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The spatial resolution of the human visual system (HVS) decreases rapidly away from the point of fixation (foveation point). By exploiting this fact, we propose a watermarking approach that embeds the watermark energy into the image periphery according to foveation-based HVS contrast thresholds. Compared to other HVS-based watermarking methods, the simulation results demonstrate an improvement in the robustness of the proposed approach against image degradations, such as JPEG compression, cropping and additive Gaussian noise, in terms of subjective measures, based on foveation. In addition, the method proposed for still images is adapted for video and the robustness of the adapted method is tested against ITU H.263+ coding.