Vulnerability Attacks of SVD-Based Video Watermarking Scheme in an IoT Environment

This study reviews the superiority and limitations of the Singular Value Decomposition (SVD)-based video watermarking scheme. First applies key frame selection to the video sequence to obtain an appropriate video frame for the purpose of watermark embedding in this paper. The Fibonacci-Lucas image transformation scrambles the grayscale watermark image before the embedding process. The former scheme satisfies the imperceptibility and robustness aspects. However, it can suffer from the False-Positive-Problem (FPP) in which a counterfeit watermark image can be easily reconstructed by a malicious attacker. This study presents a new technique for overcoming the FPP of the aforementioned scheme. The proposed method embeds the principal components of the watermark image rather than the Singular Value Matrix (SVM) into the host video. As results, the proposed methods yield promising results in terms of imperceptibility as well as robustness. At the same time, it solves the FPP. A theoretical analysis of embedded watermark information is also provided in this work. The theoretical analysis meets the experimental-based results in the SVD-based video watermarking scheme.


I. INTRODUCTION
The usage of multimedia data has grown enormously in recent years. One example of multimedia usage is multimedia data communication via computer networks, the internet, cloud service, as well as the Internet-of-Things (IoT) devices. Nowadays, multimedia data in the format of images and videos has become very popular because it contains more information compared to that of the traditional text-based data. The popularity of image and video usage is also driven by the advance of low-price storage devices and fast communication devices. Securing multimedia data in communication becomes a vital issue. Multimedia data often consists of confidential information or secret valued messages. Several attempts have been developed to protect multimedia data, such as digital image watermarking [1]- [19], secret sharing [20]- [22], etc. These aforementioned methods show promising results in securing multimedia data.
The advances in digital watermarking for securing multimedia data over communication networks and the IoT environment. Most of the SVD-based watermarking schemes simply embed the Singular Value Matrix (SVM) of the watermark information [1]- [7], [9]- [16]. The other schemes directly hide the watermark image into the singular value of the host image [8], [20]. These two simple approaches induce the FPP. This problem leads the ambiguous situation in which a malicious attacker can obtain a counterfeit watermark image from any arbitrary image or video. This condition is very serious from the perspective of copyright and authorship protection. Anyone can claim an authorized multimedia data based on the counterfeit extracted watermark image.
This work aims to solve the FPP caused by embedding the SVM of the watermark image into the host or cover media. The proposed method inherits the effectiveness of the SVD-based video watermarking scheme in [13]. The main difference between the proposed method and former scheme [13] lies in the type of watermark information embedded into the host image. Ponni and Ramakrishnan [13] inserts the SVM of the watermark image into the host VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ image, whereas the proposed method renders the principal components of the watermark image into the host image. With our method, secret watermark information is embedded into the video sequence by exploiting the key frame selection and Fibonacci-Lucas image scrambling method. The former scheme cannot suffer from the FPP because of the SVM embedding strategy. The proposed method overcomes the FPP in [13] by inserting the principal components of the watermark image into the host or cover media. This works well and achieves impressive results for satisfying the imperceptibility and robustness aspects that can be directly applied for securing the multimedia data communication via the IoT environment. Figure 1 illustrates the schematic diagram of proposed method implementation. There are two parties involved in the video watermarking scheme in the IoT environment, i.e. the real video owner and an attacker. In this scenario, the real owner of the video aims to store his own video in the owner server. Before transmitting this video to the owner server, the real owner first embeds his watermark logo into his video for authorization purposes. The watermarked video is then stored on the owner server. On another occasion, the real owner may retrieve his watermarked video from the server via the cloud service or another peripheral. In a normal situation, the real owner will successfully collect his video and watermark logo. On the other hand, a malicious attacker may steal the video from the real owner server via the cloud environment and store it in another device. The malicious attacker cannot easily claim to be the real owner of the video because he cannot show his counterfeit watermark logo. All of these situations are implemented using the proposed method presented in this work over the IoT environment. Thus, the proposed method is very useful in avoiding an ambiguous situation for copyright and ownership protection.
In most typical SVD-based image watermarking schemes, two different metrics are employed to measure the performance of the aforementioned methods. These two metrics are the Peak-Signal-to-Noise-Ratio (PSNR) and Normalized Correlation Coefficient (NCC). The PSNR examines the similarity between the original host image and watermarked image. The PSNR computation is formally defined as:  (1) where A and A w denote the original host image and watermarked image, respectively. These two images are the same size M × N . The symbol (x, y) denotes the spatial coordinates of the image pixel over x = 1, 2, . . . , M and y = 1, 2, . . . , N . The NCC evaluates the similarity between the original watermark image and its extracted version. Then, the NCC is formally defined as (2), as shown at the bottom of the next page, where W and W * denote the original watermark image and extracted watermark image, respectively. The µ W and µ * W are the mean value of W and W * , respectively. The symbol (i, j) represents the spatial position of a pixel in an image, for i = 1, 2, . . . , M and j = 1, 2, . . . , N . Higher values of PNSR and NCC indicate greater similarity between two investigated/measured images. Thus, the SVD-based image watermarking schemes should achieve a higher PSNR score for the watermarked image as well as a higher NCC value for extracted watermark image.
In the field of SVD-based video/image watermarking schemes, our key contributions can be highlighted as follows: 1) Pointing out the FPP of the former SVD-based video watermarking scheme. 2) Developing a simple method to solve the FPP in [13]. 3) Presenting a formal mathematical analysis of the FPP in terms of Squared Error (SE). 4) Proving the FPP based on theoretical analysis of the correlation coefficient. Based on our best knowledge, this is the first time theoretical analysis of the SVD-based video and image watermarking has been conducted. Thus, the other researchers may consider these analyses before developing their own SVD-based video and image watermarking scheme to avoid the FPP. Further, we offer strong evidence that embedding the principal components yields better performance compared to inserting the SVM in the SVD-based video/image watermarking scheme.
The rest of this study is organized as follows: In Section II, reviews the former SVD-based video watermarking scheme along with its minor limitations. The proposed method for overcoming the problem of the former scheme in Section III. Sections IV and V provide theoretical analyses of the former scheme and the proposed method. Section VI shows performance comparisons with other existing methods. Conclusions are given in Section VII.

