Frame-rate conversion detection based on periodicity of motion artifact

Article
  • 118 Downloads

Abstract

With the advances in digital video technology, it is becoming easier to forge the digital video without introducing any artificial visual trace. The temporal domain of the digital videos is one of the main targets of video tampering, and video frame-rate conversion is one of the common operations for temporal video tampering such as temporal splicing and video speed adjustment. This operation necessarily accommodates temporal interpolation that introduces the periodic motion artifact on the motion trajectories. In this paper, the frame-rate converted video detection method is proposed based on the motion artifact. The experimental results demonstrated the performance of the proposed method through the extensive experiments on 1300 original videos and 18,000 frame-rate converted videos in uncompressed and H.264/AVC formats. Especially, for the nearest neighbor and motion-based interpolation, the proposed method could detect over than 93.35% of the frame-rate up-converted videos while exhibiting 0.01 false positive rate.

Keywords

Digital forensics Video forensics Frame-rate conversion Motion artifact 

1 Introduction

With highly sophisticated IT technology, various multimedia tools which improve the quality of our life have been developed. Among them, digital video cameras and video editing software are the rate of exponential growth. Eventually, the high quality digital videos can be found in our daily life. The greatest advantage of the digital video, which provides the high quality immersive viewing environments to viewers compared to digital images, made the digital videos come into mainstream use in various fields. However, the increased use of digital videos has also resulted in many misuses. The most common misuse is to forge the frames in the video frames to fabricate the recorded scene. Combined with highly experienced users equipped with sophisticated editing software that can doctor the digital videos, the fabricated digital videos, which are realistic, are produced. Furthermore, it is becoming easier to edit the video footages without introducing any artificial visual trace for the ordinary users. The forged digital videos could have tremendous effects on various fields such as politics, economy, law enforcement, and so on. One of the favorable solutions for the problem is the multimedia digital forensics. The multimedia digital forensics provides the forensic information on how the multimedia data is acquired and processed without any side information [12, 14].

Last few decades have seen considerable development in the area of the digital image forensics [12, 14]. Moreover, recently, the digital video forensics has been becoming a major interest in the area of the multimedia digital forensics [20]; still, more attention is required to be paid for advancing the techniques to detect various video tampering attacks. Chen et al. proposed a method to identify individual source digital camcorders by analyzing photo-response non-uniformity (PRNU) that has proven to be the most robust digital fingerprint of the digital imaging sensor [8]. They tried to mitigate the periodic artifact, which is introduced by lossy video compression process, from estimated PRNU. Wang and Farid proposed a method to detect doubly-compressed MPEG videos by analyzing double quantization artifact, which is also used in double JPEG compression detection [18, 22], and temporal statistical perturbations that are introduced by addition/deletion of frames. The further study on the forensic analysis for the frame addition/deletion was taken by Stamm et al. [24]. They developed a theoretical model to design the new forensic and anti-forensic techniques. Also, a set of methods to evaluate the performance of the new techniques was proposed.

Video frame-rate conversion is one of the common temporal operations in video tampering. When multiple original video clips are used to create a forged video, each original video clip is often acquired at different frame-rate. Therefore, the frame-rate of each original video clip needs to be united to create a combined video clip. The frame-rate conversion also can be used to attack the video watermarking system by desynchronizing the temporal information [21]. Furthermore, the frame-rate conversion technique can be used to convert the video playback speed while the frame-rate is conserved.

The frame-rate conversion necessarily accommodates temporal interpolation to create frames to be fit into new temporal lattices. Conventional (nearest neighbor and bilinear) temporal interpolation methods have been commonly used for the frame-rate conversion in commercial and free software; however, recently, more advanced frame-rate conversion techniques that utilize the motion-based frame interpolation [1, 6, 9, 10] have been studied and utilized in commercial and free software [3]. These three types of temporal interpolation methods consist of performing linear interpolation operations in a unit of frame or block. The linear interpolation operations result in the periodic artifact on the temporal axis.

In this work, the periodic motion artifact is focused to detect the frame-rate converted video. The frame-rate conversion process introduces a traceable periodic artifact on the motion trajectories which is caused by temporal interpolation. The analysis on the periodic artifact is presented and we exploit it to build the proposed method for the detection of frame-rate conversion. The extensive experiments conducted for 1300 original videos and 18,000 frame-rate converted videos. As a result, the test results exhibited the superiority of the proposed method. The average detection accuracy could reach 93.35% on frame-rate converted videos in uncompressed and H.264 format when the nearest neighbor and motion-based interpolation methods were used for frame-rate up-conversion. Furthermore, the proposed method outperformed other detection methods even when bilinear interpolation method was used. The most outstanding point is that the proposed model can describe the frame-rate down conversion consisting of frame dropping. The remainder of this paper is organized as follows. Section 2 discusses the related work in frame-rate conversion detection. Section 3 describes the analysis of the periodicity caused by frame-rate conversion. In Section 4 the details of the proposed method based on the periodicity analysis is presented. Experimental results and conclusion are presented in Section 5 and 6, respectively.

2 Related work

In spite of recent tremendous focus on video forensics, only a few work has been investigated on the detection of frame-rate conversion [3, 4, 26, 27]. Wang and Farid proposed two different methods to detect the frame-rate conversion [26]. Their first method identifies the frame-rate converted interlaced video sequences by analyzing the motion ratio between inter-field motion and inter-frame motion. With the assumption of the constant motion over at least three sequential fields, the average value of the motion ratio between inter-field motion and inter-frame motion is almost 1 on the original video. On the other hand, if a given interlaced video is frame-rate converted, the average value would not be 1. However, this method only can be applied to the interlaced video. In their second method, the expectation/maximization (EM) algorithm was employed to detect the frame-rate up-conversion. Since only nearest neighbor and bilinear temporal interpolation methods were considered, the relationship between frames was modeled using simple weighted summation of two temporal neighbors; and the weight factors were estimated by using EM algorithm. This method can be applied to both progressive and interlaced videos. However, the it is not suitable for the frame-rate down-conversion, which is done by frame dropping, because it cannot be distinguished from original video by their relationship model.

Bian et al. proposed a scheme which targets the detection of frame-rate up-conversion only when the nearest neighbor interpolation method is used [4]. They exploited the periodic inter-frame similarity which is inevitably introduced by frame duplication. To measure the similarities between adjacent frames, the structural similarity index measurement (SSIM) [26] was employed. They quantized the SSIM values to lower the false positive detection ratio before the evaluation of the periodicity. However, their method is dedicated to the frame-rate up-conversion using nearest neighbor interpolation method.

Bestagini et al. proposed a frame-rate conversion detection scheme that is designed for the motion-based interpolation method [3]. The motion-based interpolation involves the block-based interpolation. They focused on the periodicity of the motion-based pixel value errors along the motion trajectory. Estimated motion vectors between two consecutive frames were used to calculated the motion-based errors; and the errors were analyzed in the frequency domain. If a peak exists in the frequency domain, the input video is determined as a frame-rate converted video. However, in the light of the consideration of the video compression, their method is not robust to quality degradation. Furthermore, in their experiments, only three sequences of uncompressed images were used for test set.

Above listed studies target only one or two temporal interpolation methods of the frame-rate conversion. Moreover, most of them do not consider the frame-rate down-conversion. To detect the frame-rate conversion, a new scheme, which can be applied to all three types of temporal interpolation methods and frame-rate up and down conversion, is needed. Therefore, we propose an approach explicitly devoted to the detection of the frame-rate conversion.

3 Analysis on periodicity of frame-rate conversion

In this section, we analyze the periodicity of the frame-rate conversion. To accommodate nearest neighbor, bilinear, and motion-based temporal interpolation methods, we built a simplified model. Let an original video sequence be X, whose frame-rate is fpsorg, and its frames are denoted as X(t), where t = 1, … TX. Then, the frame-rate converted video sequence is denoted as Y, whose frame-rate is fpsfrc. The frame length TY of Y is decided by the temporal resampling factor ω (fpsorg/ fpsfrc). The video sequence is up-sampled when ω < 1, and it is down-sampled when ω > 1.

