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                      Anatol.Z.Tirkel (Senior Member), Charles F Osborne.

               Scientific Technology, 21 Walstab St, E. Brighton, 3187, Australia.

           Visiting Research Fellow, Department of Physics, Monash University, Clayton 3168 Australia



This paper discusses the feasibility of coding a robust, undetectable, digital water mark on a

standard 512*512 intensity image with an 24 bit RGB format. The watermark is capable of

carrying such information as authentication or authorisation codes, or a legend essential for

image interpretation. This capability is envisaged to find application in image tagging, copyright

enforcement, counterfeit protection, and controlled access. The method chosen is based on linear

addition of the water mark to the image data. The patterns adopted to carry the watermark are

adaptations of m-sequences in one and two dimensions.                  The recovery process is based on

correlation, just as in standard spread spectrum receivers. The technique is quite successful for

one dimensional encoding with binary patterns, as shown for a variety of gray scale test images.

A discussion of extensions of the method to two dimensions, RGB format and non-binary

alphabets is presented. A critical review of other watermarking techniques is included.

1 Background

The art of hiding messages in written text was known to the ancient Greeks as steganography. Many

ingenious schemes to achieve that objective have been devised over the centuries. However, the more

recent development of computer technology and the proliferation of image and graphics type data have

generated the capability and the motivation for electronic watermarking as a means of copyright

protection. There exist two basic classes of electronic water marks: fragile and robust. This paper is

concerned with the construction of the robust type, i.e. one which is resilient to some image distortions

such as pixel or bit tampering, cropping, translation, rotation and shear. At this stage, such a watermark

possesses limited immunity against the first three distortions, but the intention is to improve its

performance in the future. This should be contrasted with a novel technique involving a fragile

watermark as described in [3], where, by deliberate design, any distortions render the watermark non-

recoverable and this becomes proof of tampering. Both methods use LSB manipulation. Walton [3],

also introduces an ingenious and effective palette manipulation technique to increase the watermark

effectiveness by involving the complete RGB image components. A totally different technique and its

variations is reviewed in [4]. Its major advantage is its compatibility with the JPEG format, whilst its

principal disadvantage is that the watermark recovery requires the presence of the unencoded image. In

this respect it differs from the other techniques. Other techniques being investigated are concerned with

encryption of JPEG bit stream and involve the use of checksums [14]. The technique described here

involves a linear addition of the watermark pattern, followed by a correlative recovery. Correlation can

be performed as cyclic or extended, global or character specific operations. Novel methods of defining

correlation can be devised. The traditional decomposition of correlation functions into even and odd, or

periodic and aperiodic components does not apply, because the embedding pattern has periodicity

commensurate with that of the image. So far, the watermarks have been chosen from one and two-

dimensional array patterns based on m-sequences or extended m-sequences [5]. An m-sequence basis is

chosen because of their balance (zero mean), random appearance, optimal autocorrelation properties and

constrained cross-correlation. The water mark has been encoded by the choice of m-sequences and their


2 Method

The encoding method uses LSB addition for embedding the water mark [1], [2], [8], [13]. A similar

method has since been developed commercially by Digimarc [10], who add random multiples of the

LSB on a pixel by pixel basis. Their decoding process is subtractive in the presence of the unencoded

image and seems to be correlative in its absence, although their internet brochure provides little detail

and the algorithm appears not to be published in the literature. The extension of the scheme described

here to multiple LSB's has been considered to be an integral part of the transition to a non-binary

alphabet, such as that offered by the RGB format. The restriction to LSB manipulation has certain

advantages, since in many imaging systems the LSB is corrupted by hardware imperfections or

quantisation noise and hence this form of implementation renders the watermark invisible. The only

significant exception to that is the case of computer generated images, which are free of noise. In that

instance, other means of watermarking are available. The linear addition process is difficult to crack

and makes it possible to embed multiple watermarks on the same image [2]. The decoding process

makes use of the unique and optimal auto-correlation of m-sequence arrays to recover the watermark

and suppress the image content. Since the correlation process involves averaging over long strings of

binary digits, it is relatively immune to individual pixel errors, such as may occur in image transmission.

