Reversible Data Hiding Scheme Based on Coefficient Pair Mapping for Videos H.264/AVC without Distortion Drift

Abstract

Reversible data hiding is a technique for embedding secret data into a cover media. Such technique has the ability to recover marked cover media to its original version after extracting the secret data. In this paper, a new reversible data hiding algorithm for videos H.264/AVC is proposed to improve the embedding capacity while the distortion drift is prevented. To embed the secret data into videos H.264/AVC without any intra-frame distortion drift, in our proposed scheme, the relationship of QDCT coefficients is explored. Then, a coefficient pair mapping mechanism in 2D histogram is introduced for embedding data. The experimental results demonstrated that the proposed scheme obtains reversibility. The proposed scheme prevents intra-frame distortion drift on the marked videos. In addition, the embedding capacity of the proposed scheme is superior to that of existing schemes while guaranteeing the high visual quality of marked videos.

1. Introduction

A huge amount of digital data containing private information is transmitted through the Internet each second. To prevent third parties from accessing the private information, many studies [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] have been proposed. Data hiding is one of the promising techniques to conceal digital secret message into the cover media i.e., audios, images, videos, database, DNA sequence, etc., to protect the security and privacy of such digital information from malicious attacks. Many data hiding algorithms [1,2,3,4,5,6,7,16,17,18,19,20] have been proposed for digital cover media in the last ten years.

Recently, Video, one of digital media, is used for data hiding due to its wide applications, i.e., surveillance camera and YouTube channels. In 2003, I.E.G. Richardson [8], proposed a new compression technique for video, called H.264/AVC (advanced video coding) for compressing the video sequences to save storage space. Recently, many data hiding schemes based on H.264/AVC coding [9,10,11,12,13,14,15,21,22,23] have been proposed to enhance the security of video sequences. In [9], Nguyen et al. embedded the secret data into motion vectors. However, their scheme obtained the low embedding capacity (EC), always smaller than 2 Kbit. Later on, to improve robustness, Zhang et al. [10] proposed a new scheme to embed a 2-D 8-bit watermark into the videos. Noorkami and Mersereau [11] used the quantized AC coefficients to conceal the watermark into H.264/AVC videos. Later, to enhance the robustness, Gong and Lu [12] employed a texture-masking-based perceptual model to hide the secret data. However, in two aforementioned schemes [11,12], the original version of embedded watermark is required to evaluate the existence of the embedded watermark in the marked video sequences.

Discrete cosine transform (DCT) coefficients of I-frames were used in all state-of-the-art schemes for embedding data into video sequences. However, these schemes suffered the intra-frame distortion drift issue. In order to solve this problem, Ma et al. [13] proposed a novel DCT-based data hiding algorithm by selecting three quantized DCT paired-coefficients (QDCT) for carrying the secret data. Nevertheless, their scheme provided the low visual quality of marked video sequences, and unsatisfied embedding capacity. In 2011, Huo et al. [14] applied controllable error-drift elimination for a new data hiding scheme to enhance the quality of the marked videos. However, their scheme offered a low embedding capacity. In 2013, to increase embedding capacity of Ma et al.’s scheme [13], in [15], Lin et al. explored the QDCT coefficients’ characteristic for data embedding. Lin et al.’s scheme obtained a higher embedding capacity than that of Ma et al.’s scheme. However, the scheme [15] obtained the unsatisfactory quality of marked videos. To enhance visual quality of marked videos while keeping high EC, Nguyen et al. [23] partitioned the blocks into two coefficient groups, i.e., hiding coefficient group and preventing coefficient group. Then, the coefficients in the hiding group are applied to conceal the secret information while the other group is utilized to avoid the distortion drift in the marked video sequences. Their scheme obtained high performance in terms of EC while maintaining good quality of marked videos. However, their cover videos are affected permanently and cannot be restored to their original version.

In order to solve this shortcoming, in 2006, Ni et al. [21] introduced histogram shifting (HS) to reversible data hiding (RDH) scheme for still images. In their scheme, zero-point values and peak-point values of the histogram are utilized to hide data. Ni et al.’s scheme guaranteed the reversibility. However, their visual quality of marked images is always smaller than 49 dB for different kinds of images. To improve the visual quality further, some RDH schemes based on histogram shifting [4,7] are proposed. Recently, several RDH studies are proposed for H.264/AVC videos [22,24,25,26,27,28]. The secret data can be embedded into the QDCT coefficients of intra-frames, which meet the directions of intra-frame prediction, therefore they could avert the distortion drift [24,25]. The algorithm [24] could achieve good visual distortion while the algorithm [25] improved the robustness by using BCH syndrome code before data hiding. However, these schemes [24,25] obtained the low EC. Later on, RDH schemes [26,27] applied motion vector (MV) data pre-processing, the selection of most suitable embedding region for H.264/AVC code. However, Chung et al.’s method [26] only embedded MVs of MBs into zero QDCT coefficients. To solve the shortcoming in Chung et al.’s scheme, in [28]. Xu et al. fully exploited the number of coefficients and produced extra nonzero residual blocks for embedding data. Although, these schemes [26,27,28] achieved the good quality of marked videos, however, their schemes suffered the distortion drift. To avert the distortion drift, in [22], Liu et al. used Shamir’s (t, n)-threshold secret sharing to embed the secret data into videos H.264/AVC. However, the EC of Liu et al.’s scheme is too low, when it is always smaller than 200 bits.

To avoid distortion drift, many data hiding schemes [13,15,22,23] have been proposed. However, most of them suffered from the low EC. Moreover, after containing the secret data, the marked videos obtained by these previous schemes are affected permanently and cannot be restored to their original version to improve. Inspired from the histogram shifting-based RDH scheme [21] for the still images, in this paper, to further improve embedding capacity while obtaining reversibility, a new RDH scheme is proposed for H.264/AVC videos. In the proposed scheme, to prevent the distortion drift, QDCT coefficient pairs of H.264/AVC videos are selected according to its context. Then, to achieve reversibility, a 2D histogram is generated by counting suitable QDCT coefficient pairs. The CPM mapping, injective mapping, is defined to project a coefficient pair to another pair for embedding the secret data. To enhance the security, the secret data are encrypted by using symmetric key cryptography. Finally, RDH algorithm is implemented by using CPM mapping. By using the 2D histogram and the CPM mapping, more pairs are applied to contain the secret bits while the distortion drift is avoided as well. Experimental results illustrated that our proposed scheme obtains reversibility. In addition, the proposed scheme outperforms some previous schemes in terms of the EC while maintaining good visual quality of marked videos.

The remainder of our paper is organized as follows. In Section 2, related works are briefly introduced. Then, our proposed scheme based on CPM and 2D histogram mechanisms is described in Section 3. Section 4 presents the experimental results. Finally, conclusions are drawn in Section 5.

2. Related Works

2.1. Intra-Frame Prediction

H.264/AVC coding [8] is proposed to decrease the redundancy of Intra-frames. H.264/AVC algorithm partitions intra-frames into 4 × 4 or 16 × 16 macroblocks (MBs). However, the alternation of 16 × 16 intra MBs is easy to be recognized in a human eye system. Therefore, to overcome this shortcoming, 4 × 4 intra MB blocks are usually used for further processing. In the H.264/AVC algorithm, the left block and the upper block are used to predict the values of the current luminance block. Sixteen samples of the current block in Figure 1, labeled from a to p in the current luminance block, will be predicted according to the boundary pixels of the left and upper blocks, labeled from A to M. The prediction of current luminance block $\widehat{B_{i,j}}$ is calculated by one of nine modes, shown as in Figure 2.

2.2. DCT-Based Data Hiding Schemes for Video H.264/AVC

In [13], Ma et al. divided 4 × 4 blocks into three different conditions, i.e., Condition 1, Condition 2, and Condition 3, as shown in

Table 1. Three different conditions of Ma et al.’s scheme.

