Abstract:
This invention is a new approach for the image watermarking in the wavelet transform domain based on sequency of the host and watermark image. For each sub-band a first transform level of the host image is thresholded and binarized. Sequencies of thresholded and binarized data host image are compared with sequencies of the discrete wavelet transformed watermark image to form a watermarking sequency mask. The watermarked wavelet domain data is formed by combining data elements of the discrete wavelet transformed host image with corresponding data elements of the wavelet transformed watermark image as filtered by the watermarking mask. A reverse process can extract the watermark with a high degree of accuracy even after attack upon the watermarked host image.

Description:
CLAIM OF PRIORITY  
       [0001]     This application claims priority under 35 U.S.C. 119(e)(1) to U.S. Provisional Application No. 60/752,583 filed Dec. 21, 2005. 
     
    
     TECHNICAL FIELD OF THE INVENTION  
       [0002]     The technical field of this invention is image watermarking.  
       BACKGROUND OF THE INVENTION  
       [0003]     Watermarking of the multimedia contents is of prime importance for claiming and establishing ownership. An image watermark is data added to the image data. This added data is included in such a way that the image quality is not degraded. Later extraction tools may be applied to the image data to recover the watermark. The recovered watermark is evidence of the original ownership claim to the image.  
         [0004]     Most of watermarking techniques are vulnerable to the attacks or are poorly extracted after the attacks. Images are very common in multimedia contents and need a robust watermarking scheme that can withstand the attacks and at the same time have a recognizable extracted watermark.  
         [0005]     In recent years, image watermarking has been a very active area of research and industry. Various techniques have been used for image watermarking in the spatial domain, the transform domain and the spread spectrum domain.  
       SUMMARY OF THE INVENTION  
       [0006]     This invention is a new sequency and wavelet transform based watermarking technique. The inventive technique is more robust in response to attacks like JPEG, Median filtering and blurring. The inventive technique provides for good extraction of the watermark image. The inventive technique performs very well in terms of subjective (perceptual) and objective (in terms of PSNR) image quality measures.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0007]     These and other aspects of this invention are illustrated in the drawings, in which:  
         [0008]      FIG. 1  illustrates the process of watermarking an image and extracting the watermark from an image subject to attack;  
         [0009]      FIG. 2  illustrates in schematic form one level of wavelet decomposition (Prior Art);  
         [0010]      FIG. 3  illustrates transformed wavelet data divided into four quadrant sub-bands (Prior Art);  
         [0011]      FIG. 4  illustrates further division of a quadrant into smaller bands (Prior Art);  
         [0012]      FIG. 5  illustrates a third level division of a subquadrant into yet smaller bands (Prior Art);  
         [0013]      FIG. 6  schematically illustrates the embedding of a watermark in the wavelet and sequency transformed domain of a host image;  
         [0014]      FIG. 7  schematically illustrates extracting the watermark from the watermarked host image;  
         [0015]      FIG. 8A  is an example 256 by 256 gray scale host image and  FIG. 8B  is an example 64 by 64 binary watermark image;  
         [0016]      FIG. 9  illustrates the corresponding watermarked image in accordance with the examples of  FIGS. 7A and 7B ;  
         [0017]      FIGS. 10A  to  10 D illustrate a comparison of the original watermark image with watermark images extracted from watermarked host images subject to JPEG attack of varying quality factors;  
         [0018]      FIG. 11  illustrates an example extracted watermark resulting from a median filtering attack of a watermarked host image;  
         [0019]      FIGS. 12A and 13B  illustrate the example host image and the corresponding extracted watermark image subject to for a blurred image attack; and  
         [0020]      FIGS. 13A and 13B  illustrate the example host image and the corresponding extracted watermark image subject a contrast enhanced host image attack. 
     
