CA2377900A1 - A method for generating and decoding image dependent watermarks - Google Patents

Abstract

A method for generating image dependent watermarks is described. The method is based on a novel magnitude coding technique which renders the watermark dependent of the image. In addition, it is shown how to incorporate constraints on the visibility of the watermark as well as constraints arisin g from the fact that pixels must be specified within the range 0 and 255. Furthermore, it is demonstrated that the method is flexible and easily applicable to any combination of transform and/or spatial domain watermarks and/or constraints.

Description

A method for generating and decoding image dependent watermarks s Technical Field The present invention relates to methods of generating and decoding watermarks in images according to the preamble of the independent claims.
Background Art The idea of using a robust digital watermark to detect and trace copyright violations has stimulated significant interest among artists and publishers in recent years. Podilchuk (Podilchuk & Zeng 1998) gives three important requirements for an effective water-marking scheme: transparency, robustness and capacity.
Transparency refers to the fact that we would like the 2o watermark to be invisible. The watermark should also be robust against a variety of possible attacks by pirates.
These include robustness against compression such as JPEG, scaling and aspect ratio changes, rotation, cropping, row and column removal, addition of noise, 2s filtering, cryptographic and statistical attacks, as well as insertion of other watermarks and the watermark copy attack proposed by Kutter (Kutter, Voloshynovskiy Herrigel 2000) in which a watermark is estimated from one image and added to another one.
3o The third requirement is that the watermark be able to carry a certain amount of information i.e.
capacity. In order to attach a unique identifier to each buyer of an image, a typical watermark should be able to carry at least 60-100 bits of information. However few 3s publications deal with 60 or more bits.
Watermarking methods can be divided into two broad categories: spatial domain methods such as (Bender, CONFIRMATION COPY

Gruhl & Morimoto 1996, Pitas 1996) and transform domain methods which have for the most part focused on DCT
(Podilchuk & Zeng 1998, Barni et al. 1998), DFT (Pereira & Pun 1999) and most recently wavelet domain methods (Podilchuk & Zeng 1998, Barni, Bartolini, Cappellini, Lippi & Piva 1999). Transform domain methods have several advantages over spatial domain methods. Firstly, it has been observed that in order for watermarks to be robust, they must be inserted into the perceptually significant Zo parts of an image. For images these are the lower frequencies which can be marked directly if a transform domain approach is adopted. Secondly, since compression algorithms operate in the frequency domain (-for example DCT for JPEG and wavelet for EZW) it is possible to optimize methods against compression algorithms.
Thirdly, certain transforms are intrinsically robust to certain transformations. For example, the DFT domain has been successfully adopted in algorithms which attempt to recover watermarks from images which have undergone affine transformations (Pereira & Pun 1999).
While transform domain watermarking clearly offers benefits, the problem is more challenging since it is more difficult to generate watermarks which are adapted to the human visual system (HVS). The problem arises since constraints on the acceptable level of distortion for a given pixel may be specified in the .
spatial domain. In the bulk of the literature on adaptive transform domain watermarks, a watermark is generated in the transform domain and then the inverse 3o transform is applied to generate the spatial domain counterpart. The watermark is then modulated as a function of a spatial domain mask in order to render it invisible. However this spatial domain modulation is suboptimal since it changes the original frequency domain watermark. In the case of a DFT domain watermark, multiplication by a mask in the spatial domain corresponds to convolution of the magnitude of the spectrum. Unfortunately, to correctly account for the effects of the mask at decoding a deconvolution problem would have to be solved. This is known to be difficult and to our knowledge in the context of watermarking this problem has not been addressed. Methods proposed in the literature simply ignore the effects of the mask at decoding. One alternative which has recently appeared is the attempt at specifying the mask in the transform domain (Podilchuk & Zeng 1998). However other authors (e. g. Swanson (Swanson, Zhu & Tewfik 1998)) have noted the importance of masking in the spatial domain even after a frequency domain mask has been applied.
The existing technologies exhibit at least one of the following problems:
s5 1. Less than 60 bits are encoded.
2. sub-optimal spatial domain modulation is applied to reduce visibility.
3. truncation is applied to deal with values greater than 255 or less than 0 in the image.

4. The watermark is not image dependent and in particular does not resist against the watermark copy attack which estimates the watermark from one image and adds it to another.

