Data Hiding Using Sequential Hamming + k with m Overlapped Pixels

Recently, Kim et al. introduced the Hamming + with overlapped pixels data hiding (Hk_ mDH) based on matrix encoding. The embedding rate (ER) of this method is 0.54, which is better than Hamming code HC ( , − ) and HC ( , − ) +1 DH (H1DH), but not enough. Hamming code data hiding (HDH) is using a covering function (1, =2 −1, ) and H1DH has a better embedding efficiency, when compared with HDH. The demerit of this method is that they do not exploit their space of pixels enough to increase ER. In this paper, we increase ER using sequential Hk_mDH (SHk_mDH ) through fully exploiting every pixel in a cover image. In SHk_mDH, a collision maybe happens when the position of two pixels within overlapped two blocks is the same. To solve the collision problem, in this paper, we have devised that the number of modification does not exceed 2 bits even if a collision occurs by using OPAP and LSB. Theoretical estimations of the average mean square error (AMSE) for these schemes demonstrate the advantage of our SHk_mDH scheme. Experimental results show that the proposed method is superior to previous schemes.