GB2390246A

GB2390246A - Method of characterising attacks on a watermarked object

Info

Publication number: GB2390246A
Application number: GB0214985A
Authority: GB
Inventors: Dominique Albert Winne; David Roger Bull; Cedric Nishan Canagarajah; Henry David Knowles
Original assignee: University of Bristol
Current assignee: University of Bristol
Priority date: 2002-06-27
Filing date: 2002-06-27
Publication date: 2003-12-31
Also published as: GB0306047D0; GB0214985D0; GB2390251A

Abstract

A method of characterising attacks on a digitally watermarked object compriseing the steps of: providing a library of possible attacks, wherein the library contains data relating to the effects of possible attacks on a variety of candidate digital objects; estimating the first digital watermark embedded in the digitally watermarked object (I'); embedding a second watermark into the digitally watermarked object (I') using said watermarking algorithm; estimating the second watermark embedded in the digitally watermarked object (I'); and determining the type of attack used by comparing the estimates of the first and second watermarks with the contents of the library of possible attacks. A method of determining whether an object has been attacked including the step of comparing the estimates of the watermarks is described. A method of estimating a watermark using threshold values and comparing estimates of the watermark with known watermarks is also disclosed.

Description

DOUBLE WATERMARRING

TECHNICAL FIELD OF THE INVENTION

5 This invention relates to watermarking digital objects, and in particular to a method and system for detecting particular attacks on a digital object, such as a digital image 10 BACKGROUND TO "E ICON

A watermark is a visible or invisible structure in an image, which can be recovered after it has been embedded. A digital watermark is a digital pattern 15 inserted into a digital creation, such as a digital image. The process of inserting a watermark into a digital image (embedding procedure) can be done directly in the spatial or transformed domain. The watermark can be inserted by altering certain image 20 coefficients in a way that minimizes the resulting distortion of the image.

The imperceptibility of the watermark is the first line of defence, since, if an image is not visibly watermarked, it is more difficult to avoid the 25 watermark by tampering with the image undetectable.

One of the aims when inserting the watermark into the image is to maximise the 'energy' of the watermark.

That is, the magnitudes of the changes should be maximized. However, neither this nor the visibility 30 constraint are essential, although they are highly desirable. As stated above, a watermark is added to an image at the embedding stage. At this time, the integrity of the image is assumed, i.e. no attacks on the image have 35 taken place. The watermarked image is then stored, and

whilst in storage may or may not be subject to some form of tampering or attack.

When the authenticity of the image is to be verified, a detection process is used. The aims of a 5 detection process are to determine whether or not an image has been tampered with, to determine the location of any such tampering on the image, to determine the method of attack used and (ideally) to be able to restore the attacked area(s) in the watermarked image.

10 Conventional watermarking systems are able to locate areas of an image that have been attacked, but cannot provide an indication of the type of attack used. 15 SUMMARY OF THE INVENTION

. It is therefore an object of the present invention to provide a watermarking system and method that is able to detect whether a watermarked image has been 20 attacked, and to provide an indication as to the type of attack used.

For many watermarking algorithms, it has been found that, when the algorithm is applied sequentially, i.e. adding a first digital watermark to an object to 25 form a first watermarked object, and adding a second digital watermark to the first watermarked object to form a second watermarked object, the strength with which the second digital watermark is embedded is approximately equal to the strength with which the 30 first digital watermark is embedded.

However, in the event that a watermarked object has been tampered with, any estimate of the first digital watermark will also include the effects of the tampering with the first watermarked object, and there 35 will be a significant difference between the estimate of the first digital watermark and the estimate of the

second digital watermark which indicates tampering with the first watermarked object.

Therefore, according to a first aspect of the present invention, there is provided a method of 5 detecting an attack on a digital object (I) into which a first digital watermark has been embedded using a watermarking algorithm to form a digitally watermarked object (I') with the method comprising the steps of: estimating the first digital watermark embedded in 10 the digitally watermarked object (I'); embedding a second watermark into the digitally watermarked object (I') using said watermarking algorithm; estimating the second watermark embedded in the digitally watermarked object (I'); comparing the estimate of the first 15 digital watermark and the estimate of the second digital watermark; and determining whether the digitally watermarked object (I') has been attacked on the basis of the comparison.

