# Two-Dimensional Histogram Shifting-Based Reversible Data Hiding for H.264/AVC Video
## 1 Introduction  
As a special type of data hiding, RDH schemes imperceptibly embed secret data into cover media in a reversible manner, meaning the cover media can be losslessly recovered after data extraction. Due to the reversibility, RDH schemes are especially useful in the scenarios where any distortion may be unacceptable, such as military applications, medical imaging, and law enforcement. For example, the integrity check code of a video can be embedded into it to assure the video used for law enforcement has not been modified. So far, many RDH schemes have been proposed, which can be classified into three main categories: lossless compression [1, 2], difference expansion [3, 4, 5, 6] and histogram shifting [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]. HS-based RDH scheme was first proposed by [PERSON] et al. [7], and it is improved for years afterwards using the histograms of difference image [8, 9] or prediction errors [10, 11, 12, 13], multiple histograms [14, 15, 16, 17] and 2D HS [18, 19, 20, 21, 22, 23]. Most aforementioned RDH schemes are only suitable for uncompressed images, and cannot be directly applied to compressed images and videos. However, compressed media such as JPEG images and H.264/AVC videos are more commonly used in daily life. Several RDH schemes have been proposed for JPEG images [24, 25, 26, 27, 28, 29]. [PERSON] et al. [24] proposed an HS-based RDH scheme for JPEG images by expanding the AC coefficients with values \(\pm 1\). Moreover, a block selection strategy is used to adaptively choose DCT blocks for data embedding. An ordered embedding method to further reduce the increase in the file size of marked images was proposed in [25]. Subsequently, two different coefficient selection methods are proposed in [26, 27] to further improve the embedding efficiency. Recently, [PERSON] et al. [28] established the negative influence models of image visual distortion and file size change, which can be employed to optimize the selection of DCT blocks and coefficient frequencies. [PERSON] et al. [29] proposed a 2D HS-based RDH scheme for JPEG images as well as a selection strategy based on the optimal frequency band of the DCT coefficient pairs. For H.264/AVC video, [PERSON] et al. [30] proposed embedding the motion vectors (MVs) into DCT coefficients using the HS method for the purpose of intra-frame error concealment. In [31], position of the last nonzero level of DCT block is used to embed secret data. Although the distortion caused by data hiding can be reduced, the embedding efficiency is not high. To avert the intra-frame distortion drift, the directions of intra-frame prediction are used in the RDH scheme of [32]. To reduce the quality distortion, a 2D HS-based RDH scheme was introduced by [PERSON] et al. [33] to embed secret data into DCT coefficients of middle and high frequencies. A different 2D HS-based method is also proposed in [34] to improve the embedding efficiency. [PERSON] et al. [35] proposed an RDH algorithm based on compensation, reducing the modification of DCT coefficients. [PERSON] et al. [36] presented an algorithm based on the HS of MVs, and to further improve the embedding performance, they also presented a 2D HS-based method of MVs [37]. Although many video coding schemes [38; 39; 40; 41] based on DCT or wavelet transform [42] have been proposed, H.264/AVC is the most commonly used video coding format. Thus, the RDH technique for H.264/AVC video is of great value. In this paper, in order to embed additional data into H.264/AVC videos, the embedding efficiency of a DCT coefficient pair in different embedding modes is firstly calculated. Then, based on the computed embedding efficiency along with the statistical distribution of DCT coefficient pairs, the defects in several 2D HS schemes are analyzed. In addition, two better embedding strategies are proposed. The secret data is finally embedded into the pairs of DCT coefficients of the middle and high frequencies using our proposed methods.