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# Video adaptive watermark embedding and detection algorithm based on phase function equation

###### Accepté: 20 May 2022
Détails du magazine
Format
Magazine
eISSN
2444-8656
Première parution
01 Jan 2016
Périodicité
2 fois par an
Langues
Anglais
Introduction

Method
All phase biorthogonal transformation

In 1990, Perona and Malik proposed a nonlinear anisotropic diffusion equation, namely the P-M model, in order to maintain image edge information. Definitions are as follows:

All phase biorthogonal transformation can be divided into the following three types according to different orthogonal transformation bases: All phase discrete cosine biorthogonal transform (APDCBT), all phase Walsh biorthogonal transform (APWBT) and all phase inverse discrete cosine biorthogonal transform (APIDCBT). All phase biorthogonal transform has similar properties to DCT transform, in which the transformation matrix of all phase discrete cosine biorthogonal transform can be expressed as: $V(i,j)={N−iN21N2[(N−i)cosijπN−cscjπNsinijπN]cosi(2j+1)π2N$ V\left( {i,j} \right) = \left\{ {\matrix{ {{{N - i} \over {{N^2}}}} \hfill \cr {{1 \over {{N^2}}}\left[ {\left( {N - i} \right)\cos {{ij\pi } \over N} - \csc {{j\pi } \over N}\sin {{ij\pi } \over N}} \right]\cos {{i\left( {2j + 1} \right)\pi } \over {2N}}} \hfill \cr } } \right.

In image coding, APBT transformation is performed on the image block X with the size of N×N, which can be expressed as: $Y=VXVT$ Y = VX{V^T} Where, Y is the coefficient matrix obtained after APBT transformation, and V is a two-dimensional APBT matrix with the same size as X. Accordingly, X = V−1 Y(V−1)T can be used to reconstruct the image. Where (⋅)T represents matrix transpose and V−1 is the inverse of matrix V.

Discrete sinusoidal transform is used in HEVC video compression standard for the first time because of its excellent performance in 4×4 coding block of intra luminance component [11]. Based on the analysis of the construction process of all phase biorthogonal transform, combined with all phase digital filter and discrete sinusoidal transform, this section proposes a new transform all phase discrete sinusoidal biorthogonal transform (APDSBT), which is used in JPEG coding framework, and proposes a JPEG like video compression coding algorithm based on APDSBT.

Derivation of all phase discrete sinusoidal Biorthogonal Transform

The idea of all phase is to intercept different phases of n-dimensional vectors containing time series {x(n)}: $X0=[x(n), x(n+1),…,x(n+N−1)]T$ {X_0} = {\left[ {x\left( n \right),\,x\left( {n + 1} \right), \ldots ,x\left( {n + N - 1} \right)} \right]^T} Where x (n) is the intersection of each column vector X. Therefore, the all phase data matrix of time series {x(n)} can be defined as AN (n) = [X0, X1, …, XN−1].

All phase digital filter is an FIR digital filter based on all phase theory, and its performance is better than other traditional filters. With the development of all phase digital filtering theory, related technologies have been further developed in recent years, such as all phase biorthogonal transform based on all phase digital filtering and windowed all phase biorthogonal transform. Based on the construction process of APBT, combined with APDF and DST, this paper proposes a new all phase biorthogonal transform, all phase discrete sinusoidal biorthogonal transform (APDSBT). Similar to the construction process of APDCBT based on APDF and DCT [12]. Where, f is the n-dimensional expected generalized frequency response vector, and the generalized frequency can also be called column rate F = [FN (0), FN (1), …, FN (N −1]T. The DST transformation adopts type VII DST transformation used in HEVC standard: $S(i,j)=22N+1sin(2i+1)(j+1)π2N+1$ S\left( {i,j} \right) = {2 \over {\sqrt {2N + 1} }}\sin {{\left( {2i + 1} \right)\left( {j + 1} \right)\pi } \over {2N + 1}} Where DST is orthogonal transformation and S−1 = ST. The input-output response of all phase digital filter based on DST, where x (n) is the input signal and y (n) is the output signal. In order to further elaborate the design process of all phase digital filter based on DST and all phase discrete sinusoidal biorthogonal transform, it will be deduced from a mathematical point of view. Assume that Xi (i = 0,1,…, N − 1) represents column I of the all phase data matrix of Time Series {x(n)}; Its output after APDF filtering based on DST is yi (n): $yi(n)=eiT{sT[F⋅(SXi)]}$ {y^i}\left( n \right) = e_i^T\left\{ {{s^T}\left[ {F \cdot \left( {S{X_i}} \right)} \right]} \right\}

Where, “.” represents the point multiplication operation. ei (i = 0, 1,…, N − 1) is the i-th column of the N-dimensional column vector, and only the i-th element in ei is “1” and the other elements are “0”.

