apply Arnold Cat Map on the W − Img with key
Key . W − ImgDivided = DivideFunc( W − ImgM apped );//Divide W I mgM apped into 64 non-overlapping blocks of size64 ×
64 pixel. counter =1; while counter ≤ do BlkApprox = FDCuTFunc( W − ImgDivided ( counter ));// Applying FDCuT transform on each block of W − ImgDivided ( counter ) and get it’s approximation sub-band (21 ×
21 pixel for each block). BlkDCT = DCT2Func(
BlkApprox );// Apply 2D-DCT transform on each
BlkApprox . HF Coef f icients = SelectHFFunc(
BlkDCT );// Select high frequency coefficients of
BlkDCT . AugmentedN oiseZero = Gain ∗ SequenceZero ; AugmentedN oiseOne = Gain ∗ SequenceOne ; Corr − AugmentedN oiseZero , HF Coef f icients ); Corr − AugmentedN oiseOne , HF Coef f icients ); if Corr − ≤ Corr − then W atermark ( counter ) = 0; if Corr − < Corr − then W atermark ( counter ) = 1; counter = counter + 1; return W atermark ; As stated in the previous sub-sections, the final locationof the embedding watermark is the high-frequency coeffi-cients generated from each 21 ×
21 block, as shown in Fig. 3.The value of these coefficients is close to zero, and chang-ing them does not cause much side effects in the originalimage. In the proposed method, in each 21 ×
21 block, onlyone bit of watermark is embedded. Therefore, based on the0 or 1 bit of the watermark, one of the two random pseudo-noise strings must be embedded. The embedding methodused in this paper is replacement method. In other words,the result of the multiplication of random pseudo-noisestrings in a relatively large gain factor, the random am-plified pseudo-noise strings are obtained and then one ofthe pseudo-noise strings is replaced in the high-frequencycoefficients of each block proportional to 0 or 1 bit of thewatermark. The gain factor used in this embedding ismuch larger than the initial coefficient value and causes achange in the quality of the embedding image. However,as a result of using Arnold Cat map to create a disturbancein the pixel location, the changes from the random ampli-fied pseudo-noise string will not be visually recognizable.The embedding algorithm of the 64-bit watermark in thehost image is shown in Alg. 2.
After embedding the watermark in the host image, theembedded image may be intentionally or unintentionallyattacked, and the extracted watermark is not exactly the same as the embedded watermark. The main parts in theextraction phase are similar to those in the watermarkembedding steps. This means that at first the ArnoldCat map must be applied on the image by the keys sim-ilar to the embedding stage, and then divided into non-overlapping 64 ×
64 blocks. Then, FDCuT and DCT trans-forms should be applied to each block to calculate the HFcoefficients of each block. An important stage to be fol-lowed is to decide on the bit embedded in the desired block.To do this, the correlation between the calculated HF co-efficients with the two randomly amplified pseudo-noisestrings is calculated for both of the 0 and 1 bit of the wa-termark. If the correlation of the HF coefficients with theamplified random pseudo-noise string related to the bit 0 isgreater than the amplified random pseudo-noise string ofbit 1, it indicates that the bit 0 was embedded, otherwiseit indicates that the bit 1 was embedded. The watermarkextraction algorithm is shown in algorithm 3.
4. Experimental result
In these experiments, 40 standard images of the USC-SIPIimage database were used [ ? ]. Many of these images suchas Lena, Zelda, Baboon, Camera Man, Pepper, etc. havebeen used repeatedly in watermarking and steganographyas a test image. To create different attacks, the Matlabsoftware was used to evaluate the proposed method andattempts were made to provide the more detailed expla-nations of the attack on the plots. The criterion referred6 ) A) C) Fig. 4. a) Original image. b) Watermarked image without Arnold Cat map (PSNR = 40.06 dB). c) Watermarked image using Arnold Catmap (PSNR = 40.13 dB). in this paper and most articles is the peak signal-to-noiseratio (PSNR). This criterion indicates the amount of noiseadded to the image by the watermark insertion in it. Itis also used in image recovery techniques to evaluate thequality of the extracted image. Although this parameterdoes not exactly imply the invisibility of the visual water-mark in the image, it provides a proper algebraic relation-ship for the optimal amount of changes in the image. Thedefinition of this evaluating criterion is presented as theequation 6.PSNR( f, f w ) = 10 log (cid:34) max ∀ ( m,n ) f ( m, n ) N f (cid:80) ∀ ( m,n ) ( f w ( m, n ) − f ( m, n )) (cid:35) . (6)Equation 6, represents the value of the PSNR in deci-bel unit. In this equation, f is the original image, f w thewatermarked image, ( m, n ) the index of the images pixels,and N f is the number of pixels in each f and f w images.The larger values of this criterion shows the impercepti-bility of watermarking method. Regularly, the values ofabout 40 dB are acceptable values for this criterion in im-age watermarking 6. One of the most commonly used criteria for evaluatingthe extracted watermark is normalized cross-correlation(NC). The definition of this parameter is as the equation 7. N C = (cid:32) (cid:80) N w j =1 W ( i, j ) × ´ W ( i, j ) (cid:80) N w i =1 W ( i, j ) (cid:33) . (7)In equation 7, W and ´ W are respectively the embeddedwatermark and extracted watermark, and N w is the sizeof the watermark bits. The value of the watermark isassumed within {− , } , and the NC value will be 1 ifthere is no error in the extracted watermark. In fact, thecloser this criterion to 1, the watermarking method is morerobust [7].The Gain factor parameter in this paper is 125 since,with this Gain factor, the average