Patent Application: US-6806305-A

Abstract:
a system and method are disclosed which may include subjecting an original , pixel domain image to an integer wavelet transform to obtain a matrix of iwt coefficients ; selecting a plurality of the iwt coefficients for incorporation of information therein ; and setting signs for the plurality of selected iwt coefficients according to bit values of a plurality of respective data bits . the system and method can also include subjecting a marked pixel domain image to an integer wavelet transform to obtain a matrix of wavelet coefficients ; selecting a plurality of the coefficients from the matrix that contain embedded information ; and for each selected coefficient , extracting the data bit embedded in the coefficient , a bit value of the extracted data bit determined based on a sign of the coefficient .

Description:
it is noted that the methods and apparatus described thus far and / or described later in this document may be achieved utilizing any of the known technologies , such as standard digital circuitry , analog circuitry , any of the known processors that are operable to execute software and / or firmware programs , programmable digital devices or systems , programmable array logic devices , or any combination of the above . one or more embodiments of the invention may also be embodied in a software program for storage in a suitable storage medium and execution by a processing unit . herein , the term “ watermark signal ” is information , which may form part of a coherent message , which an encoder may embed in an image and which a decoder can then extract from the image . thus , there may be both an unencoded form of the watermark signal which exists prior to it being embedded into an image . once embedded into an image , the watermark signal is preferably recoverable by a decoder employing a method in accordance with one or more embodiments of the present invention . herein , the terms “ frequency band ” and frequency sub - band ” correspond to the term “ wavelet sub - band .” information other than watermark signal data bits may also be embedded into an image . one of these other categories of information includes “ pseudo bits .” when a coefficient is deemed suitable for the embedding of watermark signal data , a “ real bit ,” also referred to herein as a “ signal bit ,” may be embedded therein by the encoder . when a coefficient is deemed unsuitable for embedding of watermark signal data , a pseudo bit may be embedded therein . herein , a pseudo bit is a bit which , although embedded in a coefficient , is not a part of the watermark signal embedded into an image . upon decoding , by evaluating the magnitude of a coefficient in comparison to the magnitude of a shift value , the decoder can determine whether a bit embedded in a coefficient , and then extracted therefrom by the decoder , is a signal bit or a pseudo bit . if the extracted bit is a signal bit , it may be added to the extracted watermark signal . if the extracted bit is a pseudo bit , it is preferably not included as part of the extracted watermark signal . as discussed later in this document , the magnitude of the original coefficient and the embedding of a pseudo bit therein by the encoder can notify the decoder that the original coefficient was unsuitable for the embedding of a signal bit , and that a pseudo bit was embedded instead . upon determining the “ pseudo ” status of an extracted bit , the decoder may then discard the bit to ensure it is properly excluded from the extracted watermark signal . the wavelet transform is widely applied to many different tasks in image processing . since the wavelet transform coefficients are highly decorrelated , and because the wavelet transform is consistent with the feature of the human visual system ( hvs ), the wavelet transform is also widely applied to image data hiding . evidence indicates that slight modification of wavelet transform coefficients in high frequency subbands is difficult to perceive . hence , in one or more embodiments disclosed herein , data is embedded into the high - frequency wavelet coefficients . to recover the original image losslessly , a reversible wavelet transform is preferably employed . hence , one or more embodiments of the present invention employ the integer wavelet transformation which maps integer to integer [ 14 ] and which can reconstruct the original image from the transformed image without distortion . although various wavelet families can be applied to our reversible embedding scheme , through extensive experimental comparison , it has been discovered that cdf ( 2 , 2 ) ( where cdf refers to “ cohen - daubechies - feauveau ”) is better than other wavelet families in terms of data embedding capacity and the visual quality of the marked images . in addition , it is noted that the cdf ( 2 , 2 ) format has been adopted by the jpeg2000 standard [ 15 ]. fig1 shows the forward and inverse transform formula of cdf ( 2 , 2 ). however , the present invention is not limited to the use of the cdf ( 2 , 2 ) format . one embodiment of the reversible spread spectrum data hiding method is discussed in this section . after applying the one - level integer wavelet transformation discussed in the previous section , the following three high - frequency subbands : hl , lh , and hh are preferably obtained . it is observed that most of the high - frequency wavelet transform coefficients are small , having magnitudes near zero . the magnitude distributions of the high - frequency coefficients of four frequently used images , shown in fig1 , document this observation . the method disclosed below exploits the existence of coefficients having small magnitudes of the coefficients discussed