Watermark embedding

This algorithm embeds the watermark information into the brightness space of MPEG-2 video stream frame, makes full use of MPEG-2 compression format, and embeds the watermark directly in DCT domain. The specific steps of watermark embedding are as follows:

Bit plane decomposition copyright logo image

An image P with a gray level of 28 can be decomposed into 8 binary images. According to the idea of LSB, the least significant bit of the image represents the detail part of the image. On the premise of not affecting the visual effect, when p is embedded into the video carrier as a watermark, it only needs to be embedded, and P7... Pt is decomposed from the most significant bit part, generally t = 4.

Embedded area selection

Because the human eye is sensitive to the brightness part, in order to improve the robustness of the watermark, the watermark is usually embedded in the most sensitive part of perception. Therefore, the low-frequency coefficients in the DCT block of the brightness space of I frame are selected as the watermark embedding space [13]. The brightness component of each image block is transformed by two-dimensional DCT in the unit of 8×8 image blocks. According to the idea of ISB, the weight of the low bit plane of the watermark image in the reconstructed watermark image is different, so different bit planes are embedded in DCT coefficients with different numbers [14]. Assuming F = {Fi, |0 ≤ i ≤ 63}, the coefficient sequence is obtained by zigzag scanning for the coefficients in each DCT block, and four groups of medium and low frequency coefficients Fa, Fb, Fc and Fd are continuously taken as the embedding area of the watermark. Where: $Fa={Fi|2≤i≤9,Fi∈F}Fb={Fi|10≤i≤13,Fi∈F}Fc={Fi|14≤i≤15,Fi∈F}Fd={Fi|16≤i≤17,Fi∈F}$ \matrix{ {Fa = \left\{ {{F_i}\left| {2 \le i \le 9,{F_i} \in F} \right.} \right\}} \hfill \cr {Fb = \left\{ {{F_i}\left| {10 \le i \le 13,{F_i} \in F} \right.} \right\}} \hfill \cr {Fc = \left\{ {{F_i}\left| {14 \le i \le 15,{F_i} \in F} \right.} \right\}} \hfill \cr {Fd = \left\{ {{F_i}\left| {16 \le i \le 17,{F_i} \in F} \right.} \right\}} \hfill \cr }

According to the different weights of different bit planes when reconstructing image p, the number of DCT coefficients modified when embedding the bit plane into the video carrier is also different. This algorithm embeds each data bit of bit planes P7, P6, P5 and P4 into Fa, Fb, Fc and Fd of each image block respectively.

Embedding watermark

The bit plane decomposed by the copyright mark image P is scanned into a one-dimensional 0–1 watermark sequence, and the information bits of the four bit planes that need to be embedded in the watermark carrier are spread spectrum modulated [15]. Using the opposite pseudo-random mode $St0 St1$ S_t^0\,S_t^1 to modulate 0 and 1 respectively, $St0$ S_t^0 takes the key as Kt, and the - 1 and 1 random sequence generated by the seed. The lengths of $S70$ S_7^0 , $S60$ S_6^0 , $S50$ S_5^0\, , $S40$ S_4^0 are La, Lb, Lc and Ld respectively, then the modulated watermark signal is: $Pit={St0 IFBit=0 St1 IFBit=0$ P_i^t = \left\{ {\matrix{ {S_t^0\,IFB_i^t = 0\,} \hfill \cr {S_t^1\,IFB_i^t = 0} \hfill \cr } } \right.