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS  
       [0021]     This invention is a new image watermarking technique based on the sequency of the host and watermark images in the wavelet transform domain. Sub-bands of the host image are thresholded and converted to binary format. The row sequency of the sub-bands of these binary sub-bands of the host image represents the threshold crossing (zero crossings) of the image pixels in the wavelet transform domain. Similarly in the binary discrete wavelet transform (BDWT) domain where the watermark image is being de-correlated, the row sequency of each sub-band represents the zero crossing of the watermark image pixels.  
         [0022]     This invention uses these sequencies of host and watermark images to devise a new watermarking technique. In the transform domain, the sequency of each row of respective sub-bands is used to determine a sequency dependent mask. This mask facilitates better embedding of the watermark in the appropriate sequency components in the respective sub-bands.  
         [0023]     This invention is the first use of the sequencies of host and watermark images to devise a new robust image watermarking scheme. This invention is also the first to embed the watermark in the LL band (low frequency sub-band after discrete wavelet transform in 2-dimensions) of the host image and maintain the perceptual signal to noise ration (PSNR) and the perceptual quality of the watermarked host image.  
         [0024]     This invention uses an Adaptive Parabolic Gain adjustment technique that enables effective embedding into the sub-bands of the host image.  
         [0025]     This invention includes a watermark extraction algorithm. This watermark extraction algorithm takes into account the impact of attacks on the statistics of the watermarked image such as autocorrelation change of the host due to attack and embedding of the watermark. Experiments on the new sequency based watermarking algorithm show its robustness to attacks and better normalized correlation (NC). Normalized Correlation is an objective measure and defined as:  
             NC   =         ∑   i             ⁢           ⁢       ∑   j             ⁢     (       W   ⁡     (     i   ,   j     )       ⁢       W   ′     ⁡     (     i   ,   j     )         )             ∑   i             ⁢           ⁢       ∑   j             ⁢       (     W   ⁡     (     i   ,   j     )       )     2                   (   1   )             
 
 Where: W(i,j) is original watermark image; and W′(i,j) is the extracted watermark image. 
 