II. FORMER SVD-BASED VIDEO WATERMARKING SCHEME
We briefly discuss the usability and slight limitations of this aforementioned SVD-based video watermarking. The limitations of the [13] are reported with the experimental findings and supported by theoretical analysis. Therefore, we indicate the problem and offer a simple solution for this aforementioned issue. This part starts with the formal definition of SVD on decomposing an arbitrary matrix. Let A be an arbitrary matrix of size N × M . Each entry of this matrix is the real-value, i.e. A ∈ R N ×M . The SVD operation on matrix A produces three matrices indicated as: where U and V are two unitary matrices, referred to as the left and right singular matrix, respectively. These two matrices are denoted as U ∈ R N ×r and V ∈ R M ×r , respectively. The symbols r and T denote the rank of matrix A and transpose operator on the matrix, respectively. In this work, the symbols ⇒ or ⇐ denote the right and left assignment operator, respectively. The other matrix is simply an orthogonal matrix, referred to as a SVM, in which its diagonal entry consists of the Eigen-value of matrix A. This SVM is denoted as ∈ R r×r , while each diagonal can be represented as r = diag {σ 1 , σ 2 , . . . , σ r }. The values of σ i for i = 1, 2,. . . , r represent the singular value composing and ordering in ascending manner as σ 1 ≥ σ 2 ≥ · · · ≥ σ r ≥ 0.
The typical SVD-based image watermarking schemes exploit the effectiveness of SVD operation to hide specific watermark information into the host image. Most SVD-based image watermarking methods embed the SVM of the watermark image into the host image. The main goal of this method is to obtain a good extracted watermark image in the watermark extraction step. A small disturbance of the SVM induces a slight distortion in a reconstructed image. The effect of disturbance on the SVM can be explained as follows. Suppose the SVD operation decomposes the matrix A into three matrices U , V , and . Some noises are then injected into the SVM . This noise injection is specifically denoted as + ε, where ε is generated random noise. By applying the inverse SVD operation, we obtain the reconstructed matrixÃ. This inverse process can be represented as Uˆ V T ⇒Ã. If the magnitude of noise is small enough, then the reconstructed matrixÃ is visually similar to that of the original matrix A, i.e.Ã ≈ A. Figure 2 demonstrates the effect of noise addition into the SVM. Figure 2 (a) is the Lena image used as A, whereas the Figs. 2 (b)-(c) are the reconstructed imagesÃ obtained by injecting the zero-mean white Gaussian noise ε with Standard Deviation (SD) of 10 and 25, respectively. Herein, the noise is only added into the diagonal component of the SVM , i.e.σ i ⇐ σ i +ε, to obtain reconstructed imageÃ. It impliesˆ = diag σ 1 ,σ 2 , . . . ,σ r . As shown in these figures, a small disturbance in the SVM yields an inferior effect on the reconstructed image. The reconstructed image is visually identical to that of the original image.
Another experiment is conducted to examine the effect of noise disturbance on the SVM. All entries in the SVM are added with the noise denoted asˆ = + ε.  entries of the SVM are distorted with zero-mean white Gaussian noise ε under the SD are 5, 15, and 25, respectively. Even though the quality of reconstructed imageÃ is less than the original image, we can still recognizeÃ as Lena image. This is the main reason most typical SVD-based image watermarking schemes simply embed the SVM into the host image. The extracted SVM is often distorted or different compared to the original one. In this case, the extracted SVM can be viewed as a distorted SVM with additive noise. If we simply multiply this extracted SVM with the left and right singular matrices, it obtains an almost visually identical watermark image. Therefore, we always obtain a perfect extracted watermark image. This benefit led to the huge success of SVD-based image watermarking schemes.
In other cases, the watermark information is often embedded into the SVM of the host image. In this strategy, a host image is first divided into several non-overlapping blocks. The SVD operation further decomposes each image block to obtain two unitary (U , V ) and one singular value ( ) matrices. The watermark information is simply added into the largest singular value of each block. This process can be assumed as the noise injection into the largest singular value, i.e.σ 1 = σ 1 + ε. By performing the inverse SVD operation on each image block, we obtain the reconstructed imageÃ. Figure 2 (g)-(h) are the reconstructed imageÃ while the largest singular values of each image block are distorted with zero-mean white Gaussian noise over SD are 5, 15, and 25, respectively. These figures show the reconstructed images are visually identical to that of the original Lena image. This usability motivates the proposed method to deliver secure SVD-based image watermarking. The proposed method renders the watermark information into the largest singular value of each host image block.