5. Cannot be optimized against JPEG
compression.

6. Uses an additive watermark which is easily copied, or attacked by denoising and perceptual remodulation as proposed by Voloshynovskiy (Voloshynovskiy, Herrigel, Baumgartner, Pereira & Pun 2000) .

7. At embedding the image is treated as noise.
Disclosure of the Invention It is the object of the present invention to provide a method of the type mentioned above that is capable of dealing with at least some, preferably all of these problems.
According to the present invention, the problem is solved by the method of the independent claims.
Preferred embodiments are described in the dependent claims.
The present method is suited for watermarking still images or video data.
Modes for Carrying Out the Invention Formulation of a preferred embodiment:
We formulate the embedding process as a constrained optimization problem. We assume that we are given an image to be watermarked denoted I. If it is an RGB image we work with the luminance component though the same methodology can be applied to other color spaces. We are 2o also given a masking function V(I) which returns 2 matrices of the same size of I containing the values ~pi~~ and Oni~~ corresponding to the amount by which pixel Ii~~ can be respectively increased and decreased without being noticed. These can be determined by noise visibility functoins NVF as proposed by Voloshynovskiy (Voloshynovskiy, Herrigel, Baumgaertner & Pun 1999) or other visual models such as those proposed by Osberger (Osberger, Bergmann & Maeder 1998). We note that these Opi~~ and Oni~~ are not necessarily the same since we ao also take into account truncation effects. That is pixels are integers e.g. in the range 0-255, consequently it is possible to have a pixel whose value is 1 which can be increased by a large amount, but can be decreased by at most 1. In the general case, the function V(I) can be a complex function of texture, luminance, contrast, frequency and patterns.