         [0026]     The performance results of this invention are clearly superior to exemplary prior art algorithms. This invention is more robust to JPEG attacks in its class of algorithms and maintains the perceptual quality of the watermarked host image.  
         [0027]      FIG. 1  illustrates the general watermarking problem. Watermark function  101  receives a host image H and a watermark W. Watermark function  101  embeds the watermark W into the host image H according to the function Φ(H,W,R). R is the autocorrelation of the sub-band pixels of the host image. Watermark function  101  generates a watermarked image H W  and a set of side information keys K. Keys K are used in later extraction of the watermark. Attack function  102  models the possible attacks on the watermark image H W  according to the function A(H{circumflex over ( W )}|H W ). This attack results in an image {tilde over (H)}. Watermark extraction function  103  extracts the watermark image from the attacked image {tilde over (H)} via function Ψ(H{circumflex over ( W )},K,R). Watermark extraction function  103  uses keys K which are available only to the owner of the original image and not to the attacker. The result is extracted watermark {tilde over (W)}.  
         [0028]     In this description: host image H is a matrix of size N by N where each element belongs to the set of integers Z of size N; watermark image W is a matrix of size N/4 by N/4 where each element belongs to the set of integers Z of size 2 containing elements 0 and 1; R is a correlation matrix of host image pixels of size N by N where each element belongs to the set of integers Z of size N; key vector K includes keys K 1 , K 2  and K 3 ; K 1  is a subset of Z N/8 ; K 2  is a subset of Z; and K 3  is a subset of R 4 , which is a set of real numbers or cardinality four.  
         [0029]     This application uses the following notation for wavelet transform segments. X_YZ n : where X denotes H for the host image or W for the watermark image; YZ denotes one of the sub-bands selected from LL, HL, LH or HH; and the subscript n denotes the sub-band number. Thus H_LH 3  denotes the level 3 LH sub-band of the host image. These notations will be more fully described in FIGS.  3  to  5 . The subscript w indicates the watermark image and the subscript h indicates the host image. Thus H W  is watermarked host image and Ĥ w  is watermarked host image after the attack.  
         [0030]     Wavelet encoding of image data transforms the image from a pixel spatial domain into a mixed frequency and spatial domain. In the case of image data the wavelet transformation includes two dimensional coefficients of frequency and scale.  FIG. 2  illustrates the basic technique of wavelet image transformation. Wavelet coefficients of the image are computed using one dimensional wavelet filters using a Daubechies filter for the host image and a binary wavelet filter for the binary watermark image. This decomposition provides sub-images corresponding to different resolution levels and orientations. The reconstruction process is the complementary process of this decomposition process and done by reversing the steps of the decomposition process. The two dimensional array of pixels is analyzed X and Y directions and a set for transformed data that can be plotted in respective X and Y frequency.  
         [0031]      FIG. 2  illustrates one stage of wavelet decomposition. The input is image matrix  200 . Note that this input could be the original image for a first stage decomposition or the result of a prior stage of wavelet decomposition. The rows of this image matrix are low pass filtered in low pass filter  210  and high pass filtered in high pass filter  220 . The low pass result from low pass filter  210  is subjected to a column down sample by a factor of 2 in column down sampler  215 . Similarly, the low pass result from low pass filter  220  is subjected to a column down sample by a factor of 2 in column down sampler  225 . Each of these down sampled outputs is similarly processed. Low pass filter  230  low pass filters the output of column down sampler  215 . The low pass result from low pass filter  230  is subjected to a row down sample by a factor of 2 in row down sampler  235 . The row down sampled result of row down sampler  235  is the LL output sub-band. Low pass filter  240  low pass filters the output of column down sampler  215 . The low pass result from low pass filter  240  is subjected to a row down sample by a factor of 2 in row down sampler  245 . The row down sampled result row down sampler  245  is the LH output sub-band. Low pass filter  250  low pass filters the output of column down sampler  225 . The low pass result from low pass filter  250  is subjected to a row down sample by a factor of 2 in row down sampler  255 . The row down sampled result row down sampler  255  is the HL output sub-band. Low pass filter  260  low pass filters the output of column down sampler  225 . The low pass result from low pass filter  260  is subjected to a row down sample by a factor of 2 in row down sampler  265 . The row down sampled result row down sampler  265  is the HH output sub-band. Low pass filters  210 ,  230  and  250  and high pass filters  220 ,  240  and  260  are the one dimensional wavelet filters noted above.  
         [0032]     Each of FIGS.  3  to  5  represents one stage in a multi-scale sub-band decomposition of an image.  FIG. 3  illustrates transformed data  300  with the upper left corner the origin of the X and Y frequency coordinates. This transformed data is divided into four quadrant sub-bands. Quadrant  301  includes low frequency X data and low frequency Y data denoted as LL 1 . Quadrant  302  includes low frequency X data and high frequency Y data denoted LH 1 . Quadrant  303  includes high frequency X data and low frequency Y data denoted HL 1 . Quadrant  304  includes high frequency X data and high frequency Y data denoted HH 1 .  
         [0033]     Organizing the image data in this fashion with a wavelet transform permits exploitation of the image characteristics for data analysis and manipulation. It is found that most of the energy of the data is located in the low frequency bands. The image energy spectrum generally decays with increasing frequency. The high frequency data contributes primarily to image sharpness. When describing the contribution of the low frequency components the frequency specification is most important. The energy distribution of the image data may be further exploited by dividing quadrant  301  LL 1  into smaller bands.  FIG. 4  illustrates this division. Quadrant  301  is divided into subquadrant  311  denoted LL 2 , subquadrant  312  denoted LH 2 , subquadrant  313  denoted HL 2  and subquadrant  314  denoted HH 2 . As before, most of the energy of quadrant  301  is found in subquadrant  311 .  FIG. 5  illustrates a third level division of subquadrant  311  into subquadrant  321  denoted LL 3 , subquadrant  322  denoted LH 3 , subquadrant  323  denoted HL 3  and subquadrant  324  denoted HH 3 .  
         [0034]     For an n-level decomposition of the image, the lower levels of decomposition correspond to higher frequency sub-bands. Level one represents the finest level of resolution. The n-th level decomposition represents the coarsest resolution. Moving from higher levels of decomposition to lower levels corresponding to moving from lower resolution to higher resolution, the energy content generally decreases. If the energy content of level of decomposition is low, then the energy content of lower levels of decomposition for corresponding spatial areas will generally be smaller. There are spatial similarities across sub-bands.  
         [0035]     This invention uses the sequencies of host and watermark images to devise a new watermarking scheme. In the wavelet transform domain, the sequency of each row of respective sub-bands is used to decide a sequency dependent mask. This mask facilitates better embedding of the watermark in the appropriate sequency components in the respective sub-bands.  
         [0036]     In this invention the sub-band LL 1  of the watermark is embedded in the LL 1  band of the host image. The perceptual signal to noise ratio (PSNR) of the host watermarked image is still within acceptable limits. Experimental results of the new sequency watermarking algorithm show robustness to attacks and better NC.  
         [0037]     This invention uses the sequencies of the binary image for the first time. Since the sequency is defined as the number of zero crossing of the binary data and represents the zero crossings of the binary sequence, it is a very effective way of exploring and embedding the watermark in the respective sequency indexed sub-bands of the host image in the wavelet transformed domain.  
         [0038]      FIG. 6  schematically illustrates an example  400  of the watermarking of this invention. Host image  401  is wavelet transformed using discrete wavelet transform (DWT) into wavelet transformed host image  402 . This example uses a Daubechies discrete wavelet transform into three level wavelet sub-bands LL 3 , LH 3 , HL 3 , HH 3 , LH 2 , HL 2 , HH 1 , LH 1 , HL 1  and HH 1  such as illustrated in  FIG. 5 . A binary watermark image  411  is transformed using binary discrete wavelet transform (BDWT) into wavelet transformed watermark image  412 . In this example the binary watermark image is transformed into one level sub-bands LL 1 , LH 1 , HL 1  and HH 1  such as illustrated in  FIG. 3 . In this example host image  401  has dimensions N by N pixels and binary watermark image has dimension N/4 by N/4 pixels.  
         [0039]      FIG. 6  illustrates details of process  400  of embedding the W_LL 1  sub-band into the H_LL 3  sub-band. The embedding of other sub-bands of the watermark image into respective host image sub-bands is similar. In particular the W_LH 1 , W_HL 1  W_HH 1  sub-bands are embedded into respective H_LH 3 , H_HL 3  and H_HH 3 .  
         [0040]     Process  400  next pseudo randomizes (prand) the rows of W_LL 1  ( 421 ) as shown in equation (2). 
 
 P   rand   :W   —   LL   1   →{tilde over (W)}   13    LL   1   (2)
 
 The seed used in this pseudo randomization generates the key K 2 . 
 
         [0041]     The next step in process  400  is binarization of sub-band H_LL 3  ( 422 ). This involves thresholding the gray scale image. Next process  400  calculates the row sequencies S h  ( 423 ) which are the number of crossings over a threshold (zero crossing) of H_LL 3  according to equation (3):  
               S   h     =     {             S   h     ⁡     (   i   )       ∈     Z   i       ;     i   =   1       ,     …   ⁢           ⁢     N     8   ⁢                   }             (   3   )             
 
 Similarly process  400  calculates the row sequencies S w  ( 424 ) of the binary W_LL 1  according to equation (4):  
               S   w     =     {             S   w     ⁡     (   i   )       ∈     Z   i       ;     i   =   1       ,     …   ⁢           ⁢     N     8   ⁢                   }             (   4   )             
 
 These sequencies S h  and S w  are not unique so first best match is selected. The selected sequency of the watermark image row is excluded in subsequent iterations. 
 
         [0042]     Embedding mask generation  425  sets an embedding mask function ƒ for sub-band H_LL 3  given by:  
                 f     LL   3       =     {       f   ⁡     (   1   )       =     (     j   ⁢     :     ⁢           ⁢   min   ⁢              S   h     ⁡     (   i   )       -       S   w     ⁡     (   j   )                }       }       ⁢     
     ⁢         ∀     i   ⁢           ⁢   and   ⁢           ⁢   j       =   1     ,   …   ⁢           ,       N     8   ⁢               ⁢           ⁢   where   ⁢           ⁢   i     ,     j   ∈     {     1   ,   …   ⁢           ,     N     8   ⁢                 }                 (   5   )             
 
 where: |X|is the Euclidian norm distance measure. The embedding masking function ƒ LL     3   , generates key K 1  for the sub-band LL 3 . Embedding mask generator  425  performs the transform:
 
ƒ LL     3     :{tilde over (W)}   —   LL   1 ( i,j ) →{tilde over (W)}   —   LL   1 (ƒ LL     3   ( i ), j )  (6)
 
         [0043]     Watermark embedding algorithm  430  operates for W_LL 1  as function Ψ(H,W,R) noted in conjunction with  FIG. 1  as follows:
 
 Ĥ   —   LL   3 ( i,j ) =H   —   LL   3 ( i,j )+α LL     3     *S ( H   —   R   LL     3   ( i,j ) *{tilde over (W)}   —   LL   3 (ƒ LL     3   ( i ), j )  (7)
 
 where: α LL     3    is a constant watermark strength given by:  
                   α   =       [       α     LL   3       ,     α     LH   3       ,     α     HL   3       ,     α     HH   3         ]     T                   =       [     2   ,   1   ,   1   ,   1     ]     T       ;                 (   8   )             
 
 with [x] T  the transpose of a column vector x;
 
 S ( H   —   R   LL     3   ( i,j )=(2 *√{square root over (K 3(LL     3     ) *abs(H — R LL     3   (i,j)))}+   G   LL     3   ( i,j ),  (9)
 
 which is a parabolic function of H_R LL     3   (i,j); abs(x) is the absolute value of x;
 
 G   LL     3   ( i,j )={2*√{square root over (max( H   —   R   LL     3   ( i,j ) *K   3(LL     3     ) )}+ε}  (10)
 
 which is a maximum weight factor of embedding with strength S which is function of H_R LL     3   (i,j); H_R LL     3   (i,j) is the autocorrelation of the pixel (i,j) of the wavelet transformed host image sub-band H_LL 3 ; abs(x) is absolute value of x; ε is a constant generally equal to 5; the value of K 3(LL     3     )  is given by:
 
 K   3   =[K   3(LL     3     )   ,K   3(LH     3     )   ,K   3(HL     3     )   ,K   3(HH     3     ) ] T ;  ( 11 )
 
=[ 20 ,  10 ,  10 ,  10 ] T 
 
 Partially watermarked wavelet domain image  435  is the result. 
 
         [0044]     The watermarking process proceeds to embed sub-bands W_LH 1 , W_HL 1  and W_HH 1  of the watermark image into respective sub-bands H_LH 3 , H_HL 3  and H_HH 3  of the host image. Following these watermarking steps results in watermarked wavelet domain image  440 . Performing an inverse Discrete Wavelet Transform (IDWT) on watermarked wavelet domain image  440  results in watermarked image  450 .  
         [0045]      FIG. 7  illustrates process  500  extracting the watermark from watermarked host image  450 . Original host image  401  is possibly damaged due to attack  102  illustrated in  FIG. 1 . Process  500  begins with a discrete wavelet transform (DWT) of original host image  401  yielding wavelet transformed host image  402 . This example uses a Daubechies discrete wavelet transform into three level wavelet sub-bands LL 3 , LH 3 , HL 3 , HH 3 , LH 2 , HL 2 , HH 1 , LH 1 , HL 1  and HH 1  such as illustrated in  FIG. 5 . Process  500  also discrete wavelet transforms (DWT) the watermarked host image  450  yielding wavelet transformed watermarked host image  502 . This example also uses a Daubechies discrete wavelet transform into three level wavelet sub-bands LL 3 , LH 3 , HL 3 , HH 3 , LH 2 , HL 2 , HH 1 , LH 1 , HL 1  and HH 1  such as illustrated in  FIG. 5 .  
         [0046]      FIG. 7  illustrates details of process  500  of watermark extraction operating on the H_LL 3  sub-band of wavelet transformed host image  502  and the Ĥ_LL 3  sub-band of wavelet transformed watermarked host image  502  yielding the Ŵ_LL 1 , sub-band of the extracted watermark image. The extraction of other sub-bands of the watermark image is similar.  
         [0047]     Process  510  calculates the weight factor Ŝ from the wavelet transformed watermarked host image  502  and key K 3(LL     3     ) . This calculation is as follows: 
 
 Ŝ ( Ĥ   —   R   LL     3   ( i,j )=(2 *√{square root over (K 3(LL     3     ) *abs(Ĥ   —   R   LL     3   ( i,j )))}+ Ĝ   LL     3   ( i,j ),  (12)
 
 where:
 
 Ĝ   LL     3   ( i,j )={2*√{square root over (max( Ĥ   —   R   LL     3   ( i,j ) *K   3(LL     3     ) )}+ε}  (13)
 
 Ĥ_R LL     3   (i,j) is the autocorrelation of the pixel(i,j) of the wavelet transformed host image sub-band Ĥ_LL 3 . 
 
         [0048]     Process  510  then models the effect of the attacks on the watermarked host image and decides threshold values in the extraction as follows:
 
 ΔĤ   —   R   LL     s   ( i,j ) =Ĥ   —   R   LL     s   ( i,j ) *H   —   R   LL     s   ( i,j )  (14)
 
 Process  510  performs the inverse of equation (7) to obtain {tilde over (W)}_LL 3 (ƒ LL     3   (i),j). This process uses the following thresholds:
 
T 1 =0.75 and T 2 =1.25
 
 M   LL   3 ( i,j )=( T   1 +0.75*Δ Ĥ   —   R   LL     3   ( i,j ))/2
 
 N   LL     3   ( i,j )=(5* T   2 +0.75* ΔĤ   —   R   LL     3   ( i,j ))/2; and  (15)
 
 R   LL     3   ( i,j )=( T   1 −0.75* ΔĤ   —   R   LL     3   ( i,j ))/2
 
 calculates an intermediate value D LL     3    as follows: 
 
 D   LL     3   =abs( Ĥ   —   LL   3 ( i,j )− H   —   LL   3 ( i,j ))/α LL     3     *Ŝ ( Ĥ   —   R   LL     3   ( i,j )  (16)
 
 Individual pixels (i,j) of the extracted watermark image are determined from M LL     3   (i,j), N LL     3   (i,j), R LL     3   (i,j) and D LL     3    as follows:
 
If (( D   LL     3   &gt;0 AND  M   LL     3     &lt;D   LL     3     &gt;N   LL     3   ) OR ( D   LL     3   &lt;0 AND  R   LL     3     &lt;D   LL     3     &gt;N   LL     3   )
 
Then  Ŵ   —   LL   1 (ƒ LL     3   ( i ), j )=1  (17)
 
Else  Ŵ   —   LL   1 (ƒ LL     3   ( i ), j )=0
 
 Process  510  recovers masking function ƒ using key K 1  as follows:
 
ƒ LL     3     −1   :{tilde over (W)}{circumflex over (_)}   LL   1 (ƒ LL     3   ( i ), j ) →{tilde over (W)}{circumflex over (_)}   LL   1 ( i,j )  (18)
 
 Lastly, process  510  undoes the pseudo randomization of the rows of the watermark image using key K 2  as follows:
 
 P   LL     3     −1   :{tilde over (W)}{circumflex over (_)}   LL   1 ( i,j )→ W{circumflex over (_)}   LL   1 ( i,j )  (19)
 
 The result is wavelet domain partially extracted watermark  520 . 
 
         [0049]     Process  510  repeats these steps to extract the sub-bands W{circumflex over (_)}LH 1 , W{circumflex over (_)}HL 1  and W{circumflex over (_)}HH 1 . These sub-bands combined form wavelet domain extracted watermark  525 . This is subjected to an inverse binary discrete wavelet transform to produce extracted watermark image  530 .  
         [0050]     FIGS.  7  to  12  illustrate an example host image and watermark.  FIG. 8A  is a 256 by 256 gray scale image entitled “Lena.” This particular image is widely used in image experiments.  FIG. 8B  is 64 by 64 binary watermark image of the logo of Texas Instruments Incorporated, the assignee of this invention.  FIG. 9  illustrates the corresponding watermarked image in accordance with this invention just described. The perceptual signal to noise ratio (PSNR) of the watermarked host image as illustrated in  FIG. 9  calculated as described in Hsu, C. T. and J. L. Wu, “Multiresolution Watermarking for Digital Images,” IEEE Tr. CAS-2, Vol. 45, No. 8, August 1998, pp. 1097-1101 is 38.6039 dB. Perceptually the watermarked host image of  FIG. 9  is without many visual artifacts and there is little deterioration from the original host image.  
         [0051]     Table 1 shows the extracted watermark performance evaluated on a NC scale for various JPEG attacks. The extracted NC performance is shown for various levels of JPEG compression ratio (CR) and quality factor (QF).  
                                     TABLE 1                       JPEG CR   JPEG QF   Extracted Watermark NC                                2.15   100   0.9034       6.70   80   0.9020       9.53   60   0.8813       12.05   40   0.8551       17.11   20   0.6519       20.90   10   0.5493                  
 
  FIG. 10  illustrates a comparison of the original watermark image ( FIG. 10A ) with watermark images extracted from JPEG attacked watermarked host images of qualify factor (QF)  60  in  FIG. 10B, 40  in  FIG. 10C and 20  in  FIG. 10D . 
 
         [0052]     Table 2 shows extracted watermark performance evaluated on a NC scale for various levels of median filtering attacks.  
                                         TABLE 2                                   Filter Length   Extracted Watermark NC                                        3   0.67           5   0.5191           7   0.5453           9   0.5392                      
 
  FIG. 11  illustrates an extracted watermark resulting from a median filtering attack of length  3 . 
 
         [0053]     Table 3 shows extracted watermark performance evaluated on a NC scale for various rotation angles of attack.  
                                         TABLE 3                                   Rotation Angle (Degrees)   Extracted Watermark NC                                        0.25   0.5513           0.50   0.5171           −0.25   0.5815           −0.50   0.5272                      
 
         [0054]      FIG. 12  illustrates the example host image ( FIG. 12A ) and the corresponding extracted watermark image ( FIG. 12B ) for a blurred image attack.  
         [0055]      FIG. 13  illustrates the example host image ( FIG. 13A ) and the corresponding extracted watermark image ( FIG. 13B ) for a contrast enhanced host image attack.  
         [0056]     This invention uses sequency and the wavelet transforms in a novel image watermarking algorithm. The performance results shown in FIGS.  8  to  13  demonstrate superior results over the technique described in Hsu, C. T. and J. L. Wu, “Multiresolution Watermarking for Digital Images,” IEEE Tr. CAS-2, Vol. 45, No. 8, August 1998, pp. 1097-1101. This invention is the first attempt to embed a watermark is in the LL band of a wavelet transformed host image. In this invention the PSNR and the perceptual quality of the watermarked host image maintains a good value. In the watermark extraction algorithm of this invention, the impact of the attacks on the statistics of the watermarked image can be taken into account. This invention always demonstrates better results than the existing algorithms on the basis of NC as the extracted watermark quality.