hamming code

Fragile watermarking is the task of embedding a watermark in a media (an image in this paper) such that even small changes, called tamper, can be detected or even recovered to prevent unauthorized alteration. A well-known category of spatial fragile watermarking methods is based on embedding the watermark in the least significant bits of the image to preserve the quality. In addition, Hamming code is a coding algorithm in communication that transmits the data-bits by augmenting some check-bits in order to exactly detect and recover single-bit modifications. This property is previously used to detect and perfectly recover the images modified by small tampers less than a quarter of the image in diameter. To achieve this goal, the Hamming code is applied on a distributed pixel, bits of which are gathered from sufficient far pixels in the image. It guarantees that such tampers can toggle at most one bit of each distributed Hamming code that is recoverable. It was the only guaranteed perfect reconstruction method of small tampers, based on our knowledge. In this paper, the method has been extended to support distortion in two bits of a Hamming code by use of common structures of distributed codes. It leads to guarantee recovery of tampers less than half of the image in width and height. According to the experimental results, the proposed method achieved better performance, in terms of recovering the tampered areas, in comparison to state-of-the-art.

Fragile watermarking is a technique of authenticating the originality of the media (e.g., image). Although the watermark is destroyed with any small modification (tamper), it may be used to recover the original image. There is no method yet, based on our knowledge, to guarantee the perfect recovery of small tampers. Although data-bits are embedded in Least Significant Bits of some other pixel(s), a tamper may destroy both data and authentication sets which makes recovery impossible. In this paper, a novel fragile watermarking scheme is proposed for both tamper detection and tampered image recovery. Here, all bits are reorganized in virtual pixels distributed in the image called as Distributed Pixels (DP). Distance of each pair of bits in a DP is sufficiently large. This is why; tampers smaller than a threshold, cannot destroy more than one bit of a DP. Hamming code guarantees that changing at most one bit can be perfectly detected and recovered. Then, Hamming (7,4) is extended to (8,5) to support embedding in eight-bits pixels. According to the experimental results, the proposed method could perfectly detect and recover the tampered parts not greater than a quarter of image in diameter. It also achieved acceptable performance in other conditions, compared to state-of-the-art methods.