According to a second aspect of the present 20 invention, there is provided a method of determining the type of attack used on parts, or all of a digital object (I) into which a first digital watermark has been embedded using a watermarking algorithm to form a digitally watermarked object (I') with the method 25 comprising the steps of: providing a library of possible attacks, wherein the library contains data relating to the effects of possible attacks on a variety of digital objects; estimating the first digital watermark embedded in the digitally watermarked 30 object (I'); embedding a second watermark into the digitally watermarked object (I') using said watermarking algorithm; estimating the second watermark embedded in the digitally watermarked object (I'); and comparing the estimates of the first and second 35 watermark with the contents of the library of possible attacks.

( According to other aspects of the present invention, there are provided computer devices for performing the methods described above.

5 BRIEF DESCRIPTION OF ME DRAWINGS

For a better understanding of the present invention, and to show how it may be put into effect, reference will now be made to the accompanying 10 drawings, in which: Figure 1 is a flow chart illustrating the detection process according to the present invention; Figure 2 illustrates a method of embedding a watermark in an image according to a preferred 15 embodiment; Figure 3 illustrates a preferred method of extracting embedded watermarks; Figure 4 illustrates a method of generating histograms for attack determination according to a 20 preferred embodiment; and Figure 5 illustrates the step of determining the most likely attack in the method of Figure 1.

DETAILED DESCRIPTION OF THE PREFFERRED EMBODIMENTS

A digital object (hereinafter referred to as an image, although the invention is applicable to other objects) has been generated, for example by a digital camera, and it is necessary to preserve the 30 authenticity of the image. The image data may be in any form and, for example, may be a set of luminance and chrominance values associated with respective pixels of the image.

A watermark is embedded in the image data and, 35 advantageously, the embedding procedure is carried out near to the source of the image. For example, the

( watermarking procedure can be carried out within a digital camera.

The watermarking process can be carried out by a general-purpose computer, operating under the control 5 of suitable software, or by another hardware device, such as a DSP or an ASIC, or other integrated circuit.

The watermarked image is then stored, perhaps on a computer hard disc or other storage medium, and whilst in storage may or may not be subject to some form of 30 tampering or attack.

Figure 1 shows a flow chart illustrating the detection process according to the present invention.

At step 101, the watermarked image is retrieved from storage and the embedded watermark is extracted.

15 The extraction process comprises determining an estimate of the embedded watermark.

Conventionally, the estimated watermark is then compared with the original watermark, and the differences between the two used to determine whether 20 particular parts of the image have been attacked.

However, the correlation between the estimated watermark and the original watermark is dependent not only on the attack but on the statistics of the image itself. Therefore, a reference is required to 25 determine whether the correlation observed is due to tampering or due to the statistics of the image.

Therefore at step 103, in accordance with the invention, a second watermark is added to the watermarked image, using the same watermarking 30 algorithm which was used to embed the first watermark.

At step 105, the second watermark is extracted from the doubly watermarked image using a procedure similar to that used in step 101.

As the second watermark is extracted immediately 35 after being embedded, it is known that no further attacks have occurred on the watermarked image.

( Therefore, the correlation observed between the estimate of the second watermark and the second watermark will be caused by the statistics of the image. Therefore, this second watermark estimate 5 provides a reference to determine whether the correlation observed between the estimate of the first watermark and the first watermark is due to tampering or the statistics of the image.

If the estimate of the first watermark and the 10 estimate of the second watermark are similar, then it is likely that no attack has occurred. However, if the estimates are significantly different, then the watermarked image has probably been attacked.

At step 107, the data relating to the estimate of 15 the first watermark is converted into an appropriate form to allow a determination of the type, or types, of attack that have been used on the watermarked image.

In a preferred embodiment, the data is converted into values that correspond to the elements of a histogram, 20 as will be described in more detail below.

At step 109, the determination of the most likely attack(s) used on the watermarked image is carried out.

In the preferred embodiment, each possible attack has an associated histogram stored in a library, and 25 the values generated in step 107 are compared with the histograms associated with the possible attacks. The library also contains a histogram relating to a 'no attack' attack. 'No attack' is defined as no tampering with the watermarked image. A probability can then be 30 calculated that indicates which of the attacks was most likely to have been carried out on the watermarked Image. This probability is denoted as P(PIA)' or "the probability of the parameters P taking a particular 35 value given attack A has taken place". For the image in question, the parameters P are compiled, and for

( each attack A, the probability that those particular parameter values would have been obtained is calculated. The attack for which this probability is greatest is deemed the most likely attack to have 5 happened.