We wish to embed a message m=(ml,m2...mM), where miEfO,l~ and M is the number of bits in the message. In general, the binary message may first be augmented by a checksum and/or coded using error s correction codes such as BCH or turbo codes to produce a message me of length Mc=512. Without loss of generality we assume the image I is of size 128x128 corresponding to a very small image. For larger images the same procedure is adopted for each 128x128 large block. To embed the 1o message, we first divide the image into 8x8 blocks. In each 8x8 block we embed 2 bits from mc. For each 8x8 block we select, using a key, 2 mid-frequency DCT
coefficients in which we will embed the information bits.
We then have to solve the following constrained minimization problem:
min fx ; Ax <- b (1) x where x= [x11 ... xg1 x12 .° x82 °~ x18 ~° x88 t is a vector of offsets to be added to the DCT coefficients of the 8x8 block. x is arranged column by column and the values of this vector are to be varied during minimization. f is a vector of zeros except in the positions of the 2 selected coefficients where we insert a -1 or 1 depending on whether we wish to respectively increase or decrease the value of the coefficients as determined by me and described in the next section. fx denotes the scalar product of these vectors. Ax S b contain the constraints which are partitioned as follows.
A - IDCT b - OP ( 2 ) - IDCT ~ O
where IDCT is the matrix which yields the 2D inverse DCT
transform of x (with elements of the resulting image 3s arranged column by column in the vector). If we let Did be the coefficients of the 1D DCT transform then it is easily shown that the matrix IDCT is given by:
D11D11 ... D1sD11 -D11~21 .. . Dl$D21 .. . D11D81 .. . DlsDs1 D21D11 ... DZgDlI D21D21 ... D2sD21 . .. Da1D81 .. . D2sD81 DsiDii . . . D88Dii DslDai . . . DssD2~ . . . DsiDsl . . . DssD81 IDCT = ~ DiiDia . . . D1sD12 DixDaa . . . Dl8Dz2 . . . D11Ds2 . . . DlsDsz D81D12 . . . DssDia DsiDz2 . . . D$$D2z ... Dsl..D82 . .. DssDsa DsiDis . .. DssDls DsiDzs . .. D88D2$ . .. DslDss . .. D$sDsa We also note that we take Op and On to be column vectors where the elements are taken column wise from the matrices of allowable distortions. Stated in this form the problem is easily solved by the well known 2o Simplex method.
Stated as such the problem only allows for spatial domain masking, however many authors (Swanson, Zhu & Tewfik 1996) suggest also using frequency domain masking. This is possible by adding the following constraints:
L <_ x <_ U (3) Here L and U are the allowable lower and 2o upper bounds on the amount we by which we can change a given frequency component. The Simplex method can also be used to solve the problem with added frequency domain constraints.
We note that by adopting this framework, we z5 in fact allow all DCT coefficients to be modified (in a given 8x8 block) even though we are only interested in 2 coefficients at decoding. This is a novel approach which has not appeared in the literature. Other publications select a subset of coefficients to mark while leaving the rest unchanged. This is necessarily suboptimal relative to our approach. In words, we are "making space" for the watermark in an optimal fashion by modifying elements from the orthogonal complement of the coefficients we are interested in, while satisfying spatial domain constraints.
1o Effective Channel Coding:
Rather than coding based on the sign of a coefficient as in (Pereira & Pun 2000), we propose using the magnitude of the coefficient. To encode a 1 we will s5 increase the magnitude of a coefficient and to encode a 0 we will decrease the magnitude. At decoding a threshold Tz will be chosen against which the magnitudes of coefficients will be compared. The coding strategy is summarised in table 1, where c3 is the selected DCT
2o coefficient, Table 1: Magnitude coding sign(ci) bit coding 25 + 0 decrease ci (set L to stop at 0) - 0 increase ci (set U to stop at 0) + 1 increase ci - 1 decrease ci 3o The actual embedding is performed by setting f in equation (1) based on whether we want to increase or decrease a coefficient.
The major advantage of this scheme over encoding based on the sign is that the image is no longer 35 treated as noise. As noted by Cox (Cox, Miller &
McKellips 1999) this is an important characteristic of the potentially most robust schemes since all a priori information is used. Clearly the best schemes should not treat the image as noise since it is known at embedding.
However most algorithms in the literature do not take .advantage of this knowledge except in the extraction of perceptual information. In our case, based on the s observed image DCT coefficient we encode as indicated in table 1 At decoding the image is once again not noise since it contributes to the watermark.
The decoding procedure is simple, we need only take the magnitude of the selected coefficients ci.
so We must then compare them to a threshold Ti. Coefficients greater than the threshold are assigned a value of l, and coefficients smaller than the threshold are assigned a value of 0. Tf ECC was used, the codes are then decoded.
In a superior implementation, soft decoding Zs can be used. Here we calculate the difference between the magnitude of the coefficient ci and the threshold Ti.
The result is used for the soft decoding of the coded sequence. It is well known that soft decoding can provide up to a 3dB gain over hard decoding since all the 2o information is being used. One possible set of codes are the turbo codes which provide a near optimum performance in Gaussian channels. We note that the threshold Ti can be set empirically. Typically the value Ti should be the midpoint between the average magnitude associated with a 2s 1 and the value associated with a 0 at encoding. If other information is available about the noise at decoding, then the value of Ti should be set accordingly.
Another important property of this scheme is that it is highly image dependent. This is an important so property if we wish to resist against the watermark copy attack (Kutter et al. 2000) in which a watermark is estimated from one image (typically by denoising) and added to another image to produce a fake watermark. If this is done, the watermark will be falsely decoded since 35 at embedding and decoding the marked image is an integral part of the watermark. Consequently changing the image implies changing the watermark.

It is also possible to incorporate JPEG
quantization tables into the model in order to increase the robustness of the algorithm. Assume for example that we would like to aim for resistance to JPEG compression s at quality factor 10. Table 2 contains the threshold value thri~ below which a given DCT coefficient will be set to o.
Table 2: JPEG thresholds thri~ at quality factor 10 60 90 130 130 130 l30 130 130 2o In order to improve the performance of the algorithm we can add bounds based on the values in table 2 to the amount we increase a coefficient. In particular, if we wish to embed a 1 we need only increase the mag-nitude of a coefficient to the threshold given in table 2 2s iii. order for it to survive a JPEG compression at quality factor 10. This is accomplished by setting the bounds L
and U. Since 2 bits are embedded per block, the remaining energy may be used to embed the other bit. It is important to note that it may not be possible to 3o achieve the threshold since our visibility constraints as determined by V in the spatial domain must not be viol-ated, however the algorithm will embed as much as much energy as possibly via the minimization in equation 1. We note that we choose only to embed the watermark in 35 randomly chosen coefficients where the value in table 2 is less than 70 since for larger values we will require more energy to be sure that the coefficient survives at low JPEG compression. We avoid the 4 lowest frequency components in the upper left hand part of the DCT block since these tend to be visible even with small modifications.

