Tatouage robuste d’images par turbo TCQ
Robust image watermarking using Turbo TCQ
Robust watermarking is the art of embedding secret data within an host document. This watermark must be as transparent as possible, in order to preserve fidelity between host and marked document. It must also be robust, i.e. even if marked document is attacked – this concerns both usual multimedia transforms and malicious modifications – it should be possible to read the embedded message. A watermarking scheme is a compromise between transparency, robustness and capacity, i.e. embedded message length. It is widely admitted that watermarking is a communication problem. Thus, recent literacy dealt with digital communications tools to improve watermarking’s compromise. This leaded to the re-discovery of channels with side information available at the encoder (see Fig. 2), and of the corresponding seminal paper by Costa. The author demonstrated how to dramatically improve channel capacity.
Unfortunately, his demonstration is impossible to implement in practice.
This paper deals with a new and simple code following Costa’s paradigm, and with its application to image water marking. After the recall of some theory (Sec. 1), we show how to use scalar quantization to design surjective codebooks, as shown by Fig. 1 This first approach is improved using Trellis-Coded Quantization (Sec. 2.2). Defined by a transition function (see Eq. 4), a trellis is a set of states linked by valued arcs, as illustrated by Fig. 3. In the case of TCQ, those arcs are valued by quantizers. Each possible binary message corresponds to a path, which defines a sequence of scalar quantizers according to Eq. 5. In order to encode or decode a message, we use a customized Viterbi algorithm to find the best path and thus the best sequence of quantizers. For encoding, trellis transitions are enforced by strong a priori in order to output a path equal to the message to be encoded, while decoding process deals with complete trellis. Thanks to iterative principles, Turbo TCQ (TTCQ) improves this coding scheme using two parallel TCQ and interleaving (see Fig. 4).
While TTCQ ensures informed coding (i.e. the ability of fitting codewords to side information), we also use informed embedding according to Eq. 6. Experimental results shows a good level of performance (see Fig. 5): for an embedding rate of 1/1 and to reach an error bit rate lower than 10–5, our scheme is 5.5 dB better than SCS  – a well-known implementation of Costa’s theory.
In Sec. 3, TTCQ-based code is applied to image watermarking. We use an experimental setup similar a reference paper . In order to adapt watermark embedding rate, a spread transform of host DCT samples is done to get side information (see Eq. 7). Then, message to be embedded is encoded thanks to TTCQ and inverse spread transform is computed. Final watermark is added to DCT samples shaping perceptual weights. For that purpose, we use a waterfilling algorithm, given by Alg. 1.
Results detailed in Sec. 4 confirms TTCQ-based code to be a good compromise between performance and complexity. Even with the addition of Gaussian noise, a set of 1200 watermarks has been extracted from 1200 images without any error (see Fig. 6). JPEG-based attack shows our scheme performs better than reference paper’s, as seen in Fig. 7.
Nevertheless, our approach is not completely robust to scaling attacks. This is confirmed by Figs. 8 and 9.
Finally, we conclude this article with a discussion concerning the use of vectorial quantizers. We show that quantization-based channel coding should not use the same lattices as source coding. An example is given by Fig. 10.
Cet article se concentre sur la mise en pratique du schéma idéal de Costa pour la problématique du tatouage de contenus multimédia. Après un rappel de la théorie, nous faisons une utilisation détournée de techniques de quantification pour construire un code correcteur adapté aux canaux avec information adjacente. La suite de l’article est consacrée à l’application de ce code pour le tatouage robuste d’images en niveaux de gris. Les résultats des expérimentations montrent des performances encourageantes, au niveau des papiers de référence du domaine, avec une mise en œuvre simple et efficace.
Watermarking, error correcting codes, image processing, quantization, turbo principle, TCQ
Tatouage, codes correcteurs, traitement d’image, quantification, principe turbo, TCQ
 M. H. M. COSTA, «Writing on dirty paper », IEEE. Trans. on Information Theory, Vol. 29, No. 3, 1983, p. 439-441.
 T. M. COVER, J. A. THOMAS, «Elements of information theory», Wiley-Interscience, 1991.
 I. J. COX, M. L. MILLER, A. L. MCKELLIPS, «Watermarking as communications with side information», IEEE J. Selected Areas Communi., Vol. 16, No. 4, 1998, p. 587-593.
 P. MOULIN, R. KOETTER, «Data-hiding codes », Proceedings IEEE, Vol. 93, No. 12, 2005, p. 2083-2127.
 M. W. MARCELLIN, T. R. FISHER, «Trellis-coded quantization of memoryless and Gauss-Markov sources », IEEE Trans. on Communications, Vol. 38, 1990, p. 82-93.
 J. J. EGGERS, R. BAÜML, R. TZCHOPPE, B. GIROD, «Scalar Costa scheme for information embedding », IEEE Trans. on Signal Processing, 2003.
 V. CHAPPELIER, C. GUILLEMOT, S. MARINKOVIC, «Turbo trellis-coded quantization », Proc. of Int. Symp. on Turbo Codes, 2003.
 M. L. MILLER, G. J. DOËRR, I. J. COX. «Applying informed coding and informed embedding to design a robust, high capacity watermark », IEEE Trans. on Image Processing, Vol. 3, No. 6, 2004, p. 792-807.
 I. J. COX, M. L. MILLER, J. A. BLOOM, «Digital watermarking», Morgan Kaufmann Publishers, 2002.
 L. LIN, G. J. DOËRR, I. J. COX, M. L. MILLER, «An efficient algorithm for informed embedding of dirty paper trellis codes for watermarking», Proc. of Int. Conf. on Image Processing, Vol. 1, 2005, p. 697-700.
 J. MARTINET, « Les réseaux parfaits des espaces euclidiens », Masson, 1996.
 S. PATEUX, G. LE GUELVOUIT, «Practical watermarking scheme based on wide spread spectrum and game theory», Signal Processing: Image Communication, No. 18, 2003, p. 283-296.
 J. K. SU, B. GIROD, «Power-spectrum condition for energy-efficient watermarking », Proc. of Int. Conf. on Image Processing, 1999, p. 301-305.
 Q. LI, I. J. COX, «Improved spread transform dither modulation using a perceptual model: robustness to amplitude scaling and JPEG compression», Proc. of Int. Conf. on Acoustics, Speech and Signal Processing, 2007.