visual quality of thetested images is above 40 dB. As it is observed in Fig. 4-b,with such a Gain factor, there are noticeable changes in thewatermarked image. However, in Fig. 4-c, where ArnoldCat map was used, the changes made in the watermarkedimage are not visibly observable and tangible. In fact,Arnold Cat map distributes the changes in the entire ofimage.7n Fig. 5, the output of the proposed method is shownon the 40 selected images in the presence of common imageprocessing attacks. Furthermore, considering the fact thatthe standard Lena image is important from the standpointof watermarking articles, the proposed method robustnessto this image is shown separately into the plots. As itis observed, the proposed method has a high resistanceto all kinds of noise, resizing and JPEG2000 compression.It should be noted that the compression rate used in theJPEG2000 attack indicates that how much the compressedimage size is smaller than the original image. For exam-ple, the compression rate of 10 means that the compressedimage will be a tenth of the original image size. Basedon the results of Figure 5, it is concluded that the pro-posed method is robust against JPEG compression with aquality factor of 10, however, for JPEG compression witha quality factor below 10, the watermark is severely de-graded. Additionally, the proposed method is capable ofhandling the resizing attack to the image to a quarter ofthe original size easily, however, if the image size is lessthan a quarter of the original size, the watermark will bedegraded and cannot be extracted.The comparison of the proposed method results withfour robust methods presented in recent years is shownin Tables 1 and 2. For this comparison, the same imagesare used. Moreover, the Gain factor parameter is set tomatch the quality of the embedded image obtained by theproposed method and the compared methods. In this com-parison, it was attempted to evaluate the same attacks onthe watermarked images. As it can be seen, the proposedmethod in most cases has more robustness to attacks thanthe compared methods, however, the robustness of the pro-posed method against JPEG compression attack is at thesame level of the compared methods or less.
5. Conclusion and future work
In this paper, a robust and blind image watermarking tech-nique was proposed that has the ability to extract embed-ded watermark after strong attacks such as intense noise,image compression, and image quality enhancements pro-cessing. In this method, two pseudo-noise strings withweak correlation are constructed as the symbol of each bit0 and 1 of the watermark. The embedding location in thismethod is the high frequency coefficients of the approxi-mation sub-band of FDCuT transform. Arnold Cat mapis used to enhance the security and imperceptibility of em-bedding. Using Arnold Cat map as a preprocessing in thismethod provides the possibility of amplifying two pseudo-noise strings as possible, thereby enhancing the robustnessof the proposed method. In order to more accurately eval-uate and compare the proposed method with recent ro-bust methods, it was tried to perform the comparison inthe same test conditions, such as the same image and thesame embedded image quality. Comparison of the pro-posed method with recent robust methods indicates thehigh robustness of the proposed method. As the future work, the proposed method can be eval-uated on colorful images, and different sub-bands and fea-tures of the colorful images can be used to increase therobustness of the proposed method. Some methods suchas SIFT and SURF can also be used to find the key pointsand embed the watermark in those locations to make theproposed method robust against rotation attacks.
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Robustness of the proposed method against a number of common image processing attacks. Gain factor parameter is set 125 andthe average quality of embedded images is more than 40 dB. Fig. 5a shows comparison between gain factor and PSNR for 4 standardimages. Fig. 5b shows the NC in case of JPEG compression over Lena and 40 different watermarked images. Fig. 5c shows the NC in case ofJPEG2000 compression over Lena watermarked image. Fig. 5d shows the NC in case of Gaussian noise over Lena and 40 differentwatermarked images. Fig. 5e shows the NC in case of Salt & Pepper noise over Lena and 40 different watermarked images. Fig. 5f shows theNC in case of Speckle noise over Lena and 40 different watermarked images.Fig. 5g shows the NC in case of Average filter over Lena and 40different watermarked images. Fig. 5h shows the NC in case of Gaussian filter over Lena and 40 different watermarked images. Fig. 5i showsthe NC in case of Histogram Equalization over Lena and 40 different watermarked images. Fig. 5j shows the NC in case of Cropping Lenaand 40 different watermarked images. Fig. 5k shows the NC in case of Scaling over Lena and 40 different watermarked images. Table 1
Comparison of proposed method with [6, 8]
Lena image Lena image A tt a c k P r o p o s e d m e t h o d ( P S N R = . ) [ ] ( P S N R = . ) A tt a c k P r o p o s e d m e t h o d ( P S N R = . ) [ ] ( P S N R = . ) JPEG QF=10 0.71
Median[3 × × JPEG QF=10 0.53
Scaling 1/4
Cropping 10%
Gaussian Noise 0.01 × Salt & Pepper noise 0.1 × × JPEG2000 QF=20 × Median[5 × Median[7 ×
7] 0.62
Gaussian noise 0.10
Table 2
Comparison of proposed method with [9, 10]
Lena image Lena image A tt a c k P r o p o s e d m e t h o d ( P S N R = . ) [ ] ( P S N R = . ) A tt a c k P r o p o s e d m e t h o d ( P S N R = . ) [ ] ( P S N R = . ) JPEG QF=10 0.71
JPEG QF=10 0.62
JPEG QF=20
JPEG QF=40 0.96
JPEG QF=50
JPEG QF=50
JPEG QF=60
Scaling 1/4 × Median[5 ×
5] 0.81
Average[3 × × × Histogram Eq × × × ×1.0