Extensions While the algorithm has been detailed in the case of the DCT, it is readily applicable to any watermarking domain Zo (i.e. the coefficients c can either be in the space domain or a transform domain), and further visibility constraints can be imposed in the transform and/or spatial domains. In the case of the DCT domain, we have moved coefficients towards 0 to encode a 0 and increased the magnitude to encode a 1. In the general case, we should move a coefficient ci towards its expected value Vi to encode a 0 and move it away from (increase the magnitude of the difference from) the expected value to encode a 1. In the case of a spatial domain approach, 2o this would consist of moving pixels away from the local mean Vi to encode a 1 and towards the local V mean to encode a 0. The local mean would be calculated over the pixel to be modified and neighboring pixels thereof.
In the case of the spatial domain, i.e. we select our coefficients ci in the spatial.domain, we can specify the visibility constraints in the spatial domain and/or in a transform domain and carry out the optimization from there.
We also note that instead of using just one 3o coefficient per bit, we may use error correction coding or in the simplest case the repetition code where each bit is encoded several times. At decoding, we could use the average, median or other type of estimate depending on our estimate of the noise to combine the information.
We further note the extension to video watermarking. In fact the extension is straightforward, since we need only apply the algorithm to each frame.

This is an extremely powerful method of overcoming averaging attacks within video since the watermark changes from frame to frame.
In general, the present method starts from a still image of a single video image frame I. It then derives a set c of coefficients ~c2, ... cN~ from this image. The set c can either correspond to the values of the image in the space domain (e.g. the luminance or the so r, g or b coefficients) or in some transform domain (e. g.
c can be a vector of the DCT coefficients, the Fourier magnitude coefficients or the coefficients of the discrete wavelet transform).
Then, some of the coefficients ci are s5 selected for encoding the bits of the message mc. This selection can e.g. be based on some secret key, which is used to derive the indices i of the coefficients to be selected.
The selected coefficients will either be 2o increased or decreased to encode the corresponding bit.
To decide if a coefficient is to be increased or decreased, a test function gi(c) is calculated for each coefficient. This function can depend on all or a subset of all coefficients in set c. Then, the following table 25 is used for deciding if c1 is to be increased or decreased:
Table 3: generalized magnitude coding 3o gi (c) bit encoding true 0 decrease ci false 0 increase ci true 1 increase ci false 1 decrease ci As it is obvious to a person skilled in the art, the column titled "bit" could also be inverted, i.e.
the table could equivalently be written as:
Table 3': generalized magnitude coding gi(c) bit encoding true 1 decrease ci false 1 increase ci 1o true 0 increase ci false 0 decrease ci Such a coding is considered to lie equivalent to the one of table 3.
As mentioned above, the scheme of Table 3 or 3' has the advantage that it depends on the image to be watermarked and therefore resists the watermark copy attack.
Preferably, gi(c) is defined such that it is 2o true if and only if ci > Vi, where Vi is the expected value mentioned above, e.g. 0 (in particular if the coefficients c are in the DCT or DFT domain) or a local mean at the position of said coefficients (in particular when the coefficients c are in the space domain). In this case, in the first line of table 3 (ci > Vi and bit = 0), c1 should not be decreased below Vi. In the second line of table 3 (ci < Vi and bit = 0), ci should not be increased above Vi.
However, gi(c) could e.g. also depend on the 3o values of coefficients ck that lie adjacent to ci.
The optimization step as described in Eq. (1) can be generalized as follows:
In order to apply the watermark, a set of additive offsets x = ~xl, ... xN} must be calculated, which is to be added to or subtracted from the set c of coefficients derived from the image, i.e. ci . ci + xi for all i = I to N. The offsets x are calculated by minimizing or maximizing the value of a scalar product f-x of the vectors f and x as described in Eq. (1). The condition in Eq. (1) can be expressed in more general terms by saying that a Boolean valued boundary function a(x), which depends on the offsets x, must be true.
In the above embodiments, two different possibilities for defining a(x) are described, which can be used alternatively or in combination.
1o In Eq. (2) , a (x) is true if Ax 5 b, wherein A
is a double matrix of the inverse DCT. If, more generally, a transform function t(I) of the image (also other than DCT) is used to generate the set c of coefficients, the limitation in Eq. (1) can be expressed is as follows: a(x) is false if the conditions t-2 (x) 5 Op and t-Z (x) >_ ~n (4) are not fulfilled. If transform function t is 2o a linear transform expressed as a matrix T, i.e. c = T-I, the boundary function a(x) is false if the condition A-x _< b is false, wherein matrix A and vector b are defined (analogously to Eq. (2)) by 25 A = T -1 ; b = 'p . (5) _ T ~n The boundary function a(x) can achieve one or several of the following goals:
a) prevent overflow/underflow conditions 3o and/or b) ensure a minimum quality of the image with the watermark embedded therein and/or c) prevent unnecessarily large values of the offsets x in view of a lossy compression algorithm, such 35 as e.g. the JPEG compression algorithm.

