# A Self-Recovery Fragile Image Watermarking with Variable Watermark Capacity
## 1 Introduction  
With the widespread use of mobile imaging devices like smart phones, people can easily obtain and transmit the digital images at any time. On the other hand, the emergence of a great many image-processing tools makes it more convenient for people to modify the digital images according to their wishes. Once a meaningful image is modified by attackers with an ulterior motive, it will bring a serious damage to the integrity and authenticity of the image. If the tampered image is involved with the judicial administration and news media, it will bring severe threats to the national security and social credibility. To solve this problem, digital image watermarking scheme has been born in the right moment. It exploits the redundancy of digital images and embeds some information, namely watermark, into the images. According to different application situations, digital image watermarking scheme can be divided into three main categories [1]: Robust watermarking [2; 3], fragile watermarking, and semi-fragile watermarking. The robust watermarking scheme can resist most attacks including signal processing attacks and some malicious attacks [4; 5]. This property makes robust watermarking scheme broadly used in the field of copyright protection [6; 7]. By contrast, the fragile watermarking scheme is susceptible to various attacks, which is often applied in image or video content authentication [8]. According to the level of sensitivity, the fragile watermarking scheme can be split into fragile watermarking and semi-fragile watermarking [9]. Compared to the latter, the fragile watermarking is more sensitive to different attacks, which can achieve hard authenticationfor malicious attacks. The main processes of fragile watermarking are as follow: (i) In the sending side, the sender inserts the authentication watermark to the images in advance; (ii) in the receiving or detection side, the inspector extracts the authentication information from the received images according to the embedding strategy; (iii) the extracted information is compared with the original information to determine and locate the tampered regions. The fragile watermarking can be further divided into two types: fragile watermarking only used for authentication [10] and fragile watermarking with recovery ability [11]. Compared to the former, the fragile watermarking with recovery ability can not only locate the tampered regions, but also restore the tampered image. In the sending side, the sender embeds the authentication watermark and recovery watermark into the host images. In the detection side, the authentication watermark is first extracted and used to identify the authenticity of the received image. If the received image is determined as tampered, the restoration process will be applied to the tampered regions. If the received image is verified as authentic, this image will remain unchanged. If an image has been tampered, it might be the first choice for the receiver to require retransmission. However, the authenticity of the retransmitted image still cannot be guaranteed. Besides, in some applications, like telemedicine and judicial expertise, the original image might not be easily obtained. Therefore, it becomes essential to restore the tampered image. In addition, the recovered image could be further used for the subsequent image processing. In fragile watermarking scheme with recovery ability, the recovery information for an image block is usually a content representation of the block, like average pixel value [12; 13], vector quantization (VQ) index [14], the discrete cosine transform (DCT) coefficients [15; 16], etc. In recent years, a lot of self-recovery fragile watermarking schemes have been developed. However, in most self-recovery watermarking schemes, the watermark capacity is constant for different regions of an image or even all the test images. Obviously, this is impractical, because different images have different texture characteristics. Even in the same image, different regions would have different texture characteristics.