1200 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 6, NO. 4, DECEMBER 2011 Robust Image Watermarking Based on Multiscale Gradient Direction Quantization Ehsan Nezhadarya, Student Member, IEEE, Z. Jane Wang, Member, IEEE, and Rabab Kreidieh Ward, Fellow, IEEE Abstract—We propose a robust quantization-based image wa- termarking 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 mul- tiple wavelet scales. The proposed scheme has the following ad- vantages: 1) increased invisibility of the embedded watermark be- cause 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) increased watermarking capacity as the scheme uses multiple-scale embed- ding. The gradient vector at a pixel is expressed in terms of the dis- crete wavelet transform (DWT) coefficients. To quantize the gra- dient direction, the DWT coefficients are modified based on the de- rived 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 compres- sion, Gaussian noise, salt & pepper noise, and scaling. Index Terms—Amplitude scaling attacks, digital watermarking, gradient direction quantization, quantization-based water- marking. I. INTRODUCTION W ATERMARKING approaches can generally be classified into two categories [1]: spread spectrum (SS)-based watermarking [2], [3], and quantization-based watermarking [4]–[6]. The SS type watermarking, adding a pseudorandom noise-like watermark into the host signal, has been shown to be robust to many types of attacks. Based on the distribution of the coefficients in the watermark domain, different types of optimum and locally optimum decoders have been proposed [7]–[10]. Many SS-based methods have been developed. Wang et al. used a key dependent randomly generated wavelet filter bank to embed the watermark [11]. La- houari et al. proposed a robust watermarking algorithm based on balanced multiwavelet transform [12]. Bi et al. proposed a watermarking scheme based on multiband wavelet transform and empirical mode decomposition (MWT-EMD) [13]. Manuscript received February 24, 2011; revised July 12, 2011; accepted July 18, 2011. Date of publication August 04, 2011; date of current version November 18, 2011. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Alessandro Piva. The authors are with the Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC, V6T 1Z4, Canada (e-mail: ehsann@ece.ubc.ca; zjanew@ece.ubc.ca; rababw@ece.ubc.ca). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIFS.2011.2163627 In quantization watermarking, a set of features extracted from the host signal are quantized so that each watermark bit is rep- resented by a quantized feature value. Kundur and Hatzinakos proposed a fragile watermarking approach for tamper proofing, where the watermark is embedded by quantizing the DWT co- efficients [14]. Chen and Wornell [5] introduced quantization index modulation (QIM) as a class of data-hiding codes, which yields larger watermarking capacity than SS-based methods [8]. Gonzalez and Balado proposed a quantized projection method that combines QIM and SS [15]. Chen and Lin [16] embedded the watermark by modulating the mean of a set of wavelet coef- ficients. Wang and Lin embedded the watermark by quantizing the super trees in the wavelet domain [17]. Bao and Ma proposed a watermarking method by quantizing the singular values of the wavelet coefficients [18]. Kalantari and Ahadi proposed a log- arithmic quantization index modulation (LQIM) [19] that leads to more robust and less perceptible watermarks than the con- ventional QIM. Recently, a QIM-based method, that employs quad-tree decomposition to find the visually significant image regions, has been proposed [20]. Quantization-based watermarking methods are fragile to amplitude scaling attacks. Such attacks do not usually degrade the quality of the attacked media but may severely increase the bit-error rate (BER). During the last few years, many improved techniques have been proposed to deal with this issue, including the use of pilot signals [21]–[23], the design of amplitude-scale invariant codes, such as Trellis codes [24], orthogonal dirty paper codes [25] and order-preserving lattice codes [26]. Ourique et al. proposed angle QIM (AQIM), where only the angle of a vector of image features is quantized [27]. Embedding the watermark in the vector’s angle makes the watermark robust to changes in the vector magnitude, such as amplitude scaling attacks. One promising feature for embedding the watermark using AQIM is the angle of the gradient vectors with large mag- nitudes, referred to as significant gradient vectors. A few watermarking methods that rely on the significant wavelet coefficients (which usually correspond to significant edges), have been proposed [28]–[31]. Based on the concept of subimage histogram consistency, Kim and Oh presented a watermarking method for text document images using edge direction histograms [32]. Since this consistency is only valid for text documents, their method can not be directly applied for watermarking other media types. To our knowledge, no image watermarking method based on the directions of the significant gradient vectors has been proposed so far. This paper proposes an image embedding scheme that em- beds the watermark using uniform quantization of the direction 1556-6013/$26.00 © 2011 IEEE