A. EMBEDDING THE WATERMARK INFORMATION INTO THE HOST IMAGE
This method embeds a specific watermark image in grayscale format into the video sequence. This video is further referred to as the host video or media cover. The host video sequence is first processed with the key frame selection to obtain the best and suitable part of video for the watermark embedding purpose. Therefore, the red channel of the selected video frame is acquired to embed the secret watermark information.
Since the former scheme only needs the red channel, it can be regarded as the typical SVD-based image watermarking scheme. Thus, the selected red channel of the host video is then regarded as the host image. The formal watermark embedding of the former scheme is described in detail as follows. Let A be a host image of size M × N , while W denotes the watermark image of size m × n. Herein, the image A is the red channel of the selected video frame. In [13] embeds the SVM of W into A by incorporating the two dimensional Discrete Wavelet Transform (DWT) [23]-[25] and Fibonacci-Lucas image scrambling method. Prospective readers are suggested to refer to [13] for a detailed explanation of the Fibonacci-Lucas image scrambling method. The step-by-step watermark embedding procedure in [13] is then given as follows: Step E1: Perform a one-level DWT operation on host image A to yield several transformed subbands denoted as: where I {·} and A θ denote the DWT operation and DWT transformed subbands, respectively. For θ = {LL, LH, HL, HH}.
Step E2: Select the LH-band of the DWT transformed image to hide the watermark image as: where X S denotes the selected image for the watermark embedding purpose.
Step E3: Apply the SVD operation to the selected image X S . This process is defined as: where U A and V A are two unitary matrices of A, and A is the SVM.
Step E4: Perform the Fibonacci-Lucas image scramble on watermark image W . This scrambling process is defined as: where L {· } and W b denote the operator of Fibonacci-Lucas image scrambling and the scrambled watermark image, respectively.
Step E5: Apply the SVD operation to the scrambled watermark image W b as follows: (8) where U w and V w are two unitary matrices, and w is the SVM.
Step E6: Embed the watermark information as contained in SVM w into the SVM A of the host image as: where n and α denote the modified SVM of the host image and scaling factor, respectively. This part is the most critical step in typical SVD-based image watermarking.
Step E7: Apply the inverse SVD operation by multiplying three matrices n , U A , and V A . This process is represented as: where X sw denotes the watermarked image in the LH-band. In this process, the matrices U A and V A are obtained from Step E3. Whereas, the matrix n is from Step E6.
Step E8: Perform a one-level inverse DWT operation of the host subbands by replacing the LH-band with X sw . This computation is defined as: where A w and I −1 {·} denote the watermarked image and operator of the inverse DWT process, respectively. The subbands A LL , A HL , and A HH are from Step E1. From this step, we obtain the watermarked image containing the watermark image information.

B. EXTRACTING THE WATERMARK INFORMATION FROM THE WATERMARKED IMAGE
The watermark extraction process is substantially the reverse process of the watermarking embedding. The watermark information is retrieved from the watermarked process.
In [13], the key frame selection is first applied to the watermarked video sequence. This process produces the selected frame of the watermarked video. Since the former scheme only considers the red channel of this selected frame, the watermark extraction process thus reduces to the typical SVD-based image watermark extraction. We attempt to extract the watermark information from the watermarked image obtained after key frame selection and red channel determination. The subsequent processes for the extraction procedures are then given as follows. Let A * w be the potentially corrupted the watermarked image. In most situations, the watermarked image is often destroyed by some image manipulations or geometric distortions such as noise addition, cropping, etc. The watermark extraction process aims to reconstruct the watermark image from A * w .
Step X2: Select the LH transformed image to retrieve the watermark image. It can be calculated as: where X * s denotes the selected LH-band of a potentially corrupted watermarked image.
Step X3: Apply the SVD decomposition on X * s to obtain three matrices as defined below: where U * A , V * A , and * A are the decomposed matrices. We only need matrix * A to extract the watermark image.
Step X4: Extract the SVM of the watermark image as: where w * denotes the extracted SVM of the watermark image. Herein, the matrix A is from Step E3 of the watermark embedding process. The scaling factor α should be identical to that used in Step E6 of the watermark embedding stage to yield the correct result.
Step X5: Reconstruct the watermark image using the inverse SVD operation as: where W * b denotes the extracted watermark image. It should be noted W * b is still in scrambled form. An additional step is required to obtain the final extracted watermark image. The matrices U w and V w for computing the W * b are obtained from Step E5 of the watermark embedding process. These two unitary matrices can be regarded as secret keys in the SVD-based image watermarking scheme.
Step X6: Apply the inverse Fibonacci-Lucas image scrambling method to W * b as: where W * and L −1 {·} denote the extracted watermark image and operator of the inverse Fibonacci-Lucas image scrambling, respectively. This descrambling operation forces each pixel on the extracted watermark image into the original position. Thus, we obtain an acceptable extracted watermark image.

C. VULNERABILITY ATTACKS ON ON THE FORMER METHOD
In [13], the SVD-based video watermarking scheme satisfies the imperceptibility and robustness aspects. The watermark image cannot be easily perceived in the watermarked image. Therefore, the watermark image can be successfully extracted from the watermarked image, even though this image is corrupted by some noise or destroyed by common manipulations and distortions. The following experiment reports the effectiveness of the [13]. Figure 3 shows several video clips for testing purposes. These videos in color format are regarded as the host video or cover media. A set of grayscale images in Fig. 4 are turned into the watermark image. In the first experiment, the watermark image in Fig. 4 (a) is embedded into the host video in Fig. 3 (a) by selecting the scaling factor α = 0.1. Herein, the watermark image is first scrambled with the Fibonacci-Lucas transform using the specific secret key K 1 . Figure 5 (a) displays the watermarked image yielding PSNR = 35.03 dB. Based on this result, the former SVD-based video watermarking scheme satisfies the imperceptibility aspect indicating a high PSNR value. The watermark image which is directly extracted from the watermarked image, as shown in Fig. 5 (b). It produces NCC = −0.0017. After performing the inverse Fibonacci-Lucas transform with secret key K 1 , the extracted watermark image is given in Fig. 5 (c). The NCC value of this watermark image is NCC = 0.9949. Again, the former scheme yields a good extracted watermark image with a high NCC score. Figure 5 (d) shows the extracted watermark image after applying the inverse Fibonacci-Lucas transform with different secret key K 2 . It induces the NCC = −0.0021 for the extracted watermark image. The additional step in the watermarking scheme, i.e. Fibonacci-Lucas transform, increases the robustness aspect of the high security issue. Thus, the former SVD-based video watermarking scheme yields good results in terms of imperceptibility and high security aspects. VOLUME 8, 2020  Additional experiments are conducted to test the robustness aspect of the former SVD-based video watermarking scheme. Herein, the watermarked image is manipulated by injecting noises, cropping, etc.  Figure 7 shows a set of extracted watermark images after extracting the watermark information from a set of attacked watermarked images in Fig. 6. These attacks are quite similar to the typical SVD-based image watermarking scheme because the [13] applies the key frame selection on the host video to embed the watermark information. The key frame selection in the host video produces the selected area which is in two dimensional data or image format. Thus, the host data can be regarded as an image. This situation offers an easy way to embed the watermark information in image format into the host data (in the two dimensional image). Therefore, the watermark insertion and extraction in [13] can be applied accordingly. In this experiment, we use the correct key for the Fibonacci-Lucas image scrambling that the NCC scores of The other experiment examines the FPP in the former SVD-based video watermarking scheme. This problem causes the vulnerability attack on the SVD-based video/image watermarking scheme. This vulnerability attack occurs while an unauthorized attacker tries to generate the counterfeit watermark image from any arbitrary watermark image. In this situation, an attacker can successfully obtain the counterfeit watermark image and claim authorship. The vulnerability attack can be illustrated as follows. Suppose an attacker tries to extract the watermark image from the watermarked image as given in Fig. 5 (a). In this case, we know the watermarked image of Fig. 5 (a) contains the watermark image of Fig. 4. (a). This attacker directly extracts the watermark information using the wrong side information, i.e. U w and V w obtained from Fig. 4 Herein, a set of Fig. 4 (b)-(d) are referred to as the counterfeit watermark image. In Fig. 8 (a), (c), and (e) are extracted watermark images, respectively with NCC = {0.0016, −0.0044, 0.0026}, obtained using the wrong side information from Fig. 4 (b)-(d). After applying the Fibonacci-Lucas transformation with the correct key, the extracted watermark images can be seen in Fig. 8   are identical to that of the counterfeit watermark images with acceptable NCC scores. Thus, it can expect the extracted watermark image will be similar to the counterfeit watermark image if we use the counterfeit keys U W and V W . Even though the former SVD-based video watermarking scheme satisfies the imperceptibility and robustness aspects, it cannot resist the FPP. Thus, the former scheme is not suitable for copyright protection.

III. PROPOSED SVD-BASED VIDEO WATERMARKING
The proposed method aims to solve the problem of the [13] by modifying the watermark information embedded into the video host. The proposed method embeds the principal components of the watermark image rather than the SVM into the media cover. This technique effectively solves the aforementioned problem in the former SVD-based video watermarking scheme. In addition, the proposed method also exploits the adaptive scaling factor to further increase the robustness against malicious attacks such as image manipulations and geometric distortions.