Of course, a number of different attacks may have been carried out on different areas of the watermarked image and by considering the watermarked image as a number of elements, the determination in step 109 can 10 provide an indication as to which attack(s) were most likely to have occurred in each attacked area.

Figure 2 illustrates a method of embedding a watermark in an image according to a preferred embodiment 15 This method of embedding a watermark is generally conventional, and will be described only briefly as the details thereof will be known to the person skilled in the art. Moreover, although this is a preferred algorithm, it will be appreciated that the present 20 invention is applicable to any additive watermarking algorithm where there is a dependence on the image being watermarked.

In step 201, the watermark is created. A bipolar (+1) block of size block_size x block_size is generated 25 using a random number generator. A user key acts as a seed number ( seed) for the random number generator.

The bipolar block is doubled in size by replicating each bit horizontally, vertically and diagonally such that, e.g. 1 1 - 1 - 1

30 {1 - 1 1 1 - 1 - 1

( 1) becomes 1 1 1 1 1 1 1

This is known as the watermark block WM. WM is then tiled over the whole of the image to be watermarked I. 35 At step 203, the Discrete Wavelet Transform (DWT) is applied to the whole of the image I.

( At step 205, the Discrete Wavelet Transform (DWT) is applied to the tiled M. At step 207, the Noise Visibility Function (NVF) of each subband of the DWT of the image T is 5 calculated, where NVF (i, j) = 1 1 + c(i, j) a.,a,, is the local subband variance calculated using a 3-

by-3 sliding window, D is a user defined variable in 10 the range 50-100 and Om is the maximum local variance for the subband.

The embedding strength for all of the wavelet coefficients So(i,j), is then determined using S,o(i,j) = Seiko *(l - NVF(i,j)) + Sfo * NVF(i,j), 15 where Se and Sf are matrices that denote the embedding strength in edge and flat regions of the image I respectively. Se and Sf may be defined by the user depending on the required trade-off between visibility and watermark energy. The subscripts L and O signify 20 the decomposition level and orientation respectively of the wavelet subbands, and i and j refer to the position of the current coefficient in a two dimensional space.

This ensures that the watermark is embedded in the image with as much energy as possible without the 25 watermark becoming visible.

At step 209, the watermark is embedded into image I by multiplying the DWT of the tiled watermark block AM with SL,O(1,j) and adding it to the DWT of the image I to form the watermarked image I' in the transform 30 domain i.e. I' = I + WE * S,o(i,j) At step 211, an inverse Discrete Wavelet Transform is performed on I' to obtain the watermarked image in the spatial domain.

35 Then, I' is rounded to take integer values in an appropriate range.

The image has now been watermarked and can be stored in a suitable device.

Figure 3 illustrates a method of extracting the embedded watermark according to the preferred 5 embodiment.

At this stage, the watermarked image I' has been stored, and it is not known whether it has been attacked. The (possibly) attacked watermarked image is denoted I'.

10 The watermark block WM and the watermark block size block_size are known.

At step 301, WM is tiled so that it is the same size as the (possibly) attacked watermarked image I'.

The Discrete Wavelet Transform (DWT) is applied to 15 the tiled watermark block WM.

At step 303, the Discrete Wavelet Transform is applied to the watermarked image I'.

Then the transformed tiled watermark block WM is split back into blocks of size block_size/(2eVel) x 20 block_size/(2teVel) and for each transformed watermark block the process in steps 307 to 321 is performed.

It should be noted that the block size decreases in area by a factor of 4 in the wavelet domain each time the DWT is applied. 'Level' indicates the number 25 of times the image has been decomposed using the DWT to get the current wavelet subband.

At step 307, a range of possible thresholds is set. The range depends upon whether soft or hard thresholding is used.

30 The process of estimating the watermark works by taking coefficient values with a magnitude below the threshold. By varying the threshold, different estimates of the watermark are obtained.

Then, for each threshold value, steps 311 to 319 35 are performed.

At step 311, the embedded watermark is estimated using the current threshold value.

The thresholded image block, comprising the watermarked image coefficients that are larger than the 5 threshold, is subtracted from the image block to give an estimate of the watermark WM. An image block is defined as a block of the image I' of size block_size/(2teVei) x block_size/(2eVel).

The estimation process involves first thresholding 10 the image to give an estimate of the image without the watermark. The difference between the estimate of the watermark-free image and the watermarked image is an estimate of the watermark.

