Embedding distortion analysis in wavelet-domain watermarking

Imperceptibility and robustness are two complementary fundamental requirements of any watermarking algorithm. Low-strength watermarking yields high imperceptibility, but exhibits poor robustness. High-strength watermarking schemes achieve good robustness but often infuse distortions resulting in poor visual quality in host images. This article analyses the embedding distortion for wavelet-based watermarking schemes. We derive the relationship between distortion, measured in mean square error (MSE), and the watermark embedding modification and propose the linear proportionality between MSE and the sum of energy of the selected wavelet coefficients for watermark embedding modification. The initial proposition assumes the orthonormality of discrete wavelet transform. It is further extended for non-orthonormal wavelet kernels using a weighting parameter that follows the energy conservation theorems in wavelet frames. The proposed analysis is verified by experimental results for both non-blind and blind watermarking schemes. Such a model is useful to find the optimum input parameters, including the wavelet kernel, coefficient selection, and subband choices for wavelet domain image watermarking

A generalised model for distortion performance analysis of wavelet based watermarking

A model for embedding distortion performance for wavelet based watermarking is presented in this paper. Firstly wavelet based watermarking schemes are generalised into a single common framework. Then a mathematical approach has been made to find the relationship between distortion performance metrics and the watermark embedding parameters. The derived model shows that for wavelet based watermarking schemes the sum of energy of the selected wavelet coefficients to be modified is directly proportional to the distortion performance (the mean square error) measured in the pixel domain. The propositions are made using the energy conservation theorem between input signal and transform domain coefficients for orthonormal wavelet bases. Such an analysis is useful to choose the wavelet coefficients during watermark embedding procedure and to find suitable input parameters such as wavelet kernel or the choice of subband