A. PROPOSED WATERMARK EMBEDDING STRATEGY
In contrast to the [13], the proposed method embeds the principal components of the watermark image into the host video. The principal components are the matrix obtained from the multiplication between the left singular vector and SVM. The usage of the principal component effectively overcomes the FPP. In similar fashion to that of [13], the proposed method employs key frame selection to acquire the best and suitable video sequence for injecting the watermark information. Only the red channel is needed on the selected frame. Therefore, the proposed method can also be considered a typical SVD-based image watermarking scheme.
The proposed method requires a host image A of size M ×N and watermark image W of size m × n that the method embeds W into A with the block-wise strategy, i.e. one piece of watermark image information is embedded into one image block of the host image. The proposed method also needs the DWT and SVD in the watermark embedding and extraction process. Thus, the proposed watermark embedding can be explained step-by-step as follows: Step WE-1: Perform one-level DWT operation on host image A as: Step WE-2: Select the LL-band of the DWT transformed host image. The selected subband is further divided into several non-overlapping blocks denoted as: 1 , a 2 , . . . , a i , . . . , a MN 2mn (19) where a i denotes the i-th image block of LL-band, for i = 1, 2, . . . , MN 2mn . Herein, the number of image blocks should be identical to the number of pixels on the watermark image.
Step WE-3: Perform the Fibonacci-Lucas image scrambling on the watermark image as: where W b denotes the scrambled watermark image.
Step WE-4: Apply the SVD operation to the scrambled watermark image W b as follows: Step WE-5: Compute the principal components of the watermark image as: where W U denotes the principal components of the watermark image. Herein, the size of W U is also m×n. In contrast with the [13], the proposed method embeds the principal components into the host image.
Step WE-6: Apply the SVD operation to each image block a i that the decomposition process can be denoted as: where U i , V i , and i are three matrices of image block a i . Herein, we apply the SVD operation over all image blocks, for a i and i = 1, 2, . . . , MN 2mn . The diagonal component of matrix i is i = diag (σ 1 , σ 2 , . . . , σ r , 0, . . . , 0). We only consider the largest singular value, i.e. σ 1 , for the watermark embedding purpose.
Step WE-7: Embed the principal components of the watermark image into the largest singular value of each image block as: where λ w (x, y) denotes the modified largest singular value. The value of W U (x, y) indicates the principal component of the watermark image on position (x, y), for x = 1, 2, . . . , m and y = 1, 2,. . . , n. Similar to the [13], this step is the most critical point in the proposed watermark embedding process.
Step WE-8: Replace the largest singular value (σ i ) of each image block a i with the value of λ w (x, y). This replacement process can be performed as: where iw denotes the modified SVM on the i-th image block, for i = 1, 2, . . . , MN 2mn .
Step WE-9: Apply the inverse SVD operation on each image block a i that can be denoted as: where a iw is the i-th modified image block, for i = 1, 2, . . . , MN 2mn . The matrices U i and V i are obtained from Step WE-6.
Step WE-9: Collect all modified image blocks, a iw , and construct a modified LH-band. This process can be given as follows: where A w LL is the modified LL-band.
Step WE-10: Perform inverse one-level DWT operation to obtain a watermarked image as: where A w denotes the watermarked image.

B. PROPOSED WATERMARK EXTRACTION STRATEGY
The watermark extraction process of the proposed method can be simply performed over several steps. The key frame selection and red channel determination are applied to the watermarked video sequence to obtain a specific watermarked image. The watermark extraction process of the proposed method is explained as follows. Let A * w be the potentially corrupted watermark image. The following steps are conducted for extracting the watermark image from A * w : Step WX-1: Perform one-level DWT operation on image A * w as: where A * θ denotes the transformed subbands, for θ = {LL, LH, HL, HH}.
Step WX-2: Select the LL-band and divide it into several non-overlapping image blocks. The size of the image block should be identical to that used in the watermark embedding process as: where a * i denotes the i-th image block of transformed LL-band, for i = 1, 2, . . . , MN 2mn .
Step WX-4: Extract the principal component of the watermark image from the largest singular value σ * 1 of each image block. This extraction process can be computed as follows: where W * U (x, y) denotes the extracted principal component on pixel position (x, y), for x = 1, 2, . . . , m and y = 1, 2,. . . , n. The value of σ 1 is from Step WE-7 under the same position (x, y).
Step WE-5: Reconstruct the watermark image by multiplying the extracted principal component W * U with V w that can be calculated as follows: where W * b denotes the reconstructed extracted watermark image. Herein, the matrix V w is obtained from Step WE-4. The matrix V w can be regarded as a secret key in the proposed SVD-based image/video watermark method.
Step WE-6: Apply the inverse Fibonacci-Lucas image scrambling to image W * b . This image descrambling process can be defined as: where W * denotes the extracted watermark image. Herein, the secret key for Fibonacci-Lucas image scrambling should be identical to the watermark embedding and extraction process.

C. PROPOSED METHOD WITH ADAPTIVE SCALING FACTOR
The scaling factor plays an important role in the SVD-based image/video watermarking schemes. The scaling factor, α, determines the robustness strength as well as the imperceptibility aspects. A suitable α value effectively hides the watermark image such that its presence cannot be perceived by human vision. It can be said the SVD-based image and video watermarking methods satisfy the imperceptibility criterion for good algorithm design. In addition, the developing watermarking methods with specific α should be robust against several image manipulations and geometric distortions that can be regarded as malicious attacks. A good watermarking scheme should meet the robustness issue against several unauthorized malicious attacks. The determination of α is not easy task. The presence of the watermark image cannot be perceived by setting a small α value. However, it is less robust against several malicious attacks with small α. In contrast, the SVD-based image/video watermarking becomes more robust against various attacks by incorporating a high value α. Therefore, the watermark image will be easily recognized in the watermarked image with high α. In addition, choosing a single scaling factor is less suitable for the SVD-based image/video watermarking scheme in adapting to hard malicious attacks [19]. Despite using a single scaling factor, in [13] employs an adaptive scaling factor. This strategy gives different scaling factors by examining the magnitude of the watermark information. The adaptive scaling factor can be viewed as constructing α in matrix form rather than a single value that the factor α of size N × M is formally defined as follows: For i = 1, 2, . . . , N , where α min and α max are the minimum and maximum limit of the factor. These two values are commonly set as α min = 0.25 and α max = 1 [19]. Herein, the symbol j denotes the row of watermark images. Different rows of watermark images own different scaling factors. Thus, the robustness and imperceptibility will increase using the adaptive scaling factor.

IV. THEORETICAL ANALYSIS IN TERMS OF SQUARED-ERROR
This section delivers the theoretical analysis between the proposed method and [13] in terms of SE. The problem of the former scheme is explained in detail in this section and supported by theoretical analysis. Therefore, the benefit and correctness of the proposed method are also given in this section. Thus, we can expect an objective measurement between the proposed method and former scheme. This section starts with discussion of SE and PSNR. The effects of embedding the SVM and principal components are then analyzed with formal mathematics to illustrate the occurrence of the FPP.

A. SQUARE-ERROR AND PEAK-SIGNAL-TO-NOISE-RATIOS
The value of SE is simply the norm of difference between two compared matrices/images. This value can be computed as: where · 2 denotes the Euclidean norm. Therefore, the Euclidean norm of difference between A 1 and A 2 is given as The symbols M and N denote the image size. The SE score between the two images can be simply calculated from the sum of the squared difference between each pixel of two measured matrices/images. Thus, the PSNR value can be also defined in terms of SE as follows: where A 1 − A 2 2 2 denotes the SE between A 1 and A 2 . This PSNR computation is identical to that of the PSNR calculation in (1). If A 1 and A 2 are diagonal matrices, the PSNR calculation in (37) implies a simpler computation compared to that used in (1). The SE in (37) can be only calculated over diagonal entries between A 1 and A 2 , not in element-wise computation as used in (1).

B. EFFECT OF EMBEDDING A SINGULAR VALUE
This subsection presents the effect of embedding a singular value into the host image used in [13]. This technique induces the FPP. The formal analysis is given as follows. Let W and W * be the original watermark image and extracted watermark image, respectively. These two matrices employ two identical matrices, U w and V w . The only difference between W and W * lies in their SVM. In the watermark embedding step [13], the SVD decomposes W to yield three matrices U w , w , and V w , as indicated by the following process: The matrices U w and V w are secretly kept as secret keys for the watermark extraction purpose. Some malicious attacks or rounding operations after the watermark embedding process may destroy the quality of the watermarked image. Thus, the extracted watermark image cannot be perfectly obtained in the extraction process. Let * w be the extracted SVM obtained from the potentially corrupted watermarked image. Then, the extracted watermark image W * can reconstruct by multiplying the extracted SVM * w with secret keys U w and V w as indicated below: The similarity between W and W * can be assessed in terms of SE between these two matrices with the element-wise computation as formulated: By substituting (38) and (39) into (40), the SE between W and W * can be further recomputed as: The SE score between W and W * are simply the Euclidean norm of difference in terms of SVD decomposed matrices. The SE between W and W * can be further redefined as the matrix trace as follows: where Tr {·} denotes the trace of the matrix operator. With simple matrix algebraic manipulation, the last form can be further simplified as Since U w is the unitary matrix, it implies U T w U w = I . The property of identity matrix tells us AI = IA = A. Thus, the SE in (42) can be subsequently simplified as By incorporating the unitary property of V w , i.e. V W V T w = V T w V w = I , each entry in (43) can be simply as below: Substituting (44) to (47) into (43), one can trivially obtain: The SVM consists of non-zero entries in the diagonal element. Therefore, the two entries in (48) are equivalent as summation between their diagonal element indicated as T Subsequently, the form (48) can be further recalculated as Using the definition of matrix trace, the form in (49) is then given as Tr w − * w T w − * w . Finally, one obtains the final form as w − * w 2 2 . The last form indicates the SE between W and W * is equivalent to: The SE between the original and extracted watermark is equivalent to the SE between their singular value matrices if they incorporate identical U w and V w . The PSNR score between the original watermark image W and extracted watermark image W * can be computed as:   where w − * w 2 2 is the SE between singular value matrices w and * w . This SE is simply given as . Thus, the PNSR value can be alternatively computed with the SE of the singular value matrices. It requires simpler computation because it only considers relements on the singular value matrices, where r is the matrix rank of w or * w . The effect of changing the SVM is first investigated under visual inspection. The Lena image of Fig. 2 (a) is utilized for the testing image, whereas a set of grayscale images in Fig. 9 are used for counter examples. These images are denoted as {I 1 , I 2 , . . . , I 6 }. The SVM of the Lena image is replaced with the SVM from images in Fig. 9. Figure 10 demonstrates a set of Lena images, while its singular value matrices are replaced with the SVM of Fig. 9. All of these images are visually similar to that of the original Lena image. The differences are their brightness.
The effect of changing the SVM is subsequently investigated under the SE and PSNR comparison. Tables 1 and 2 summarize the effect of changing the SVM in terms of SE and PSNR values, respectively. These tables show A, B 2 2 = A , B