above and shown in fig1 . in the following , w denotes one coefficient selected from one of the sub - bands hl , lh , hh , and | w |& lt ; a , a & gt ; 0 . to embed one bit in w , we have where w ′ denotes the modified coefficient , a is the shift value , and s is the sign factor which is before discussing data extraction , the following property is identified . specifically , because | w |& lt ; a , we have : this indicates that we can extract the hidden bit by examining the sign of w ′. that is , if sign ( w ′) is positive , bit “ 1 ” is extracted , while bit “ 0 ” is extracted if sign ( w ′) is negative . to recover the original image , the iwt coefficient w is preferably recovered . according to equation ( 1 ), we can restore w as follows . in a preferred embodiment , for the above data embedding scheme to be reversible , the following two conditions must be satisfied . first , there is no overflow and / or underflow when the integer inverse wavelet transformation is applied . this condition is discussed in detail in the next section . second , as was assumed at the beginning of the algorithm , the relation | w |& lt ; a holds true . ( the effect of variation in the value of a on data - embedding capacity and the visual quality of marked images is discussed later in this document ). attention is now directed to a situation where the above assumption regarding the relative values of a and | w | do not satisfy the above - stated assumption , thus where | w |≧ a . fortunately , this situation can be handled by embedding a pseudo bit into each coefficient for which | w |≧ a . ( a ) if w ≧ a , we set s = 1 . thus , one pseudo bit having a bit value “ 1 ” is embedded into the coefficient w . when decoding , the decoder will preferably extract a bit value of “ 1 ” from w ′ because w ′, given the foregoing conditions , would be positive . subsequently , the original value of w can be recovered through equation ( 4 ), shown above . upon noting that | w |≧ a ( a condition which fails to satisfy the second condition stated above for the reversibility of the disclosed data embedding scheme ), the decoder can determine that the extracted bit having a value of “ 1 ” is a pseudo bit which is not a part of the watermark signal . thus , this pseudo bit may be safely discarded without losing any part of the watermark signal . the discussion continues considering the case where the coefficient , w , is negative . ( b ) if w ≦− a , we let s =− 1 . thus , a pseudo bit with a bit value of “ 0 ” is preferably embedded into the coefficient w . thus , when decoding , the decoder preferably extracts a bit having a value of “ 0 ” from w ′ because w ′ is negative . subsequently , we can recover the original w using equation ( 4 ). thus , the original value of the coefficient w may be obtained . moreover , the decoder can determine that the absolute value ( magnitude ) of the original coefficient w has the following relationship to the shift value a : | w |≧ a . since this violates one of the second above - stated condition for reversible data hiding , the decoder preferably determines that the extracted “ 0 ” bit is a pseudo bit . hence , the decoder can safely discard this bit , and decoding can proceed . two pieces of information can be provided to enable a decoder to know which coefficients to extract data from to reconstruct the watermark signal ( the hidden data ). first , information can be provided which identifies a group of coefficients into which data , whether signal bits or pseudo bits , are embedded . second , information indicating whether the bit embedded into each coefficient in the identified group is a signal bit ( i . e . a bit forming part of the watermark signal ) or a pseudo bit ( a bit which is not part of the watermark signal and which can be safely discarded without losing any of the data for the watermark signal ). in one or more embodiments , the group of coefficients into which data are embedded may be identified for a decoder separately from the data embedded in the image itself . this approach provides security since any entity intercepting the image will not be able to identify the marked coefficients ( coefficients having data embedded therein ) using information within the image . however , in an alternative embodiment , data describing the group of coefficients into which data are embedded may be included in the image itself . where information describing the group of coefficients into which data are embedded is communicated separately from the data in the image itself , various options are available for providing this information to a decoder . where an entire block of coefficients exists for a frequency sub - band , coefficients within one quadrant of this block could be used for embedding data , and the location of this quadrant can be identified to the decoder . this is a space - efficient approach , since once the quadrant is identified , there is preferably no need to send data identifying each individual coefficient . alternatively , one of many frequency sub - bands employed in the image could be identified , where all the coefficients in the identified frequency sub - band have data embedded therein . another approach involves a pre - existing understanding between the encoder and the decoder regarding the coefficients that will be used for encoding . this identification could be simplistic , as in identifying an entire quadrant of a block of coefficients having embedded data , or an entire frequency sub - band all of whose coefficients have embedded data . alternatively , the identification could be more involved , specifically identifying marked coefficients by number and / or by location , these marked coefficients potentially being