At step 313, the coherence between the estimate of 15 the watermark block WM and the original transformed watermark block WM is calculated.

At step 315, it is determined whether the coherence of the estimate of the watermark block WM is greater than a maximum coherence obtained with any 20 other threshold value used in calculating previous estimates. If the current coherence is greater than the maximum coherence obtained thus far, the process moves to step 317. Here, the estimate of the watermark WM 25 and its coherence are stored as the maximum. The process moves to step 319, where steps 309 to 317 are repeated for another threshold value.

If the current coherence is less than the maximum, the process moves to step 319, where steps 309 to 317 30 are repeated for the remaining threshold values.

By comparing the coherence of the current estimated watermark block V with the maximum coherence obtained thus far, the estimate of the watermark that is most similar to the original is obtained.

35 Once all of the threshold values for a particular watermark block WM have been examined, the process is

( repeated for each watermark block tile WE in the image I'. At step 323, an inverse DWT is performed on a composite of the estimated watermark blocks WE to 5 convert them into the spatial domain.

The method of extracting watermarks described above is used for extracting both the first watermark and the second watermark.

If the object was tampered with, the tampering 10 would affect the estimates of the watermark.

Nevertheless, it should be noted that, irrespective of the possibility of tampering, the estimate of the watermark that is most similar to the original watermark is still taken as the best estimate for these 15 purposes.

There are potentially an infinite number of different attacks that can be performed on a particular image and it is not possible to determine a definite mathematical formula to describe how different attacks 20 affect particular watermarks. Therefore, in accordance with the invention, histograms are generated for different attacks based on observed data. As attacks can affect different images in different ways, a wide range of different images are used in compiling the 25 histograms.

Figure 4 illustrates a method of generating histograms for attack determination according to the preferred embodiment.

A histogram is generated for each possible attack 30 stored in a library. The histogram is constructed from the analysis of the results of attacks on a number of sample images stored in a database.

One or more times, each image in the database is watermarked and subjected to each attack stored in the 35 library in turn. For each attack, the individual

( elements (pixels) in the watermarked (and attacked) image are analyzed.

At step 407, the values contained in the data are converted into an appropriate form for compiling a 5 histogram. For all values contained in the data, the histogram index corresponding to these values is calculated in order that the value stored in each of the calculated histrogram indices, or bins, may be incremented. For each element, a number of different 10 parameters are used as inputs to the histogram, for example, the parameters may include the watermarked image, estimated first watermark, estimated second watermark or the average difference in watermark coherence (or correlation coefficient) for the 15 horizontal, vertical and diagonal orientations in Level 1 (or Level 2) of wavelet decomposition.

Some parameters may vary on a block-by-block basis, while others may vary on a pixel-by-pixel basis.

For a parameter that varies on a block-by-block basis, 20 the parameter value is replicated block_size x block_size times.

The level is the number of times the image has been decomposed using the DWT, where for each decomposition, apart from the first time when the input 25 is the original image, the input to the OWT is the low frequency subband from the previous decomposition.

Within each level, there are 4 different subbands or orientations. These are: the approximation which contains the low frequency information mentioned 30 previously, and the horizontal, vertical and diagonal subbands, which correspond to components of the image that vary horizontally, vertically and diagonally respectively. The average difference in coherence for the horizontal, vertical and diagonal orientations for 35 a given level is defined thus. It is the difference between the coherence of the first extracted watermark

with its original, and the second extracted watermark with its original, averaged over the appropriate subbands. It is possible to use separate inputs relating to 5 each of these orientations, or to reduce the number of inputs by taking an average of them.

The number of inputs determines the number of dimensions in the histogram, and so reducing the number of inputs reduces the data handling requirements.

10 Other parameters that may be used as inputs to the histogram include: the variance of the watermarked image, the variance of individual subbands, the sum of the magnitude of blocks of watermarked image coefficients in the wavelet domain, the coherence of 15 the estimated with the original watermarks for level 1, 2 etc. Values are obtained for each of these parameters, and the values are assigned to appropriate histogram bins. That is, for each parameter, there are a number 20 of bins, each relating to a range of possible values for the parameter. The appropriate bin is then incremented. Once this process has been completed, there will exist, for each particular attack, a histogram that 25 indicates the probability of the values that the various parameters are likely to take in the event that that particular attack has been used on an image.