C. EFFECT OF EMBEDDING PRINCIPAL COMPONENTS
This subsection describes the effect of embedding the principal components into the host image. The usage of principal components in the proposed method effectively overcomes the FPP. The detailed formal mathematical analysis of embedding principal components for the proposed method is given as follows. Let W and W * be the original watermark image and extracted watermark image, respectively. First, the SVD decomposes W to yield three matrices as: Therefore, the W * is composed by multiplication of its principal components, i.e. U * w * w , with the left singular vector V w of W . This process is illustrated as: The SE between W and W * is then computed as: Bringing (53) and (54) into (55), the SE score between W and W * can be alternatively calculated as W − W * 2 2 = U w w V T w − U * With simple algebraic manipulation, the form (65) drives the following From (65), it concludes the SE between W and W * are simply Euclidean norm of difference between their principal components. Specifically, the SE is given as . From this observation, the SE score between W and W * is only determined by the difference between their principal components. In accordance with the PSNR value, the similarity between W and W * can be objectively measured using the PSNR (W , W * ) = 10 log 10 Since the W − W * 2 2 is identical to U w w − U * w * w 2 2 , the PSNR score can be alternatively assessed with the metric 10 log 10 . The difference between the principal components of W and W * determines the PSNR value. If the difference is relatively small, it implies the PSNR value between W and W * will be high enough, and vice versa. We examine the effect of changing the principal components of the Lena image in Fig. 2 (a) with the principal components of the images in Fig. 9. Figure 11 shows a reconstructed Lena image set while its principal components are exchanged with the principal components of Fig. 9. One obtains nothing by exchanging the principal components over two images. This conclusion is also supported by the experimental finding, as summarized in Tables 3 and 4. The SE and PSNR between two images are simply determined with the SE and PSNR between their principal components, respectively. Thus, the choice of principal components for watermark embedding is better in comparison to the SVM. This is the main reason for the proposed method, which  embeds the principal components into the host cover or host video sequences.

V. THEORETICAL ANALYSIS IN TERMS OF NORMALIZED CORRELATION COEFFICIENT
The NCC measures the similarity between the original watermark image and extracted watermark image. The different watermark insertion strategies yield different NCC values. The former scheme embeds the singular values of the watermark image into the host image. This leads to a higher NCC score. The proposed method inserts the principal components of the watermark image to produce a lower NCC score. This issue is further elaborated in the following subsection.

A. EFFECT OF EMBEDDING A SINGULAR VALUE
The former scheme embeds the SVM of watermark image into the host image. This technique induces FPP. The extracted watermark image is often with a high NCC score. This high NCC score can be explained as follows. Suppose W and W * denote the original watermark and extracted watermark image, respectively. These two matrices own identical left and right singular vectors, but they have a different SVM. Specifically, these two matrices are denoted as W ⇐ U w w V T w and W * ⇐ U w * w V T w . Beside of computation in (2), the NCC value between W and W * can be alternatively calculated as follows: where (i, j) denotes the spatial pixel position. Note, W and W * in (66) are in the normalized version. As similar to SE between W and W * , the NCC between these two matrices can also be analytic derived. With the help of matrix trace computation, the first term in (66) can be rewritten as  the SVM and principal components. In case of the embedding SVM, Table 5 shows the relationship with the NCC score NCC (A.B) = NCC( A , B ). The Table 6 proves NCC (A, B) = NCC(U A A , U B B ) if the principal component of watermark image is embedded into the host image. Embedding principal components of watermark image gives better performance compared to that of inserting SVM as indicated with lower NCC score. Thus, the proposed method gives better performance.

VI. EXPERIMENTAL RESULTS
The performance of the proposed method is first assessed in terms of the imperceptibility test. In this experiment, the occurrence of the watermark image in the host video is simply judged by visual investigation as well as objective measurement. Two objective metrics (PSNR and NCC) are employed to measure the proposed method performance. This section also discusses the robustness and vulnerability tests for the proposed method against various malicious attacks and FPPs. The end of this section summarizes the performance comparison in choosing a single and adaptive scaling factor for the proposed method.