distributed throughout various coefficient blocks and / or various frequency sub - bands of the image . yet another approach involves using a random number generator which produces a particular output of numbers given an initial seed . in this embodiment , a common seed can be provided to both the encoder and the decoder . thereafter , when either the encoder or the decoder needs an identification of the coefficients for data embedding and extraction , the output of the random number generator for the selected seed may be obtained by either the encoder or the decoder . once the coefficients to be used for embedding are identified by one or more of the methods identified above , the encoder preferably proceeds to embed the data as needed . however , as described above , when the magnitude of a coefficient , w , within the group of coefficients slated for data embedding is too large to be used for embedding watermark signal data ( as discussed above ), a pseudo bit is embedded in that coefficient instead of a signal bit . thereafter , the decoder , upon calculating the original value of w using equation 4 , is able to determine from the coefficient itself that the bit embedded in that coefficient is a pseudo bit . where a pseudo bit is detected , the decoder preferably discards the pseudo bit , thereby correctly omitting this bit from data to be included in the extracted watermark signal . the embedding of a pseudo bit into a coefficient in the manner described preferably indicates to the decoder that the coefficient into which the pseudo bit was embedded had an original value or original magnitude (“ original ” meaning the coefficient value prior to embedding data therein ) that was too large to use for embedding watermark signal data in conjunction with a particular value of the shift value a . if the coefficient w is equal to or larger than the shift value a , then adding the product of a and s ( where s is negative ) will not succeed in forcing the sign of w ′ to equal the sign of the sign factor s . and the data embedding and decoding scheme disclosed herein depends on the property that sign ( s )= sign w ′. when the decoder examines a coefficient , the decoder preferably first examines the sign of the coefficient to determine the sign of s , thereby also determining the sign of w ′. thereafter , the decoder preferably subtracts the product of a and s from the marked coefficient w ′ ( which was generated in the encoding process ), thereby providing the original coefficient w . the decoder can then compare the original coefficient w to a . if absolute value of w is equal to or greater than a , thus violating a condition for encoding a signal bit in to w , the decoder preferably determines that this coefficient contained a pseudo bit and preferably discards it . by embedding the pseudo bits in unusable coefficients as described , the need for a location map or other bookkeeping scheme to describe for the decoder which coefficients , among the coefficients into which data has been embedded , have signal bits embedded therein and which coefficients have pseudo bits embedded therein is removed . this is true because the decoder can preferably make this determination on its own from the very data it is decoding . compared with the method in [ 10 ] which uses the “ location map ” to record the modified coefficients , where data are hidden , then losslessly compresses the map and embeds the compressed map into the image as overhead data , embedding pseudo bits is a simpler and more effective bookkeeping scheme . for a given image , after data are embedded into some iwt coefficients , it is possible to cause overflow and / or underflow . this means that after the inverse integer wavelet transform is performed , the grayscale values of some pixels in the marked image may exceed the upper bound ( the upper bound being 255 for an eight - bit grayscale image ) and / or the lower bound ( the lower bound being 0 for an eight - bit grayscale image ). in this situation , truncation is generally applied to restore the resulting grayscale value to a permissible numerical range , thereby violating the reversibility of the data hiding . this is a challenging issue confronting all lossless data hiding algorithms . in one or more embodiments of the present invention , in order to prevent overflow and / or underflow , a histogram modification procedure is adopted which narrows the range of histograms from both the left and right sides . preferably , after the histogram modification , some grayscale values on the left - hand side of the histogram are merged towards the center of the histogram and left empty , while some grayscale values from the right - hand side are merged towards the center of the histogram and left empty . in the following discussion , it is assumed that we are going to narrow a histogram by g grayscale levels , which means that g grayscale values should be empty after the histogram gets modified . a general example of histogram modification is presented below , followed by a more specific application of histogram modification to the reversible data hiding method disclosed herein . for the sake of simplicity , in this section , g is restricted to being an even number . ( g is assigned a value of 40 in a later section within this document ). thus we can narrow down the histogram in g / 2 passes , and in each pass the histogram is preferably narrowed down by two grayscale levels , one from the left - hand side , the other from the right - hand side . in narrowing down a histogram to the range [ g / 2 , 255 - g / 2 ], the histogram modification information is preferably recorded within data embedded into the image . the data to be embedded into the image therefore may arise