In the above examples, goals a) and b) are achieved by the boundary conditions in Eqs. (1) and (2) or (4) and (5) because the values of Op and On prevent overflow/underflow in the space domain as well as image degradation.
Goal c) is can be achieved by the limitation of Eq. (3), i.e. with the lower and upper limits L and U
of c. To do this, L and U are calculated for each selected coefficient ci by the following steps:
so - Retrieving a threshold value thri for ci.
This value is given by the compression algorithm the watermark is to be proof against: It is the value thrl for which the compression algorithm suppress-es ci if the magnitude of ci is smaller than thrz, and - If the magnitude of the coefficient ci is smaller that the threshold value thri and the magnitude of the coefficient is to be increased, the upper limit Uz is set approximately to the difference between thri and the magnitude of ci. By "approximately", it is understood 2o that the upper limit is exactly equal to or slightly higher than this difference. This ensures that the coefficient will make it through the compression without wasting too much energy, i.e. without making them unnecessarily large.
While there are shown and described presently preferred embodiments of the invention, it is to be dis-tinctly understood that the invention is not limited thereto but may be otherwise variously embodied and prac-so ticed within the scope of the following claims.

References:
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E. J. Delp, eds, 'Security and Watermarking of Multimedia Contents', Vol.
3657, The Society fox Imaging Science and Technology (IS&T) and the International Society for Optical Engineering (SPIE), SPIE, San Jose, California, U.S.A., pp. 31-39.
*http://lci.die.unifi.it/Publications/swmc99-b4.ps.gz Barni, M., Bartolini, F., Cappellini, V., Piva, A. & Rigacci, F. (1998), A
M.A.P. identification criterion for DCT-based watermarking, in 'EUSIPCO'98', Rhodes, Greece.
Cox, I. J., Miller, M. L. & McKellips, A. L. (1999), 'Watermarking as communications with side infoxmation', Proceedings of the IEEE 8'T(7), 112'1-1141. .
Kutter, M., Voloshynovskiy, S. &. Herrigel, A. (2000), Watermark copy attack, iw P. Wah Wong & E. J. Delp, eds, 'IS&T/SPIE's 12th Annual Symposium, Electronic Imaging 2000: Security and Watermarking of Multimedia Content II', Vol. 39'T1 of SPIE Proceedings, San Jose; California USA.
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Pereira, S. & Pun, T. (1999), Fast xobust template matching for affine resistant watermarks, in '3rd International Information Hiding Workshop', Dreseden, Germany.
Pereira, S. & Pun, T. (2000), A framework for optimal adaptive dct watermarks using linear programming, in 'Tenth European Signal Processing Conference (EUSIPCO'2000)', Tampere, Finland.
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Swanson, M. D., Zhu, B. & Tewfik, A. (1996), Robust data hiding for images, in '7th TEEE Digital Signal Processing Workshop', Loen, Norway, pp. 3?-40.
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Voloshynovskiy, S., Herrigel, A., Baumgartner, N., Pereira, S. & Pun, T.
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Claims (18)

Claims

1. A method for embedding a watermark in an image I comprising the steps of:

selecting at least one coefficient c i from a set c = {c1, ... c N} of coefficients, wherein said set of coefficients corresponds to said image or a transform thereof, and wherein said coefficients c i are selected to be used for encoding a message m c, calculating, for each of said selected coefficients c i, a Boolean valued test function g i(c) depending on at least one of said coefficients and modifying each of said selected coefficients c i to encode a bit of said message m c by increasing or decreasing said selected coefficient c i according to the following table:

g i(c) bit encoding true 0 decrease c i false 0 increase c i true 1 increase c i false 1 decrease c i

2. The method of claim 1 wherein g i(c) is true if the coefficient c i is larger than a value V i and false if c i is smaller than said value V i, wherein said value V i is an expected value of said coefficient c i.