A. IMPERCEPTIBILITY TEST
The performance of the proposed method is measured under the watermarked video as well as the extracted watermark image. Two criterions are used to examine the proposed method performance, i.e. visual inspection and objective assessment. The proposed method satisfies the imperceptibility aspect if the presence of the watermark image cannot be visually perceived by human vision. The quality of the extracted watermark image is measured over the NCC criterion. In addition, the PSNR score indicates the imperceptibility aspect for the watermarked video.
First, the proposed method embeds the grayscale watermark image, as shown in Fig. 4 (a) in the color host video, as given in Fig. 3 (a). The proposed method selects a suitable frame from the host video using the keyframe selection strategy for watermark information embedding. It employs a single scaling factor, α = 0.1. Figure 12 (a) shows the watermarked video with PSNR = 39.78 dB, where Fig. 12 (b) delivers the extracted watermark image before applying the Fibonacci-Lucas image descrambling. It gives the NCC = 0.0033 for this extracted watermark image. The extracted watermark image after applying the inverse of Fibonacci-Lucas image transformation with correct scrambling secret key K 1 , as shown in Fig. 12 (c). The proposed method yields the NCC = 0.9758 for the extracted watermark image. However, one obtains nothing if an incorrect scrambling secret key K 2 is applied to the extracted watermark image with NCC = 0.0143. This experiment concludes the proposed method effectively achieves the imperceptibility aspect. In addition, the security of the proposed method is improved by exploiting the Fibonacci-Lucas image scrambling.

B. ROBUSTNESS TEST
Extensive experiments are also conducted to further examine the proposed method performance in terms of the robustness aspect. Herein, the experiments consider the watermarked video of Fig. 12 (a). Some attacks such as common image manipulations, geometric distortions, noise addition, etc., are applied to the watermarked video. The proposed method performs well if it can successfully extract the correct watermark image from the distorted watermarked video. Figure 13 depicts a set of attacked watermarked images over various distortions and manipulations. A set of attacks corrupted in Fig. 13 are identical to that of being used in Fig. 6 of Section II. C. We attempted to extract several watermark images from watermarked video given in Fig. 13. The effectiveness of the proposed method is measured in terms of the NCC over the extracted watermark images. Figure 14 shows a set of extracted watermark images obtained from a set of watermarked video as given in Fig. 13. The values of NCC are respectively reported as NCC = {0.9317, 0.8377, 0.8710, 0.9189, 0.7379, 0.7936, 0.9053, 0.7301, 0.8847, 0.9156, 0.8734, 0.4167}. Note, the scaling factor is the same as used previously, i.e. α = 0.1. Figure 14 shows the proposed method produces a set of watermark images with acceptable quality. Therefore, it can be concluded the proposed method meets the indicated robustness aspect with the correct and acceptable quality of extracted watermark images. This work is robust against malicious attacks.

C. VULNERABILITY TEST
The occurrence of the FPP is examined for the proposed method. The vulnerability test is almost identical to that of being used to examine the former scheme. This experiment considers the watermarked video, as shown in Fig. 12 (a). The counterfeit watermark images are reconstructed by multiplying the principal components extracted from the watermarked video with the counterfeit secret keys U w and V w . These two secret keys are calculated from images, as shown in Fig. 4. Figure 15 displays the extracted watermark images constructed with the malicious counterfeit secret keys. As shown in this figure, the content of all extracted watermark images   are also considered to test the proposed method performance. Each watermark image is embedded into the each host video after applying the video keyframe selection, as mentioned in former method. The quality of the watermarked images is further calculated in terms of the PSNR by averaging its value over all watermarked images. Herein, a single scaling factor is used. We examine the scaling factor in the range [−2,2]. Figure 16 (a) reports the comparison in terms of average PSNR values over various scaling factors. The effect of the image scrambling method, i.e. Fibonacci-Lucas transform, is compared against the proposed method without image scrambling. Under the same scaling factor, the proposed method without image scrambling gives a better performance compared to that of the proposed method with the image scrambling. This experiment overlooks the effect of image scrambling for the extracted watermark image. In this case, a set of watermark images are extracted from several watermark videos as previously used. The quality of the extracted watermark image is examined by averaging the NCC scores over all extracted watermark images with various scaling factor. Figure 16 (b) displays the performance comparisons of the proposed method with and without the image scrambling technique in terms of average NCC values. In contrast to the previous experiment, the proposed method with image scrambling yields better NCC performance than the proposed scheme without image scrambling. The Fibonacci-Lucas image scrambling increases the robustness aspect of the proposed method. The effects of the single and adaptive scaling factors are further examined in this experiment. The performances of the proposed method with a single and adaptive scaling factor  are examined over all videos in Fig. 3 as host videos and all images in Fig. 4 as watermark image. The comparison is conducted in terms of average scores. The performance comparison for the proposed method with a single and adaptive scaling factor over various malicious attacks, as shown in Fig. 17. The proposed method with an adaptive scaling factor is more robust against various attacks compared to that using a single scaling factor. Table 7 also supports this conclusion. Even though the proposed method with an adaptive scaling factor yields lower PSNR, it can resist various attacks on the watermarked image. Thus, this work can be regarded as a good candidate for applying the image watermarking technique in the IoT environment.

VII. CONCLUSIONS
A new technique on the SVD-based video watermarking scheme has been presented in this work. This technique overcomes the FPP occurring in the former existing scheme. The proposed method hides the principal components of the watermark image in the host image. This simple technique yields good performance in terms of imperceptibility aspect as well as the robustness issue. In addition, the adaptive scaling factor gives a more robust ability for the proposed method. In future work, the determination of scaling factor will be viewed as an optimization problem. The optimized scaling factor will hopefully increase the robustness and other aspects of the proposed SVD-based video watermarking scheme.