from three sources : 1 ) the watermark signal ; 2 ) pseudo data ( if needed ) and 3 ) the bookkeeping information of histogram modification . preferably , data are embedded in the order from high frequency ( hh , hl , lh ) to low frequency ( ll ), from low level to high level , and from least bit - plane to high bit - planes . in this way , the visual quality of the marked image can be optimized . in order to illustrate the histogram narrow - down process , we use a simplified example , where the size of an original image is 6 × 6 with 8 = 23 gray scales ( 6 × 6 × 3 ) as shown in fig3 - 4 . from fig3 - 5 , it can be seen that the range of the modified histogram now is from 1 - 6 instead of 0 - 7 , i . e ., no pixel has a grayscale value of either 0 or 7 . after modification , grayscale value 1 is merged into grayscale value 2 . grayscale value 0 becomes gray scale 1 . in the same way , grayscale value 6 is merged into grayscale value 5 . grayscale value 7 becomes grayscale value 6 . the original and modified histograms are shown in fig2 . data for the original and modified histograms are shown in fig5 . fig6 illustrates bookkeeping information describing the histogram modification which can be recorded and which may be embedded into the image . the left - hand side record bits with its left neighbor grayscale value ( 101101 ) in fig6 show that both the second and fifth values of “ 2 ” by scanning (& lt ; x = 5 , y = 1 & gt ;,& lt ;( x = 1 , y = 4 & gt ;) in fig4 b have values of “ 1 ” in fig4 a originally . moreover , the right - hand side record bits with its right neighbor grayscale value ( 110111 ) in fig6 shows that the third “ 5 ” by scanning (& lt ; x = 4 , y = 2 & gt ;) in fig4 b has the value “ 6 ” in fig4 a . in the following , the discussion of histogram modification continues with an example more particularly directed to histograms of images having data embedded using methods in accordance with one or more embodiments of the present invention . one embodiment of a histogram narrowing algorithm is described in fig7 . an example of histogram modification of the “ lena ” image with g = 40 is shown in fig7 . in this example , the entries for grayscale values between 1 and 20 and between 235 and 255 are merged into the grayscale values of the central portion of the histogram . this process thereby shortens the grayscale range from ( 0 - 255 ) to ( 20 - 235 ). see fig8 a and 8c . after the data are embedded into the image , the grayscale range is extended to some extent , but still remains in the range of ( 0 - 255 ) so as to avoid possible overflow and / or underflow . see fig8 c . in narrowing down a histogram to the range [ g / 2 , 255 - g / 2 ], it is beneficial to record the histogram modification information such as the grayscale values that are merged ( l k and r k in fig6 ) and the position of pixels whose grayscale values are equal to l k or r k . and which are a part of the embedded data . this recorded information is referred to herein as bookkeeping information . preferably , the original image can be losslessly restored using the recorded bookkeeping information . generally speaking , the amount of bookkeeping information is small . the block diagram of this new reversible embedding method is given in fig9 . for most images , most of the iwt ( cdf ( 2 , 2 )) coefficients in the high - frequency sub - bands have small magnitudes . this has been verified viewing statistics of some frequently used images , as shown in fig1 . fig1 illustrates the percentages of high - frequency iwt coefficients falling into various ranges of coefficient magnitude . hence , we can embed one bit into most of the high - frequency coefficients even when using small values of shift value , a . the value of shift value a can be adjusted to achieve different payloads . specifically , if the required payload is small , we may choose a small value of a so that the distortion of the marked image can be minimized . on the other hand , if the required payload is large , we may choose a larger a , resulting in larger distortion in the marked image . this method is more flexible and simpler than the mean square error ( mse ) minimization method proposed in [ 10 ]. fig1 - 18 present some experiment results of the payload vs . the peak signal to noise ratio ( psnr ) of the embedded versions of the images shown in fig1 - 14 . the performance comparison with the state - of - the - art reversible data hiding schemes [ 6 , 10 , 11 ] in terms of data embedding capacity versus distortion of marked image on the “ lena ” and “ barbara ” test images is shown in fig1 and 29 , respectively . the top curves in both figures are for one or more embodiments of the wavelet spread - spectrum method disclosed herein . it is observed that , at the same data embedding capacity , the psnr of the marked images versus the original image when using the wavelet spread - spectrum method is higher than that obtained using other methods . j . m . barton , “ method and apparatus for embedding authentication information within digital data ,” u . s . pat . no . 5 , 646 , 997 , 1997 . 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[ 14 ] a . r . calderbank , i . daubechies , w . sweldens , b . - l . yeo , “ wavelet transforms that map integers to integers ,” in : applied and computational harmonic analysis , july ( 1998 ) 332 - 369 . [ 15 ] rabbani and r . joshi , “ an overview of the jpeg2000 still image compression standard ”, signal processing : image communication 17 ( 2002 ) 3 - 48 . although the invention herein has been described with reference to particular embodiments , it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention . it is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims .