# Robust Image Watermarking in Spatial Domain Utilizing Features Equivalent to SVD Transform
## 1 Introduction  
In recent years, digital media has evolved into an essential component of the routine activities of each and every person. Due to recent technical breakthroughs, it is now simpler than ever to manipulate and share digital multimedia files. However, this has raised concerns about the unauthorized copying of copy-protected media, and its protection is a challenging task [1; 2; 3]. The digital watermarking scheme was developed to handle such issues [4; 5; 6; 7; 8], and since then, it has been developed into a novel area of study and is generating substantial attention among scientists [9; 10]. Watermarking is a relatively new field of study that provides effective solutions for a number of security applications, such as authentication and copyright protection [11; 12]. Several watermarking methods have been created, which can be classified according to various factors, such as robust or fragile watermarking, visible or invisible watermarking, spatial or frequency domain watermarking, and hybrid domain watermarking. In the following paragraphs, a concise analysis of watermarking schemes that take these factors into consideration is provided. However, interested researchers may refer to [9; 10; 12; 13; 14; 15] to obtain more details about watermarking techniques. There are two main components of any watermarking scheme--embedding and extraction. A general framework for image watermarking is given in Figure 1.  
Watermarking schemes that directly modify the image pixels to insert the watermark's information without any transformation are considered spatial domain watermarking schemes [16; 17; 18]. The most basic method of watermarking in this category is to introduce the watermark by modifying the least significant bits (LSBs) of the pixels in the cover image [19; 20]. These watermarking techniques are simple to implement and require less effort than other schemes, although they generally compromise the quality. In contrast, frequency-domain watermarking techniques incorporate watermark information in frequency coefficients by converting spatial representation into the frequency domain. Several transforms have been used in watermarking, including discrete wavelet transform (DWT), discrete cosine transform (DCT), discrete Fourier transform (DFT), discrete fractional Fourier transform (DFrFT), quaternion wavelet transform (QWT), singular value decomposition (SVD), and their combinations [21; 22; 23; 24; 25; 26]. [PERSON] et al. [27] presented image watermarking based on the redistributed invariant discrete wavelet transform (RIDWT). This scheme is invariant relative to row and column flips as well as ninety-degree rotations. It is accomplished by simply relocating the image's pixels to their new places, applying the wavelet transform, and performing some normalization. [PERSON] et al. [28] suggested a blind color image watermarking approach with variable steps based on the Schur decomposition. Using the Walsh-Hadamard transform (WHT), [PERSON] et al. [29] presented an effective, resilient, and invisible blind color image watermarking technique. [PERSON] et al. [30] proposed a robust image watermarking strategy that focuses on the protection of biometric images by combining discrete wavelet transform, SVD transform, and chaotic encryption. Using a hybrid transform consisting of discrete wavelet transform and singular value decomposition, [PERSON] et al. [31] proposed a watermarking scheme to preserve medical images. The suitable choice of the parameters used in watermarking and location selection to embed the watermark has been a hectic task. Several researchers have used optimization techniques and machine learning for this task, such as fuzzy logic, neural networks, support vector machine, and evolutionary algorithms (EAs) [17; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41].