# Blind Watermarking of Color Medical Images Using Hadamard Transform and Fractional-Order Moments
## 2 Related Work  
Color medical images are the result of medical imaging of the interior of the human body for clinical analysis and medical intervention to reveal internal structures hidden by the skin and bones for diagnosing and treating disease. Medical images have also been established as a public database for medical purposes. Due to the rapid increase in different types of attacks on color image watermarking systems, the successful extraction of the embedded watermark has become a common challenge in any current watermarking system because of higher sensitivity for different geometric, signal processing, and combination attacks. Any slight change in image pixel geometry leads to a false extraction process. For this, many researchers have enhanced their efforts toward realizing many watermarking systems based on different invariant moments to attain the highest robustness and invisibility of watermarking systems. [PERSON] et al. [19] introduced a robust watermarking method according to polar harmonic Fourier moments (PHFMs) and chaotic maps; accurate and robust PHFMs of the original cover image are computed and chosen depending on Gaussian numerical integration (GNI). The watermark was shuffled using a tent map and then concealed in the amplitudes of the selected PHFMs. The watermark extraction was done by applying PHFMs on watermarked images and the inverse of the embedding process in a blind extraction; this scheme is robust to different common geometric attacks. [PERSON] et al. [20] suggested a digital watermark algorithm based on fractional Charlier moments (FCMs) and singular value decomposition (SVD). In this method, the host cover images are split into \(8\times 8\) blocks. Then, the FCMs are computed for every block to obtain the FCM matrix, which SVD has decomposed by using adaptive pixel embedding with a quantization step. The method introduced the best superior fineness to reconstruct the watermarked images reasonably. [PERSON] et al. [21] introduced a watermarking algorithm depending on the TRHFMs' computation of the input image. The selection of TRHFMs is randomly made using logistic maps to generate a zero-watermarked image by applying XOR between a binary watermark image and a binary feature image. This algorithm is robust to diverse types of attacks compared to similar methods. [PERSON] [22] introduced a method using the Tchebichef-moments-based watermarking concept. The binary watermark is first shuffled using Arnold transformation and then concealed in the randomly selected Tchebichef moments matrix. This scheme is resistant to different classes of attacks, especially processing attacks. [PERSON] et al. [23] introduced a watermarking system for medical images using PHFT, where the accurate computation of the chosen moment leads to a robust extraction process. [PERSON] et al. [24] introduced a blind watermarking method using radial Krawtchouk moments and an MLNCML chaotic system. The scheme was tested over standard signal processing and geometric attacks. [PERSON] and [PERSON] [25] introduced a scheme using Tchebichef moments. The watermark logo is shuffled using an Arnold cat map and then embedded in the modified part of the selected moments over the chosen embedding blocks. Finally, the scheme is assessed for robustness versus widespread attacks. Many researchers have revealed the use of quaternion-type moments (QTMs) in most current watermarking methods due to the ability and the advantages of dealing with cover images in a holistic manner [26]. It is more invariant to different image amendments such as rotation, translation, and scaling, since it can eliminate the transmutation parameters due to its invariance properties. It is also more efficient for computational analysis. As a result, [PERSON] et al. [27] introduced a scheme based on QLFMs and logistic maps. Logistic maps were employed on random selections of QLFM coefficients. The extraction process is the inverse operation of the embedding process.