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A robust data hiding scheme that embeds the watermark bits by quantizing the gradient directions of an image is proposed. By embedding the watermark in the angle, the watermark becomes robust to amplitude scaling attacks. To keep the watermark imperceptible and enhance its robustness, it is embedded in the significant gradient vectors of the image. The significant gradient vectors are obtained using discrete wavelet transform (DWT). Thus, the gradient vector at a pixel is first obtained in terms of the DWT coefficients. Then the gradient direction is quantized by modifying the DWT coefficients corresponding to the gradient vectors. Experimental results confirm that the proposed gradient direction watermarking (GDWM) method is robust to various types of attacks, specially amplitude scaling at tacks, and results in watermarked images of high fidelity.