# Robust Image Watermarking in Spatial Domain Utilizing Features Equivalent to SVD Transform
## 1 Introduction
From the evolutionary algorithm family, the firefly algorithm (FA) [42], artificial bee colony (ABC) [43], particle swarm optimization (PSO) [44], genetic algorithm (GA) [41], differential evolution (DE) [17], and teaching-learning based optimization (TLBO) [45] have all made significant contributions to watermarking. By viewing watermarking as a multi-objective problem, [PERSON] et al. [46] proposed an intelligent watermarking scheme that uses PSO to determine the optimal parameters. In some instances, it is possible to achieve transform domain-equivalent features in the spatial domain, which could be used for watermarking with the same effect as transform domain watermarking. The direct current (DC) value of the DCT of any image is the average of its pixels value. Considering the complexity of DCT, some researchers have proposed watermarking in the spatial domain by directly altering the pixel's value, which has the same effect, as the watermark information is embedded by modifying the direct current (DC) value [17; 47; 48; 49; 50]. Similarly, watermarking techniques based on SVD transform mostly insert the watermark in the singular values of the host image obtained by the SVD transform [24; 51]. The implementation of SVD is a time-consuming process due to the multiplication of matrices [49; 52]. In response to this issue, [PERSON] et al. [49] proposed a  
Figure 1: The general framework of an image watermarking scheme. robust watermarking scheme in the spatial domain based on SVD. Using matrix norm, a binary watermark is inserted in the maximum singular value of each image block in the spatial domain. Although the SVD-based image watermarking schemes, discussed above, have achieved a certain level of success, their resistance to some simple attacks is not yet acceptable. These attacks simply attempt to harm the watermark by relocating pixels without changing their intensity. In order to combat such attacks, this research aims to develop a scheme capable of performing effective image watermarking in the spatial domain. Unlike the existing schemes [49], the proposed approach uses the redistributed invariant discrete wavelet transform (RIDWT) concept proposed by [PERSON] et al. [27] before obtaining singular values for watermark embedding. It is invariant to row and column flips as well as ninety-degree rotations. The proposed scheme replicates the concepts in the spatial domain that they have used in the transform domain. This is accomplished by simply relocating the image's pixels to their new locations and performing a normalization process. The singular values of a matrix, as well as its transpose, rotation, and row and column flip matrices, are all the same. The singular values will remain the same regardless of how the values are permuted, so the order of the entries in a matrix is irrelevant. Motivated by the property of a matrix's singular values, this study proposes a novel approach to image watermarking. Initially, the pixels in the cover image are rearranged to ensure that every block of the image has the same pixel values when rotated by 90\({}^{\circ}\) degrees, and its row and column are flipped. Blocks of this new image under these attacks will have the same pixel values, and subsequently, the singular values of these blocks are invariant to these attacks. Due to the high complexity of the SVD transform, in the proposed scheme, the matrix 2-norm is utilized to obtain the maximum singular block-wise value. This maximum singular value is modified by a quantization factor, and the difference between the original and modified singular values is calculated. Based on this, a difference block is obtained to directly modify the host image block's pixel value so that the total magnitude of change equals the change in the singular values before and after embedding. Using a set of common image distortion attacks, ten standard test images, and four binary watermarks, we evaluated the efficacy of the proposed watermarking scheme.