# A Robust Image Watermarking Scheme Based on SVD in the Spatial Domain
## 1 Introduction
Though it achieves a certain degree of robustness under different attacks, the extracted watermark has poor image quality. In [11], [PERSON] and [PERSON] proposed a robust watermarking scheme based on DWT, DCT, and SVD. The host image is segmented into four parts: the up-left part, the up-right part, the bottom-left part, and the bottom-right part. For each part, the DWT followed by the DCT transform is applied. The first two alternating current (AC) coefficients in each DCT coefficient matrix are selected to form a new matrix. At last, a 32 \(\times\) 32 binary watermark is embedded into the AC coefficients matrix in the SVD domain. This method provides a high robustness for image cropping attack, since the four parts in different directions are embedded by the same watermark. However, at the same time, this also brings a high computational cost compared with other algorithms. By using the redundancy of redundant discrete wavelet transform (RDWT), [PERSON] and [PERSON] [12] proposed an RDWT and SVD based watermarking scheme. However, in [13], [PERSON] and [PERSON] presented three vulnerable attacks and proved that the watermarking scheme in [12] is not secure for image copyright protection. To avoid the false positive problem, [PERSON] and [PERSON] [14] proposed a DWT and shuffled SVD (SSVD) [15] based robust watermarking scheme. Instead of embedding the whole watermark, the principal component of the watermark is embedded into the largest singular value of each block. The experimental results show that the quality of the reconstructed watermark is greatly improved due to the use of SSVD. [PERSON] and [PERSON] [16] proposed a DWT-SVD and DCT based robust watermarking method, which provided another solution for the false positive problem. In their method, a grayscale watermark image is first split into two planes called the most significant bits (MSBs) plane and the least significant bits (LSBs) plane. Then, the DCT coefficients of these two planes are embedded into the middle singular values of each 4 \(\times\) 4 block in HL and LH sub-bands. Compared with the traditional SVD-based watermarking scheme, the hybrid domain watermarking schemes achieve better robustness and invisibility. However, in these methods, a constant scaling factor is used to control the watermark embedding strength, which may not applicable for different images. To make a trade-off between robustness and imperceptibility,Lai [17] proposed a robust watermarking scheme based on SVD and tiny genetic algorithm, where the tiny genetic algorithm was exploited to search for an adaptive scaling factor for watermark embedding. In [18], [PERSON] et al. firstly analyzed the effect of different scaling factors on the quality of host images and extracted watermarks, and then they proposed an optimized watermarking scheme for grayscale images. An optimal scaling factor is identified by a novel evolutionary algorithm called the firefly algorithm (FA) [19]. Unfortunately, these two methods mentioned above cannot resolve the false positive problem during the watermark extraction process [20; 21]. [PERSON] et al. [22] introduced an integer wavelet transform (IWT) and SVD based watermarking scheme, where the artificial bee colony (ABC) algorithm was applied to determine a best scaling factor. To avoid the false positive problem, an extra signature generated by singular vectors is embedded into the host image along with the watermark. Though these improved watermarking schemes have achieved great performance, the use of multiple transforms and optimization algorithms increases the complexity of these schemes immensely. In addition, the false positive problem is still a major challenge in SVD domain watermarking schemes. Therefore, a robust image watermarking scheme with less computational cost and without the false positive problem is urgently needed in SVD domain watermarking schemes. In [23], it was pointed out that the essence of transform domain watermarking is to distribute the energy of the embedded signal over all pixels in the spatial domain.