Once the first and second watermarks have been estimated and compared, the attack determination is 30 carried out.

Figure 5 illustrates the step of determining the most likely attack in the method of Figure 1.

The process contained in steps 503 to 513 is repeated for each element in the (possibly) attacked 35 watermarked image.

( At step 503, the values contained in the data for each element are converted into an appropriate form for indexing a histogram. Thus, values are obtained for each of the parameters used in the histograms.

5 As described above, a number of different parameters may be used, depending upon the complexity of the histogram.

If the average difference in coherence for the horizontal, vertical and diagonal orientations in Level to 1 (or Level 2) of wavelet decomposition is used, these values are calculated from the coherences of the first and second watermarks with their estimates.

Then, in steps 505 to 511, the histogram data for each element in the (possibly) attacked watermarked 15 image is used to determine, via the histograms in the library, which attack is most likely. Specifically, for the histogram index corresponding to each element in the (possibly) attacked watermarked image, it is determined which of the histograms has the highest bin 20 value for that index.

In step 507, it is determined whether the current attack is the most likely to have been used on the element in question. This is achieved by comparing the current histogram bin value to the maximum obtained so 25 far.

The higher the histogram bin value, the more likely it is that this attack has occurred. So the attack that is most likely to have occurred will correspond to the histogram that has the highest bin 30 value corresponding to the current input value.

If the current bin value is the highest obtained so far, the process moves to step 509 where the current attack from the library is stored as the most likely.

The attack ID is stored in an output array, where each 35 element of the array corresponds to an element in the image.

If the current bin value is not greater than the maximum obtained so far, the current attack is not stored, and the process returns to step 505, where the next attack in the library is evaluated.

5 Once all attacks in the library have been evaluated for all elements in the image I', the process ends. The output of the process is an array where each element of the array corresponds to an element of the 10 image, and the content of each element in the array indicates what attack is most likely to have occurred on the corresponding element in the image. A further step can compare these indications across the whole image, for example such that higher confidence can be 15 placed in an answer if it indicates that many contiguous elements have been the subject of a particular attack, rather than if it indicates that isolated elements have been the subject of different attacks. 20 There is therefore described a method of detecting and characterizing attacks on a watermarked image.

Claims

1. A method of characterizing attacks used on a digital object (I) into which a first digital watermark 5 has been embedded using a watermarking algorithm to form a digitally watermarked object (I'), the method comprising the steps of: providing a library of possible attacks, wherein the library contains data relating to the effects of 10 possible attacks on a variety of candidate digital objects; estimating the first digital watermark embedded in the digitally watermarked object (I'); embedding a second watermark into the digitally 15 watermarked object (I') using said watermarking algorithm; estimating the second watermark embedded in the digitally watermarked object (I'); and determining the type of attack used by comparing 20 the estimates of the first and second watermarks with the contents of the library of possible attacks.

2. A method as claimed in claim 1 wherein the library of possible attacks further contains data 25 relating to the effects of no attacks on the variety of candidate digital objects.

3. A method as claimed in claim 1 or 2, further comprising the step of comparing the estimate of the 30 first digital watermark and the estimate of the second digital watermark.

4. A method as claimed in claim 3 wherein the step of comparing the estimates comprises:

( determining a measure of the differences between the estimate of the first digital watermark and the first digital watermark; determining a measure of the differences between 5 the estimate of the second digital watermark and the second digital watermark; and comparing the measure of the differences between the estimate of the first digital watermark and the first digital watermark and the measure of the 10 differences between the estimate of the second digital watermark and the second digital watermark.

5. A method as claimed in any preceding claim, wherein the step of determining the type of attack used 15 comprises assigning an a priori probability value to each possible attack stored in the library.

6. A method as claimed in any preceding claim, wherein the steps of estimating the first and second 20 watermarks comprise considering elements of the digitally watermarked object (I') in turn to provide an indication of the areas of the digital object (I) that have been subjected to attack.

25 7. A method as claimed in claim 6 wherein an element is a pixel.

8. A method as claimed in claim 6 wherein an element is a block of pixels.

9. A method as claimed in claim 6 wherein an element is a transform coefficient.

10. A method as claimed in claim 6 wherein an 35 element is a block of transform coefficients.

( 11. A method as claimed in one of claims 6 to 10, wherein the step of determining the type of attack used comprises assigning an a posterior) probability value for each possible attack stored in the library to each 5 element of the digitally watermarked object (I').