The correlation process requires the examination of the complete bit pattern and must therefore be

performed off-line, unless some form of dedicated, real-time, parallel processing is involved. Presently,

two image processing hardware platforms (SGS Thomson IMSA100 and a Philips OPTIC-Optimized

Pixel Template Image Correlator) are being evaluated as candidates for on-line performance of the

decoding algorithm. The decoding process is not completely error free, due to partial correlation of the

image data with the encoding sequence. The presence of significant correlation betweeen the image and

the watermark typically results in false peaks and true peak erosion. This in turn can result in

ambiguous or false decoding. In previous work, this was overcome by filtering and dynamic range

compression [2]. These artificial steps would be undesirable in a practical system. Other means such as

redundancy coding restrict the data content of the watermark.          Morphological methods of peak

detection, based on the unique neighbourhood characteristics of the pixel corresponding to the peak

correlation have been evaluated, but so far the improvement attributable to them appears similar to that

of filtering. Neural nets trained for local peak detection are another option for future evaluation.

A typical 128*128 (unfiltered) image encoded with a one dimensional watermark is shown in Fig.1(Top

left). The message is encoded on a line by line basis, using the ASCII character to select a sequence

phase shift. There are numerous message repeats. The decoder output Fig.1(centre left) shows distinct

message correlation peaks (white).         Note that there are significant sidelobes due to image

crosscorrelation effects. The top half of Fig.1. shows encoded images that have been progressively

high-pass filtered, removing 10, 60 and 100 of the spatial frequency components from the total of 128.

The watermark peaks survive all these filtering processes, demonstrating the robustness of the

technique. The image content in the original and the decoded version is rendered negligible after the

second or third of the filters. A different presentation of this process is shown in Fig.2.

3. Watermark properties

An ideal watermark would possess:

(i) High in-phase autocorrelation peak for rows and columns

(ii) Low out-of-phase autocorrelation for rows and columns

(iii) Low cross-correlation between rows and between columns & between rows and columns

(iv) Low cross-correlation with image content

(v) Array diversity

(vi) Balance

(vii) Compatibility with standard image transmission format such as JPEG

(viii) Long span in order to prevent unauthorised cracking

                                              Figure 1
             Upper (left to right: Encoded image after high pass filtering, removing
               (a) 0, (b) 10, (c) 60, (d) 100 of 128 Spatial Frequency Components
 Lower (Centre Left, Bottom Left, Centre Right, Bottom Right) : Corresponding Decoded Patterns
(Medium gray=0, darker=negative, lighter=positive - all image intensities have been suitably scaled)

                                           Fig 2.
         Correlation presented in line format (Watermark peaks are clearly visible)

The first two criteria are required for unambiguous watermark registration, the third is necessary to

avoid scrambling, the fourth minimises image related artefacts, whilst the fifth is concerned with the

information capacity of the watermark. The sixth criterion maximises the significance of the correlation

operation: in the binary case, the minority symbol determines the correlation score.

The seventh criterion requires robustness against the low-pass filtering along a diagonal raster. The

eighth criterion relates to code inversion property. All codes can be generated by a recursion relation

and this can be deduced from a sample of the of the code by solution of a set of simultaneous equations

(matrix inversion). The minimum number of terms required for unambiguous inversion is called the

span. M-sequences have a short span of 2n, where n is the order of the polynomial describing the

recursion relation. This is because of their linear nature. GMW codes use non-linear recursion, which

is optimised to yield much larger spans, with minimum impact on sequence properties. They are

therefore ideal in situations where security is paramount. The sidelobe performance of these has not yet

been evaluated. A search for a mapping to convert two dimensional arrays into GMW format is


Constructions can be optimised for each of these requirements. However, a global optimisation requires

compromise. All criteria have been examined in detail with particular reference to (iv) [8] and (vii).

