Multiscale Gradient Direction Quantization

We propose a robust quantization-based image watermarking scheme, called the gradient direction watermarking (GDWM), based on the uniform quantization of the direction of gradient vectors. In GDWM, the watermark bits are embedded by quantizing the angles of significant gradient vectors at multiple wavelet scales. The proposed scheme has the following advantages: 1) increased invisibility of the embedded watermark because the watermark is embedded in significant gradient vectors, 2) robustness to amplitude scaling attacks because the watermark is embedded in the angles of the gradient vectors, and 3) increasedwatermarking capacity as the scheme uses multiple-scale embedding.

The gradient vector at a pixel is expressed in terms of the discrete wavelet transform (DWT) coefficients. To quantize the gradient direction, the DWT coefficients are modified based on the derived relationship between the changes in the coefficients and the change in the gradient direction. Experimental results show that the proposed GDWM outperforms other watermarking methods and is robust to a wide range of attacks, e.g., Gaussian filtering, amplitude scaling, median filtering, sharpening, JPEG compression, Gaussian noise, salt & pepper noise, and scaling.