Modify the DCT medium and low frequency coefficients of the luminance component of the video I frame image block and embed the watermark. When modifying the DCT coefficients of image blocks, the restriction that must be met is that it can not cause perceptual distortion. In the general embedding mode, the watermark embedding strength of the modulated watermark signal obtained from experience is directly superimposed on the carrier, which is formally expressed as follows: $CW=C0+α*PT$ {C^W} = {C^0} + \alpha *{P^T} Where: α is the watermark intensity factor. This algorithm uses the Wascn visual model to calculate the maximum allowable modification value of each coefficient in the embedded vector, that is, the brightness sensitivity coefficient. Each coefficient is modulated according to the brightness sensitivity of the image block, which can ensure the maximum embedding intensity under the condition of observing the distortion limit. The embedding process of bit watermark signal $Pit$ P_i^t of bit plane Pt can be expressed as: $C,TIW=C,TI0+TL,ij*Pit$ C_{,TI}^W = C_{,TI}^0 + {T_{L,ij}}*P_i^t Where: $C,TIW$ C_{,TI}^W , $C,TI0$ C_{,TI}^0 are the DCT coefficients before and after watermark embedding; TI,ij is the luminance sensitivity of each DCI block coefficient calculated according to Watson visual model.

Results and analysis

The program of this experiment is implemented with MATIAB and VC + +. In the experiment, the foreman video test sequence is used as the watermark carrier, and the copyright logo image designed by ourselves is used as the watermark image to test the video watermarking system. The key experimental parameters are shown in Table 1. The PSNR before and after embedding watermark is 43.69. Table 2, Figure 1 and Figure 2 show the accuracy of extracting each bit plane under different coding rates.

Experimental parameter setting

Parameter Value
frame size 353×289
frame rate 26 fps
frame in GOP 13
I/P frame distance 4
bit rate 4Mbps
Y:U:V 6:4:0
video pattern PAL

Extraction accuracy of each watermark bit plane under different coding rates

Bit plane Accuracy of extracting watermark /%

Non-compressed 3Mbps 2.6Mbps
P7 100 100 100
P6 100 97.99 97.01
P5 100 96.01 95.02
P4 100 95.99 94.98

In MPEG2 coding, the reference frames of P and B cannot be deleted and skipped. This algorithm selects the frame of video to embed watermark. It can be seen from Table 3 that this algorithm is robust to common video watermark attacks (MPEG compression, frame loss, frame clipping and frame rearrangement) on the premise of ensuring video quality.

Extraction accuracy of watermark under different attacks

Attack type Specific attack methods Watermark extraction results
Lost I frame Delete frame 12 Video quality is seriously degraded
Lost B or P frames Delete frame 4 and 7 Correct extraction
Frame clipping Frame I part cut Partial loss of watermark
Frame rearrangement Rearrange frames 4 ∼ 8 ∼ 9 ∼ 12 Correct extraction
Conclusion

This paper is a research on video adaptive watermark embedding and detection algorithm based on phase function equation. Aiming at the problems of video watermark embedding strength in balancing the robustness and invisibility of watermark system, a video watermark algorithm based on variable length bit plane decomposition is proposed. According to the different weights of each plane in reconstructing the watermark image after the bit plane decomposition of the 8-bit gray watermark image, the algorithm embeds different bit planes into different numbers of DCT medium and low frequency coefficients, and adaptively adjusts the watermark embedding intensity by using the brightness masking characteristics of HVS and Watson visual model, so as to realize the adaptive embedding of watermark. Experiments show that the video watermarking system is robust and highly transparent. In order to make the application range of HEVC video watermarking more extensive and practical, based on the video watermarking algorithm in this paper, some feature points in the video are selected for watermark embedding, which can further reduce the impact of watermark on video quality. Whether it is HEVC video coding or HEVC video watermarking, there is still room for further improvement. Send some w as further research work in the future.

#### Extraction accuracy of each watermark bit plane under different coding rates

Bit plane Accuracy of extracting watermark /%

Non-compressed 3Mbps 2.6Mbps
P7 100 100 100
P6 100 97.99 97.01
P5 100 96.01 95.02
P4 100 95.99 94.98

#### Experimental parameter setting

Parameter Value
frame size 353×289
frame rate 26 fps
frame in GOP 13
I/P frame distance 4
bit rate 4Mbps
Y:U:V 6:4:0
video pattern PAL

#### Extraction accuracy of watermark under different attacks

Attack type Specific attack methods Watermark extraction results
Lost I frame Delete frame 12 Video quality is seriously degraded
Lost B or P frames Delete frame 4 and 7 Correct extraction
Frame clipping Frame I part cut Partial loss of watermark
Frame rearrangement Rearrange frames 4 ∼ 8 ∼ 9 ∼ 12 Correct extraction

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