4 Two-dimensional m-sequence based arrays

M-Sequences can be formed from starting vectors by a Fibonacci recursion relation. They are of

maximal length (2n-1) for a vector of length n. Typically, the alphabet of symbols used to generate the

sequence forms a finite base field, a Galois Field (GF). In most applications, binary or binary derived

base fields such as GF(2) are involved. A good review of non-binary bas field applications can be found

in [12]. The recursion relation can be described by a generating polynomial over the GF. These

polynomials, whose roots are not elements of the base field, themselves form an extension field. Their

solutions (in the extension field) are powers of each other, which is equivalent to sequences being

decimations of each other.

Two dimensional patterns are generated by polynomials in two variables. This is equivalent to a two-

dimensional shift register. One dimensional polynomials have been studied extensively, whilst higher

dimensional constructions have been devised ad-hoc, with specific applications in mind. [5] is one of

the few references which attempts to treat this problem and its extensions to base fields other than


4.1 Some Two-Dimensional Constructions

The autocorrelation function of binary m-sequence is two valued: 2n-1 (in phase), -1 (out of phase). A

two-dimensional construction can be performed using a row by row phase shift. The effect on columns

is that of decimation. Unique phase shifts as determined from Galois Field theory lead to the formation

of columns, which are themselves m-sequences. The resulting array is an unbalanced Hadamard Matrix.

Alternatively, a long sequence can be folded diagonally into an array format [5]. In this manner, the

desirable one-dimensional autocorrelation property can be extended to two dimensions. The encoding

and decoding performance of the Hadamard technique suffers from the image related effects because the

correlations are performed on the (short and thus interference prone) row or column basis. The folded

m-sequence is more immune to these effects, owing to its increased length. However, its information

storage capacity is inferior. We have encoded watermarks by both methods and have found them


There exist other fundamentally two-dimensional constructions. Costas Arrays are optimal in that their

out-of-phase autocorrelation is minimum for shifts in either or both dimensions [6]. (Uniformly low

sidelobe point-spread-function). They have been successfully deployed in radar and sonar, where time

delays and frequency shifts (Doppler) can occur simultaneously. However, they are highly unbalanced

and therefore prone to image related artefacts. Perfect Maps are constructions, where every m*n basis

vector occurs once in a large pattern or map and hence can be used for automatic location. (An m-

sequence is a one dimensional example of this category). The construction algorithm for Perfect Maps

of large dimensions, commensurate with our image sizes is complicated . However, some perfect maps

are also Hadamard Matrices. We have examined examples of these, but still found them to be inferior at

rejecting image related artefacts.

4.2 Extensions to Non-Binary Alphabets

The watermarking scheme demonstrated in the diagrams has been confined to one and two-dimensional

spatial constructions employing a gray scale image. Extensions to colour (RGB) encoding have the

potential of expanding the capabilities. This could be employed for:

(i) Increasing the information content of the watermark.         For example, three independent, two-

dimensional messages could be encoded instead of one.

(ii) Increasing the length of the watermark code to reduce image related effects.

(iii) Redundancy coding.

(iv) Non-binary character sequences.

The last feature is of particular interest because of the difference between the encoding process of the

watermark and the standard embedding of the spreading code on the carrier as practiced in spread

spectrum communications. There, the use of QPSK calls for GF(4) as a natural base field. It also

permits the use of an isomorphism of the characters with complex roots of unity to derive convenient

constructions of the complex correlation. The existence of two quadrature carriers is beneficial, but is

quite irrelevant to the watermarking scheme. The RGB format permits the use of GF(8) as a base field

and does not imply the need for the use of the roots of unity. In fact, it may be possible to devise a

distance based correlation measure, as opposed to the use of complex multiplication. The merits of such

a technique are still being investigated. It may also be feasible to reduce the spectral occupancy of the

watermark by modulating RGB components alternately and using differential coding, as in a more

generalised form of OQPSK or Frank coding. Such a scheme could be incorporated into the JPEG

conversion table. There may be applications of such techniques to spread spectrum communications,

where QPSK is combined with polarization modulation.

