A new robust digital watermarking based on exponent moments invariants in nonsubsampled contourlet transform domain

Geometric distortions are usually difficult for watermark to survive. It is a challenging work to design a robust image watermarking scheme against geometric distortions. Exponent moments (EMs) is a new kind of orthogonal moment defined on the circular domain. EMs are free of numerical instability so that high order moments can be computed accurately. The modulus of EMs is invariant to geometric transformation. In this paper, we propose a new robust image watermarking based on EMs invariants in nonsubsampled contourlet transform (NSCT) domain. Firstly, the NSCT, which has better directional frequency localization and a fast implementation, is applied on host image. Secondly, the EMs of the low-pass NSCT subband are computed, and the accurate EMs are selected. Finally, the digital watermark is embedded by quantizing the modulus of the selected EMs. Experimental results confirm the validity of our approach and its higher robustness against geometric distortions.