3. The method of claim 2, wherein said value V i is 0 or a local average at a position of said coefficient c i.

4. The method of one of the preceding claims comprising the step of calculating a set of additive offsets x = {x1, ... x N} to be added to or subtracted from said set c by minimizing or maximizing the value of a scalar product f.cndot.x, wherein f is a vector containing -1 for each of said selected coefficients to be increased and 1 for each of said selected coefficients to be decreased and 0 of all other coefficients, wherein said minimizing or maximizing is carried out under the condition that a Boolean valued boundary function a(x) of said set of offsets x is true, and wherein said boundary function a(x) provides a limitation against overflow/underflow and/or ensures a minimum quality of said image with said watermark embedded therein and/or prevents unnecessarily large values of the offsets x in view of a lossy compression algorithm.

5. The method of one of the preceding claims, wherein said set of coefficients c is a transform function t of said image I, i.e. c = t(I).

6. The method of claims 4 and 5, wherein said boundary function a(x) is false if the conditions t-1(x) <= .DELTA.p and t-1(x) >= .DELTA.n are not fulfilled, where .DELTA.p and .DELTA.n are sets of upper and lower boundaries of modifications in the values of said image.

7. The method of claim 6, wherein said transform function is a linear transform expressed as a matrix T, i.e. c = T.cndot.I, and wherein said boundary function a(x) is false if the condition A.cndot.x <= b is false, wherein matrix A and vector b are defined by

8. The method of one of the claims 4, 6 or 7, wherein said boundary function a(c) is false if the condition L <= x <= U is false, wherein L = {L1, ... LN} and U
- {U1 ... U N} are lower and upper limits of x.

9. The method of claim 8, wherein g i(c) is true if the coefficient c i is larger than a value V i and false if c i is smaller than said value V i, wherein said value V i is an expected value of said coefficient c i, and wherein, if said coefficient c i is to be decreased and is larger than said value V i, its lower limit L i is set at least to said value V i and, if said coefficient c i is to be increased and is smaller than said value V i, its upper limit U i is set smaller or equal to said value V i.

10. The method of one of the claims 8 or 9 comprising, for each of said selected coefficients c i, the steps of, retrieving a corresponding threshold value thr i of a lossy compression scheme, wherein, in said lossy compression scheme, said selected coefficient c i would be suppressed if its magnitude is smaller than thr i, and if the magnitude of said coefficient c i is smaller that the threshold value thr i and the magnitude of said coefficient is to be increased, setting the corresponding upper limit U i approximately to the difference between the threshold value thr i and the magnitude of the coefficient c i.

11. The method of claim 10, wherein said lossy compression scheme is selected from one of the following compression schemes: JPEG, MPEG, LZW, in particular JPEG.

12. The method of one of the claims 5 - 11, wherein said transform function f is the discrete cosine transform, discrete Fourier transform or discrete wavelet transform.

13. The method of one of the preceding claims wherein said expected value V i is 0 or a local mean at a position of said coefficient c i.

14. The method of one of the preceding claims wherein at least two coefficients c i are selected from said set c of coefficients.

15. The method of one of the preceding claims, wherein said message m c is derived from an original message using turbo codes.

16. A method for decoding the watermark generated by the method of one of the preceding claims comprising the step of comparing each selected coefficient ci to a threshold value Ti, wherein said threshold value Ti is a value between an expected value of ci when encoding a bit of 1 and an expected value of ci when encoding a bit of 0.

17. The method of claim 16 wherein soft decoding is used based on a difference ci - Ti.

18. A method for watermarking video data comprising a plurality of consecutive video frames, wherein the method of one of the claims 1 - 15 is applied to at least some of said video frames.