5 Non-imaging applications

The watermarking technique discussed here has potential applications to audio copyright protection and

audio system and equalisation control. Two one-dimensional patterns can be embedded in each of the

stereo channels on CD-ROM or DAT. These codes could designed to have a deliberately long span

(such as GMW codes), in order to prevent cracking. These codes could also be employed in automatic

spectral and delay calibration/equalisation of the sound system, because of their optimal impulse

response. This feature could be particularly useful in dynamic situations, where the audio environment

is constantly changing. A technique called Argent has been located on the internet as a commercial

version of CD copyrighting, but so far, meaningful details on this method have been unavailable.

6 Conclusions

This paper demonstrates a method of encoding and recovery of a digital water mark on test images,

using spread spectrum techniques. A critical analysis of the extension of the method to genuine two-

dimensional patterns using non-binary characters is presented.         The ultimate objective is the

construction of an optimal set of colour patterns. A brief outline of the current state of the art is


7 Acknowledgements

The authors would like to extend their gratitude to Ron van Schyndel for his assistance in computer

based image analysis and generation. Their contributions have been invaluable. Acknowledgement is

also made of numerous constructive discussions on the mathematical theory of coding with Dr.Alisdair

McAndrew, Nicholas Mee and Dr.Derek Rogers.

8 References

[1] A.Z.Tirkel, G.A.Rankin, R.M.van Schyndel, W.J.Ho, N.R.A.Mee, C.F.Osborne. Electronic Water

Mark. DICTA-93 Macquarie University, Sydney, December 1993. p.666-672.

[2] R.G. van Schyndel, A.Z.Tirkel, N.R.A.Mee, C.F.Osborne. A Digital Watermark. First IEEE Image

Processing Conference, Houston TX, November 15-17, 1994, vol II, p.86-90.

[3] S.Walton. Image Authentication for a Slippery New Age. Dr.Dobb's Journal, April 1995. p.18-26,


[4] F.M.Boland, J.K.K. Ó Rouanaidh and C.Dautzenberg. Watermarking Digital Images for Copyright

Protection. In publication.

[5]. F.J. MacWilliams and N.J.A.Sloane. Pseudo-random Sequences and Arrays. Proc.IEEE, vol 64,

1715-1729, Dec.1976.

[6] S.W.Golomb and H.Taylor. Two-Dimensional Synchronization Patterns for Minimum Ambiguity.

IEEE Trans. on Information Theory, vol IT-28, no.4, p.600-604, July 1982.

[8] R.G. van Schyndel, A.Z.Tirkel, C.F.Osborne. Towards a Robust Digital Watermark. ACCV'95

Conference, Nanyang Technological University, Singapore, December 5-8, 1995, vol 2, p.504-508

[9] I.S.Reed and R.M.Stewart. Note on the Existence of Perfect Maps. IRE Trans. on Information

Theory. vol IT-8, p.10-12, Jan. 1962

[10]     G.Rhoads.   Frequently   Asked    Questions   About     Digimarc   Signature      Technology.


[11] M.Cooperman. Digital Information Commodities Exchange (DICE). Argent Algorithm used by

CANE Records (Independent Music Label run by University of Miami) Ref.


[12] D.P.Rogers. "Non-Binary Spread Spectrum Multiple-Access Communications". Ph.D.Thesis,

Department of Electrical and Electronic Engineering, University of Adelaide, March 1995.

[13] A.Z.Tirkel, R.G.van Schyndel, C.F.Osborne. "A Two Dimensional Digital Watermark", DICTA'95,

University of Queensland, Brisbane, December 6-8, 1995. p.378-383.

[14] J.A.Lim, A.J.Maeder. “Image Authentication Extension for Lossy JPEG”. DICTA'95, University

of Queensland, Brisbane, December 6-8, 1995. p.210-216.


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