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Optimal Transport for Secure Spread-Spectrum Watermarking of Still Images

Benjamin Mathon 1, 2, * François Cayre 2 Patrick Bas 3 Benoît Macq 4
* Corresponding author
3 LAGIS-SI
LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
4 Communications visuelles
TELE - Laboratoire de Télécommunications et Télédétection [Louvain]
Abstract : This article studies the impact of secure watermark embedding in digital images by proposing a practical implementation of secure spread-spectrum watermarking using distortion optimization. Because strong security properties (key-security and subspace-security) can be achieved using Natural Watermarking (NW) since this particular embedding lets the distribution of the host and watermarked signals unchanged, we use elements of transportation theory to minimize the global distortion (MSE). Next, we apply this new modulation, called Transportation Natural Watermarking (TNW), to design a secure watermarking scheme for grayscale images. TNW uses a multiresolution image decomposition combined with a multiplicative embedding which is taken into account at the distribution level. We show that the distortion solely relies on the variance of the wavelet subbands used during the embedding. In order to maximize a target robustness after JPEG compression, we select different combinations of subbands offering the lowest BERs for a target PSNR ranging from 35 to 55 dB and we propose an algorithm to select them. The use of transportation theory also provides an average PSNR gain of 3.6 dB on PSNR with respect to the previous embedding for a set of 2,000 images.
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Benjamin Mathon, François Cayre, Patrick Bas, Benoît Macq. Optimal Transport for Secure Spread-Spectrum Watermarking of Still Images. IEEE Transactions on Image Processing, Institute of Electrical and Electronics Engineers, 2014, 23 (4), pp.1694-1705. ⟨10.1109/TIP.2014.2305873⟩. ⟨hal-00940754v2⟩

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