	Mode Name	Mode Value	Reference Pixels
Condition 1	Right-Mode	0, 3, or 7	d, h, l, p
Condition 2	Under-Left-Mode & Under-Mode	1 or 8 and 0, 1, 2, 4, 5, 6, or 8	m, n, o, p
Condition 3	Under-Right-Mode	0, 1, 2, 3, 7, or 8	p

. Condition 1, named Right-Mode, is defined by prediction of the right block, effects by mode 0, 3, or 7. Meanwhile, Condition 2 is determined by Under-Left-Mode ∈ {0, 1, 2, 3, 4, 5, 6, 8} and Under-Mode ∈ {1, 8} in 4 × 4 block mode. The determination of Condition 3 is performed by Under-Right-Mode ∈ {0, 1, 2, 3, 7, 8}. By doing so, Ma et al.’s scheme [13] prevented the distortion drift in the MB blocks during the embedding process. However, Ma et al.’s scheme offered the low EC.

Later on, to increase the EC of Ma et al.’s scheme, in [15], Lin et al. fully exploited the characteristic of MB blocks; up to the remaining 54% MB blocks are used for embedding. For embedding data, Lin et al. re-classified 4 × 4 blocks into five different categories, i.e., Cat1, Cat2, Cat3, Cat4, and Cat5. Then, the Cat3 has no reference pixels, thus, they can embed more secret bits, up to 16 bits into one block. While the reference pixels in Cat5 are all of the pixels at under and right of the block, so only one bit can be embedded. According to schemes [13,15], three types can be launched as shown in

Table 2. Three launched cases according to schemes [13,15].

Types	Condition 1	Condition 2	Condition 3	Reference Pixels
Type 1	T	F	X 1	d, h, l, p
Type 2	F	T	X	m, n, o, p
Type 3	F	F	T	p

¹ Do not care.

. In Type 1, Condition 1 is equal to True (T) and Condition 2 is equal to False (F), respectively. This type refers to pixels d, h, l, and p. The Case2, with the reference pixels m, n, o and p, is used if the Condition 2 is True, and Condition 1 is False. For the Type 3, by reference pixel is p, the Condition 3 must be True, but the Condition 1 and Condition 2 are both False.

By applying five categories, Lin et al.’s scheme [15] obtained the higher EC when the remaining 54% of MB blocks are exploited. However, Lin et al.’s scheme suffered losing a part of the video stream which cannot be completely recovered after extracting the secret data. Therefore, to reconstruct the marked videos to its original version completely, the new RDH scheme for videos H.264/AVC is proposed and described in the next section to obtain reversibility while maintaining the high EC and good quality of marked videos.

3. Proposed Scheme

In this section, the RDH scheme is proposed without intra-frame distortion drift. In the proposed scheme, an 2D QDCT histogram is constructed. Then, a coefficient pair mapping (CPM) which is an injective mapping defined on QDCT pairs is used for embedding data. In this section, we first introduce the CPM technique defined on QDCT coefficient pairs in Section 3.1. Then in Section 3.2, we present our CPM-based RDH scheme. By using the 2D QDCT histogram, the secret data can be embedded by our approach without any distortion drift while the reversibility is maintained. Then, the detailed embedding and extracting algorithms of our proposed scheme are summarized in Section 3.3 and 3.4, respectively.

3.1. Coefficient Pair Mapping

In H.264/AVC coding, integer discrete cosine transform (IDCT) is used for the 4 × 4 residual block R_i,j. Then, Equation (1) is applied to generate quantized DCT (QDCT) coefficients.

$$R_{i,j}^{qdct}=C_f{R}_{i,j}{C}_f^T\otimes \left(\frac{PF}{Q}\right)=\left[\begin{array}{cccc}{Y}_{1,1}& Y_{1,2}& Y_{1,3}& Y_{1,4}\\ Y_{2,1}& Y_{2,2}& Y_{2,3}& Y_{2,4}\\ Y_{3,1}& Y_{3,2}& Y_{3,3}& Y_{3,4}\\ Y_{4,1}& Y_{4,2}& Y_{4,3}& Y_{4,4}\end{array}\right]$$

(1)

where $R_{i,j}^{qdct}$ is the QDCT coefficients of the residual block R_i,j; the matrix C^T_f is transformed from the matrix C_f,

$$C_f=\left[\begin{array}{cccc}1& 1& 1& 1\\ 2& 1& -1& -2\\ 1& -1& -1& 1\\ 1& -2& 2& -1\end{array}\right]$$

$$PF=\left[\begin{array}{cccc}{a}^2& \raisebox{1ex}{$ab$}\!\left/ \!\raisebox{-1ex}{$2$}\right.& a^2& \raisebox{1ex}{$ab$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\\ \raisebox{1ex}{$ab$}\!\left/ \!\raisebox{-1ex}{$2$}\right.& \raisebox{1ex}{$b^2$}\!\left/ \!\raisebox{-1ex}{$4$}\right.& \raisebox{1ex}{$ab$}\!\left/ \!\raisebox{-1ex}{$2$}\right.& \raisebox{1ex}{$b^2$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\\ a^2& \raisebox{1ex}{$ab$}\!\left/ \!\raisebox{-1ex}{$2$}\right.& a^2& \raisebox{1ex}{$ab$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\\ \raisebox{1ex}{$ab$}\!\left/ \!\raisebox{-1ex}{$2$}\right.& \raisebox{1ex}{$b^2$}\!\left/ \!\raisebox{-1ex}{$4$}\right.& \raisebox{1ex}{$ab$}\!\left/ \!\raisebox{-1ex}{$2$}\right.& \raisebox{1ex}{$b^2$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\end{array}\right], a=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right., b=\sqrt{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}$$

The ⊗ operator denotes an element-by-element product of two matrices, and Q is the step size of quantizer which is determined by a quantization parameter.

Then, a dequantization mechanism is used to reconstruct the residual block R_i,j, and inverse IDCT operation is performed by using Equation (2).

$$R_{i,j}=C_r^T(R_{i,j}^{qdct}Q\otimes \left(E_r\right)C_r)$$

(2)

where $C_r=\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& 1/2& -1/2& -1\\ 1& -1& -1& 1\\ 1/2& 1& 1& -1/2\end{array}\right]$,

$$E_r=\left[\begin{array}{cccc}{a}^2& ab& a^2& ab\\ ab& b^2& ab& b^2\\ a^2& ab& a^2& ab\\ ab& b^2& ab& b^2\end{array}\right],a=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.,b=\sqrt{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}$$

To avoid distortion drift, in Ma et al.’s scheme, the pair of coefficients is perturbed. Take a pair of coefficients (Y₁₁, Y₃₁) belonging to Type 2 in Table 2 as an example. It can be seen that after permutation, (Y₁₁ + 1, Y₃₁ − 1) is obtained. Then, the difference value between two matrices, $R_{i,j}^{qdct\prime }$ and $R_{i,j}^{qdct}$, is presented in Equation (3).

$$\Delta R_{i,j}^{qdct}=R_{i,j}^{qdct\prime }-R_{i,j}^{qdct}=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 0& 0& 0\\ -1& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right]$$

(3)

Assume that the block $R_{i,j}^{\prime }$ is perturbed to generate $R_{i,j}^{\prime }$, then their difference value $\Delta R_{i,j}$ can be computed by Equation (4).

$$\Delta R_{i,j}=R_{i,j}^{\prime }-R_{i,j}=C_r^T(\Delta R_{i,j}^{qdct}Q\otimes \left(E_r\right)C_r)=Q\times \left[\begin{array}{cccc}0& 0& 0& 0\\ 2a^2& 2a^2& 2a^2& 2a^2\\ 2a^2& 2a^2& 2a^2& 2a^2\\ 0& 0& 0& 0\end{array}\right]$$

(4)

It is obvious that in $\Delta R_{i,j}$, the fourth row is a zero vector and $B_{i,j}^{r\prime }=R_{i,j}+B_{i,j}^p+\Delta R_{i,j}$. Obviously the fourth row of both $B_{i,j}^{r\prime }$ and $B_{i,j}^r$ is the same value, as a result, in this type, the reference pixels are kept unchanged during the process, meaning that distortion drift is free. Taking these characteristics, to achieve the reversibility, in the proposed scheme, coefficient pair mapping (CPM) is used. All suitable coefficient pairs in three types in Table 2 are selected for containing the secret bits. In addition, to prevent the distortion drift, an 2D histogram is constructed according to the frequency of pairs of coefficients. Then, the secret data are hidden by shifting the 2D histogram. It is obvious that the pair of coefficients is an element of $Z^2$. Then, we need to partition $Z^2$ into three disjoint subsets in Figure 3, one subset (black point) is kept unchanged during the embedding process, the second one (blue point) is used to embed the secret data by expansion process, and the third one (red point) is shifted to generate vacant room to guarantee reversibility. It is obvious that each blue point is projected to red one (orange arrows). Each red point is projected to another red point (indicated by dash green arrows).

In particular, each point indicates a coefficient pair. According to the CPM mechanism, for each cover coefficient pair (A_i, B_i), the marked value is obtained by using the following way:

(1)

If (A_i, B_i) is the black point, it is kept unchanged.

(2)

If (A_i, B_i) is the blue point

• If the secret bit w = 0, the marked coefficient pair is equal to (A_i, B_i).
• If the secret bit w = 1, the marked coefficient pair is set to the corresponding red point.

(3)

If (A_i, B_i) is the red point, the marked coefficient pair is set to the corresponding red point.

The process of the data extraction and the cover image reconstruction can be applied to the CPM mechanism because of the injection property, i.e., each point has at most one inverse.

3.2. CPM Based RDH Scheme

To embed the secret bit w into a coefficient pair (A_i, B_i), we will modify this pair to either (A_i + w, B_i − w) or (A_i − w, B_i + w). In this situation, since the pair (A_i, B_i) has two modification directions, only the direction with minimum modification is selected for concealing the secret data. Based on these two modification directions, we will introduce a new RDH scheme based on the CPM algorithm.

Here, our embedding algorithm based on CPM is briefly described. First, to avoid distortion drift, for each selected type, four pairs of coefficients are extracted as (A_i, B_i) = {(Y₁₁, Y₁₃), (Y₂₁, Y₂₃), (Y₃₁, Y₃₃), (Y₄₁, Y₄₃)}. Then, each pair is located in the 2D histogram. To embed one secret bit, each blue point in the histogram is projected to a red one while each red point is projected to another red one. This means that the shifting process is easily implemented in the 2D histogram to guarantee the reversibility, as shown in Figure 3. Note that there are many ways to utilize the CPM for various RDH schemes. As for CPM shown in Figure 3, the main idea is to choose as many as the high frequency points to conceal the secret information. It is obvious that most of QDCT coefficients A_i of video streams are concentrated on around the value of 0 in the histogram. To obtain the high embedding capacity, the coefficient A_i with the value of 0 should be used. To give a better explanation, we take blue points (A_i, B_i) = (0, B_i) for containing the secret data. In addition, the other points are shifted according to the one selected direction with the minimum distortion. The superior performance of CPM will be experimentally shown in the next section.

Notice that the coefficient pairs selected to carry secret data belong to the block case of these coefficient pairs. By this means, when the block case is equal to 1, coefficient pairs are vertically selected as Figure 4a, while the block case is equal to 2 or 3, the pairs of coefficients in the current block are horizontally used as Figure 4b. Suppose that the secret data bit is w. For Type 1, the coefficient A_i is equal to Y_i,1, i = 1, …, 4. And for Type 2 and Type 3, the coefficient A_i is equal to Y_1,i, i = 1, …, 4. The proposed embedding process is implemented by CPM mapping in the 2D histogram. The secret bit w is hidden into the coefficient pair by Equation (5).

$$[A_i,B_i]=\left\{\begin{array}{l}[A_i+w,B_i-w]\mathrm{if}{A}_{\mathrm{i}}=0,\\ [A_i+1,B_i-1]\mathrm{if}{A}_{\mathrm{i}}>0\end{array}\right..$$

(5)

3.3. Embedding Algorithm

In this section, the secret data M is embedded into the H.264/AVC video H. In Figure 5, the embedding process contains several basic steps. First, the entropy encoder is used to decode the raw video streams into the intra-frame modes and QDCT coefficients. Then, the appropriate coefficient pairs of the blocks in Types of 1, 2, or 3 are collected for constructing the 2D histogram. It is noted that the I-frames, P-frames, and B-frames both are obtained after decoding. To preserve the quality of marked videos, embedding algorithm is only performed on the I-frames. After the decoding process, the I-frames are used for mode prediction. Then, macroblocks are determined. For each macroblock, all corresponding embeddable coefficient pairs are selected for CPM mapping.

For each coefficient pair, the value of coefficient A_i is checked to embed the secret bit by using Equation (5). To avoid drift distortion, as discussed above, the CPM mechanism is used. Therefore, if the value of A_i is increased, then the value of B_i is reduced, and vice versa. Moreover, in the proposed scheme, to increase the security of the proposed scheme, before the embedding process, the secret data M should be encrypted with encryption key K by using one of the well-known encryption algorithms, i.e., RSA, AES, … [29]. The detailed embedding algorithm, Algorithm 1, is described as following.

Algorithm 1: Embedding algorithm

Input: The original H.264/AVC video stream H, the secret data M and the encryption key K. Output: The marked H.264/AVC video stream H’. Step 1: The H.264/AVC video stream H is decoded by Entropy encoder to generate blocks of QDCT coefficients. Step 2: Encrypt the message M with the encryption key K. Step 3: $\mathrm{Read}\mathrm{the}\mathrm{block}{R}_{i,j}^{qdct}$ from QDCT coefficient blocks. Step 4: Read coefficient pair (Ai, Bi) from the QDCT coefficient blocks, and apply Equation (5) to hide the secret bit w. Step 5: Steps 3 to 4 are repeatedly used until the entire of QDCT coefficients are handled completely, then the entropy encoder is used to generate the marked video stream H’.

After the above-mentioned four steps are processed completely, the marked H.264/AVC video stream is obtained and transferred to the receiver. To ensure the security of the proposed scheme, the encryption key K is sent to the receiver through the secure channel.

3.4. Extracting Algorithm

After receiving the marked video, the receiver applies the extracting algorithm to extract the secret message and to restore the marked video to its original version. Figure 6 shows all the main steps of the extracting process. After entropy decoding, the hidden data are extracted from MB blocks. The hidden data W (w₁, w₂, …, w_n), where w_i ∈ {0, 1}) is extracted by Equation (6).

$$w_i=\left\{\begin{array}{c}1\hspace{1em}if A_i=1\\ 0\hspace{1em}if A_i=0\end{array}\right..$$

(6)

Since the hidden data are extracted completely, the values of coefficient pairs are restored by Equation (7).

$$[A_i,B_i]=\left\{\begin{array}{ll}[A_i-1,B_i+1]& \mathrm{if}{A}_i\ge 1,\\ [A_i,B_i]& \mathrm{if}{A}_i=0\end{array}\right.$$

(7)

The following algorithm, Algorithm 2, illustrates the extracting process.

Algorithm 2: Extracting algorithm

Input: The marked video stream H’ and the encryption key K. Output: The original video stream H, the secret data M. Step 1: The Entropy encoder is used to decode the marked video H’ into QDCT coefficient blocks. Step 2: Read the block $R_{i,j}^{qdct}$ from QDCT coefficient blocks. Step 3: Read coefficient pairs (Ai, Bi) from the QDCT coefficient block. For each QDCT coefficient pair, one secret bit is extracted by Equation (6) while the original coefficient pair is reconstructed by Equation (7). Step 4: Repeat Steps 3 to 4 until the entire QDCT coefficient blocks are encoded completely, the encrypted secret data are extracted and decrypted with the encryption key K to obtain the secret data M. Then the entropy encoder is used to generate the original H.264/AVC video stream H.

4. Experimental Results

A number of experiments are conducted to compare existing algorithms [13,15,22,23] with the proposed algorithm on ten test video streams with quarter common intermediate format, QCIF, 176 × 144, i.e., Akiyo, Bridge-Close, Bridge-Far, Carphone, Claire, Claire, Container, Hall, Mother-Daughter, News, Salesman. The test streams are encoded into 300 frames at 30 fps (frames per second) with ten I-frames for each stream. All algorithms are programmed by Matlab R2015a. All implementations were realized on a computer with Core i3 CPU, 4 GB RAM. The operating system was Microsoft Windows 10. All of them with the size of GOP were selected to be 30 frames and its structure was equal to IBPBP. To compare with other methods, we used six different QPs, 22, 24, 26, 28, 30, and 32 for the above ten sequences. This study used encoding and decoding methods developed by Muhit et al.’s [30].

Table 3. The embedding capacity of ten test videos with various QPs.

	22	24	26	28	30	32
Akiyo	18,165	19,461	19,986	20,706	22,200	22,623
Bridge-close	15,097	17,179	17,898	18,596	20,220	21,357
Bridge-far	17,283	18,938	21,508	22,077	22,916	26,287
Carphone	13,780	15,110	16,230	16,816	18,052	18,995
Claire	22,002	22,286	23,278	24,454	25,618	27,504
Container	13,730	14,872	16,535	17,268	18,548	19,576
Hall	16,016	17,387	18,973	20,138	21,133	21,526
Mother-daughter	18,072	18,932	20,657	21,350	22,625	23,417
News	16,759	18,148	19,074	19,708	21,443	22,145
Salesman	11,225	12,718	14,111	14,398	15,588	16,406
Average	16,213	17,503	18,825	19,551	20,834	21,984

shows the statistics of possible data that can be embedded into each video when the quantization parameter (QP) is in {22, 24, 26, 28, 30, 32}. The embedding capacity of Claire video (27,504 bits) is highest with QP = 32 while the embedding capacity of Salesman video (11,225 bits) is lowest with QP = 22 among ten test videos. The average capacity of videos with QP = 28 is 19,551 bits.

The peak signal-to-noise-ratio (PSNR) is applied to evaluate the quality of two frames as follows.

$$PSNR=10\times {\log }_{10}\left(\frac{255\times 255}{MSE}\right)$$

(8)

where MSE which is computed by Equation (9) is mean square error.

$$MSE=\frac{1}{m\times n}\times {\displaystyle \sum _{i=0}^{m-1}{\displaystyle \sum _{j=0}^{n-1}\left(O(i,j)-M(i,j)\right)}}$$

(9)

where m, n are the number of rows and columns of the current frame, O and M are the original and marked frames, respectively.

The well-known SSIM index [31] is adopted to evaluate the visual quality. In our experiment, the SSIM index between the original and marked frames is computed by Equation (10).

$$SSIM=\frac{1}{N-1}\times {\displaystyle \sum _{i=0}^{N-1}\frac{(2{\mu }_{O_i}{\mu }_{E_i}+c_1)\times (2{\sigma }_{O_i{E}_i}+c_2)}{({\mu }^2{}_{O_i}+{\mu }^2{}_{E_i}+c_1)\times ({\sigma }^2{}_{O_i}+{\sigma }^2{}_{E_i}+c_2)}}$$

(10)

where O_i and E_i indicate the ith MB block of original and marked frames; N is the number of MB blocks; ${\mu }_{O_i},{\mu }_{E_i}$ and ${\sigma }^2{}_{O_i},{\sigma }^2{}_{E_i}$ are the mean variance of the block O and the block E; ${\sigma }_{O_i{E}_i}$ is the covariance of O and E; c₁ = (k₁ × L)2 and c₂ = (k₂ × L)2 with L = 255, k₁ = 0.01, and k₂ = 0.03.

In the experiment, to evaluate the visual quality of marked video, both PSNR and SSIM values are used.

Table 4. The quality of the marked videos with various QPs.

QPs	PSNR	SSIM
22	38.21	0.942
24	36.24	0.915
26	34.23	0.880
28	32.48	0.842
30	30.38	0.784
32	28.41	0.722
Average	33.33	0.848

presents the proposed scheme’s visual quality when embedding maximum secret bits. It is obvious that the PSNR and SSIM values are reduced when the value of QP is increased. The main reason is since the large value of QP is used, more QDCT coefficient pairs are found for embedding data causing more distortion in the marked videos. However, the average PSNR of the proposed scheme is still larger than 33 dB, while the value of SSIM is greater than 0.84.

