# Fragile Watermarking for Image Authentication Using the Characteristic of SVD
## 1 Introduction  
Nowadays, digital multimedia like digital images plays an indispensable role in our daily lives. However, with the development of image processing techniques, it has become easier to refine and edit the images. The authenticity and integrity of digital images are suffering from a serious threat. To cope with this problem, the fragile watermarking scheme has recently been proposed. Generally, the fragile watermark used for image authentication can be divided into two types including semi-fragile watermark and complete fragile watermark (also known as fragile watermark). Compared to the semi-fragile watermarking method, the fragile watermarking is more susceptive to various alterations [1]. Therefore, it is more effective for image authentication, especially for the images used in safety-critical applications. According to detection resolution, the fragile watermarking scheme is further split into two categories [2]: the block-wise method and the pixel-wise method. In a block-based watermarking algorithm, the image is firstly partitioned into many sub-blocks. Each image block is inserted with the identification code produced from the block itself. In [3], [PERSON] presented a classical block-wise fragile watermarking algorithm. The least significant bit (LSB) of image sub-block is inserted by the check-sum of the most significant bits (MSBs). However, a false certification arises whereby one can exchange the image block without affecting its authentication information. To resolve this problem, [PERSON] et al. [4] suggested a hash function-based watermarking algorithm. In their scheme, the authentication data of each block is generated via a cryptographic hash function. The binary form of watermarking information is integrated and inserted into the LSB of the center pixel in the corresponding block. They claimed that this method can recognize and locate any manipulation to the watermarked images. However, later research in [5] pointed out that this method is not secure enough for image authentication. In [6], [PERSON] and [PERSON] introduced a fragile watermarking algorithm,where the authentication data was obtained by applying fuzzy c-means (FCM) clustering. To achieve image authentication in JPEG images, [PERSON] et al. [7] introduced a reversible fragile watermarking method. Experimental results indicate that it can locate the forged blocks when the falsified area is not too large. From the above analysis, it can be noted that the block-wise fragile watermarking algorithm has achieved great success in tamper identification and localization. However, the detection precision of the block-based watermarking method is limited to the block level [8]. To solve this issue and improve the detection accuracy, many pixel-based fragile watermarking algorithms have been presented in recent years. In [9], [PERSON] et al. presented a simple fragile watermarking algorithm, where a binary authentication watermark was produced by a pixel-value difference between a chaotic image and the host image. [PERSON] and [PERSON] [10] presented a chaotic map-based method, but this algorithm has a potential security risk since it does not consider the image content in the watermark embedding process [11]. Based on the security analysis, [PERSON] et al. [11] introduced an improved fragile watermarking method. The MSBs of the host image are taken into account in the process of watermark generation, which ensures the safety of the algorithm. The main problem existing in the above pixel-wise fragile watermarking schemes is that an extra binary watermark image is needed on the receiving end for tamper detection and localization. To achieve blind forgery detection, [PERSON] et al. [12] introduced a chaos-based watermarking algorithm. The authentication data is constructed by the local pixel contrast between neighborhood pixels and average pixel value of each block. To achieve image authentication for stereoscopic images, [PERSON] et al. [13] put forward a binocular visual characteristic-based fragile watermarking method.