12. A method as claimed in any one of claims 6 to 11, wherein an array is produced that indicates which type of attack is most likely to have been used in each 10 element of the digitally watermarked object (I').

13. A method as claimed in any preceding claim, wherein the library of possible attacks comprises data relating to the effects of possible attacks on a 15 variety of candidate digital objects in the form of histograms and the step of comparing the results comprises: converting the results of the step of comparing the estimates into a form suitable for comparing the JO histograms stored in the library.

14. A computer system, programmed to carry out a method as claimed in any one of claims 1 to 13.

25 15. A method of detecting an attack on a digital object (I) into which a first digital watermark has been embedded using a watermarking algorithm, to form a digitally watermarked object ( I f), the method comprising the steps of: 30 estimating the first digital watermark embedded in the digitally watermarked object (I'); embedding a second watermark into the digitally watermarked object (I') using said watermarking algorithm; 35 estimating the second watermark embedded in the digitally watermarked object (I');

! comparing the estimate of the first digital watermark and the estimate of the second digital watermark; and determining whether the digitally watermarked 5 object (I') has been attacked on the basis of the comparison. 16. A method as claimed in claim 15, wherein i is determined that the digitally watermarked object 10 (I') has not been attacked if the estimates of the first and second digital watermarks are similar.

17. A method as claimed in claim 15, wherein it is determined that the digitally watermarked object 15 (I') has been attacked if the estimates of the first and second digital watermarks are substantially different. 18. A method as claimed in claim 15, wherein the 20 step of comparing the estimates comprises: determining a measure of the differences between the estimate of the first digital watermark and the first digital watermark; determining a measure of the differences between 25 the estimate of the second digital watermark and the second digital watermark; and comparing the measure of the differences between the estimate of the first digital watermark and the first digital watermark and the measure of the 30 differences between the estimate of the second digital watermark and the second digital watermark.

19. A method as claimed in claim 18, wherein it is determined that the digitally watermarked object 35 (I') has not been attacked if the measure of the differences between the estimate of the first digital

watermark and the first digital watermark and the measure of the differences between the estimate of the second digital watermark and the second digital watermark are similar.

20. A method as claimed in claim 19 wherein the watermarking algorithm generates digital watermarks using properties of the digital object (I) and the step of comparing indicates whether the measure of the 10 differences are due to properties of the digital object (I) or due to one or more attacks.

21. A method as claimed in claim 20, wherein it is determined that the digitally watermarked object 15 (I') has not been attacked if the estimates of the first and second watermarks are similar to their respective originals.

22. A method as claimed in claim 20, wherein it 20 is determined that the digitally watermarked object (I') has been attacked if the estimates of the first and second watermarks are substantially different to their respective originals.

25 23. A method as claimed in one of claims 15 to 22, wherein the steps of estimating the first and second watermarks comprises considering elements of the digitally watermarked object (I') in turn to provide an indication of the areas of the digital object (I) that 30 have been subjected to attack.

24. A method as claimed in claim 23 wherein an element is a pixel.

35 25. A method as claimed in claim 23 wherein an element is a block of pixels.

i 26. A method as claimed in claim 23 wherein an element is a transform coefficient.

5 27. A method as claimed in claim 23 wherein an element is a block of transform coefficients.

28. A computer system, programmed to carry out a method as claimed in any one of claims 15 to 27.

29. A method of estimating a watermark in a digital object (I) into which a first digital watermark has been embedded using a watermarking algorithm to form a digitally watermarked object (I'), wherein the 15 first digital watermark block is known, the method comprising the steps of: setting a range of threshold values; estimating the embedded watermark using each of the threshold values; 20 comparing the estimates of the embedded watermark with the known watermark block; and storing the estimate of the embedded watermark that is most similar to the known watermark block.

25 30. A method as claimed in claim 29 wherein the step of comparing the estimates comprises calculating the coherence between the estimates and the known watermark block.

30 31. A method as claimed in claim 29 or 30, further comprising the steps of: embedding a second watermark into the digitally watermarked object (I') using said watermarking algorithm; 35 estimating the second watermark embedded in the digitally watermarked object (I') by:

setting a second range of threshold values; estimating the second embedded watermark using each of the second range of threshold values; 5 comparing the estimates of the second embedded watermark with the known second watermark block; and storing the estimate of the second embedded watermark that is most similar to the known second 10 watermark block.