An adaptive watermarking using fractal dimension based on random fractional Fourier transform

Based on random fractional Fourier transform (RFrFT), a novel adaptive watermarking algorithm using fractal dimension is proposed. Under fractal dimension, this algorithm is adaptive in the embedding position and the embedding intensity. The robustness and the imperceptibility of the watermarking algorithm are in good balance when block selection, high amplitude selection and amplitude shift keying are employed in this algorithm. Numerical simulation results have demonstrated the effectiveness of the proposed scheme and shown the robustness against attacks of noising, cropping and JPEG compression.

► Based on random fractional Fourier transform, an adaptive watermarking is proposed. ► Under fractal dimension, the algorithm is adaptive in embedding position and intensity. ► Block selection and high amplitude selection are employed in the proposed algorithm. Hence, the robustness and the imperceptibility are in good balance. ► Numerical simulation results have demonstrated the effectiveness and robustness.