In this section, to show the solid results of the proposed scheme, two DNA sequences [32], downloaded from the GenBank database, are also used as the secret data. The DNA sequence consists of four base types, i.e., A, G, C, and T. Each base type is encoded by a corresponding bits of 00, 01, 10, and 11, respectively.

Table 5. The quality of marked videos with the large embedding capacity after embedding DNA sequences NC_007020 (11,440 nts = ~22,880 bits)) with QP = 28.

Videos	PSNR	SSIM
Akiyo	32.50	0.834
Bridge-close	32.01	0.847
Bridge-far	32.70	0.766
Carphone	32.89	0.880
Claire	33.69	0.825
Container	32.55	0.834
Hall	32.62	0.860
Mother-daughter	32.49	0.833
News	32.44	0.864
Salesman	32.36	0.900
Average	32.63	0.844

and

Table 6. The quality of marked videos with the smaller embedding capacity after embedding DNA sequences NC_007203 (6909 nts = ~13,818 bits) with QP = 28.

Videos	PSNR	SSIM
Akiyo	34.58	0.878
Bridge-close	32.49	0.861
Bridge-far	34.78	0.831
Carphone	33.40	0.889
Claire	36.36	0.884
Container	33.30	0.854
Hall	33.70	0.882
Mother-daughter	34.38	0.876
News	33.66	0.889
Salesman	32.29	0.898
Average	33.90	0.874

show the quality of marked videos after embedding the different size of the DNA sequences, i.e., the sequence NC_007020, contained 11,440 nucleotides (~22,880 bits) and the sequence NC_007203 with 6909 nts (~13,818 bits), respectively. It is noted that, in Table 5, with the larger embedding capacity, the average of PSNR and the average of SSIM are still high, with 32.63 dB and 0.844, respectively. It is obvious that if the smaller embedding capacity is embedded then the better visual quality is obtained by the proposed scheme and vice versa.

Table 7. Performance comparison among five schemes with QP = 28.

Schemes	Maximum Capacity (bits)	Average PSNR of Marked Video (dB)	Average SSIM of Marked Video	Reversibility
Proposed	19,551	32.48	0.842	Yes
Liu et al. [22]	141	34.17	0.987	Yes
Ma et al. [13]	11,559	35.31	0.935	No
Lin et al. [15]	14,357	34.78	0.936	No
Nguyen et al. [23]	19,077	34.34	0.932	No

compares the performance of the proposed scheme with four previous schemes, including: Liu et al. [22], Ma et al. [13], Lin et al. [15], and Nguyen et al. [23], when the quantization step QP = 28 is used. The PSNR and the SSIM of the proposed scheme is smaller than the other four schemes [13,15,22,23]. However, the maximum capacity of the proposed scheme is the highest one among the five schemes, up to ten times larger than that of Lui et al.’s scheme [22]. Moreover, the proposed algorithm has the ability to reconstruct the marked videos to their original version.

5. Conclusions

In this paper, a new RDH scheme is proposed for videos H.246/AVC. In the proposed scheme, the cover video is decoded by using the entropy encoder to generate QDCT coefficients. The 2D histogram of QDCT coefficients is generated by counting suitable coefficient pairs. Then, the CPM mapping mechanism, injective mapping, is defined for embedding data. To increase the security of the proposed scheme, the secret data are encrypted by using symmetric key cryptography. Then, the CPM mechanism is used to hide the encrypted secret data into the videos without any distortion drift while guaranteeing the reversibility. The experimental results showed that the proposed algorithm obtains the highest embedding capacity among five schemes while maintaining the good visual quality of marked videos. Moreover, the proposed algorithm obtains the reversibility and prevents intra-frame distortion drift on the marked videos during the embedding process. Although obtaining both the high embedding capacity and the good quality of marked videos, however, in the future, more research should be taken to improve the quality of marked videos when containing the large embedding capacity.