# Robust Image Watermarking Algorithm Based on ASIFT against Geometric Attacks
## 1 Introduction  
With the fast development of information technology, multimedia data has become the most important carrier for information transmission. Digital images, as one of the most important ways for transmitting the information in one or more images, can be easily altered and destroyed by the developed techniques. Thus, to protect the authenticity and integrity of images, schemes applied for copyright protection of images can be essential and meaningful. Based on this purpose, there are mainly two methods proposed to overcome the above problems, which are digital signature [1; 2] and digital image watermarking [3; 4; 5]. Digital signature is a kind of number string produced by the sender, which can be used as the secret key for both senders and receivers. But it can only detect that images have been tampered or not, and it cannot identify the tampered region location. Thus, watermarking technique is proposed as an effective method to solve the copyright issue of image contents. The categories of digital watermarking algorithms can be divided on the basis of their different robustness and functions: robust watermarking, semi-fragile watermarking, and fragile watermarking. Robust watermarking, as its name implies, should have robustness to all kinds of attacks, which is used for copyright protection. On the converse, fragile watermarking is sensitiveto image modification, which includes malicious tampering and un-malicious processing. The last one is semi-fragile watermarking, which can be utilized to make the judgement between malicious tampering and non-malicious modification. Actually, semi-fragile watermarking integrates advantages in robust and fragile watermarking with each other. In addition, semi-fragile watermarking is superior to fragile watermarking when considering the ability of resisting common image operations. In perspective of the domain where the watermark works, watermarking technique can be categorized as spatial or frequency domain [6]. The embedding method of watermark information in spatial domain methods is to directly alter the pixel value of the digital image, and advantages of spatial domain watermarking are easy implementation and low computational complexity. But it has shortcoming that spatial watermarking is not robust to some image processing operations in some degree. Accordingly, the frequency domain methods embed the watermark information by use of modifying frequency coefficients of the original image after transforms. Compared with spatial methods, with the help of mathematical transform, frequency domain watermarking has the better imperceptibility and robustness. There are common mathematical transforms applied in the frequency domain watermarking: discrete wavelet transform (DWT), discrete cosine transform (DCT), singular value decomposition (SVD), and discrete Fourier transform (DFT) [7]. Many typical watermarking schemes are proposed as well as applied in the field of the medical research. Based on Lagrangian support vector regression (LSVR) and lifting wavelet transform (LWT), [PERSON] et al. [8] proposed an efficient image watermarking scheme, where the Arnold scrambled watermark is embedded into the selected blocks from low frequency sub-band by one level DWT. [PERSON] et al. [9] presented an innovative image watermarking scheme based on SVD and integer wavelet transform (IWT) to overcome the false positive problem (FPP). In [9], the singular matrix of the watermark is embedded into the singular values of the host image. To obtain the optimized scaling factor, multi-objective ant colony optimization (MOACO) is utilized. [PERSON] et al. [10] proposed a colour image watermarking algorithm to divide the host image into three channels and calculate the entropy of the patches obtained in the blocks. Certain patches are selected according to the comparison with a predefined threshold for further transforms to embed the watermark. In the aspect of functional magnetic resonance imaging (FMRI) protection, [PERSON] et al.