We can suppose a temporal interpolation function h(x), whose sum of each element is one, x ∈ ℝ. Then the temporal interpolation model is described as below:
$$ {\mathbf{Y}}_{po{ s}_{frc}}^B(x) = {\displaystyle {\sum}_{k=-\infty}^{\infty }{\mathbf{X}}_{po{ s}_{org}}^B(k) h\left(\frac{x}{\varDelta}- k\right)} $$
(1)
where YB, XB, Δ, posfrc, and posorg denote the blocks of the interpolated frame and the original frame, the sampling step \( \left(\frac{1}{\upomega}\right) \), the spatial indexes in the interpolated frame and the original frame, respectively. Furthermore, \( \upomega \left(\frac{1}{\varDelta}\right) \) determines the cycle of the change of the interpolation function and the sum of each element of h(x) is one. For the conventional temporal interpolation methods, posfrc = posorg. The nearest neighbor temporal interpolation method requires only one non-zero element for h(x), that is, the only a single original frame is required for the temporal interpolation. On the other hand, the bilinear and motion-based temporal interpolation methods use at most two non-zero elements for h(x). The motion compensation for the motion-based interpolation frame-conversion is omitted for the simplicity.
From the Eq. 1, we can derive the equation for the detection of the interpolated video sequence. If the original signal satisfies stationary signal requirements, the periodicity of the interpolated signal can be detected based on the n -th derivative [15, 17, 19]. The n -th derivative of the interpolated video sequence is defined as
$$ {D}^n\left\{{\mathbf{Y}}_{po{ s}_{frc}}^B\right\}(x)=\frac{\partial {\mathbf{Y}}_{po{ s}_{frc}}^B(x)}{\partial {x}^n},\kern0.5em f o r\kern0.5em n>0. $$
(2)
Thus, the n -th derivative of the interpolated signal is denoted as shown below:
$$ {D}^n\left\{{\mathbf{Y}}_{po{ s}_{frc}}^B\right\}(x)={\displaystyle {\sum}_{k=-\infty}^{\infty }{\mathbf{X}}_{po{ s}_{org}}^B(k){D}^n\left\{ h\right\}\left(\frac{x}{\varDelta}- k\right).} $$
(3)
When the video sequence has a stationary property with a variance σ2, the variance of \( {D}^n\left\{{\mathbf{Y}}_{po{ s}_{frc}}^B\right\}(x) \) as a function of temporal index x can be represented by
$$ v a r\left\{{D}^n\left\{{\mathbf{Y}}_{po{ s}_{frc}}^B\right\}(x)\right\}={\upsigma}^2{\displaystyle {\sum}_{k=-\infty}^{\infty }{D}^n\left\{ h\right\}{\left(\frac{x}{\varDelta}- k\right)}^2} $$
(4)
From above equation, the following equation for γ ∈ ℤ is derives as below:
$$ v a r\left\{{D}^n\left\{{\mathbf{Y}}_{po{ s}_{frc}}^B\right\}\left( x+\gamma \varDelta \right)\right\}={\upsigma}^2{\displaystyle {\sum}_{k=-\infty}^{\infty }{D}^n\left\{ h\right\}{\left(\frac{x}{\varDelta}-\left( k-\gamma \right)\right)}^2.} $$
(5)
Therefore, the variance is periodic over temporal index x with period Δ [20].
$$ v a r\left\{{D}^n\left\{{\mathbf{Y}}_{po{ s}_{frc}}^B\right\}(x)\right\}= v a r\left\{{D}^n\left\{{\mathbf{Y}}_{po{ s}_{frc}}^B\right\}\left( x+\gamma \varDelta \right)\right\},\kern0.5em \gamma \in \mathrm{\mathbb{Z}}. $$
(6)
Afterwards, the periodicity of the video sequence \( {\mathbf{Y}}_{po{ s}_{frc}}^B \) can be computed by locating a peak from the magnitude of the variance signal in the frequency domain [15].
$$ p= peak\left(\left| FFT\left( var\left\{{D}^n\left\{{\mathbf{Y}}_{po{ s}_{frc}}^B\right\}\right\}\right)\right|\right). $$
(7)
The most common n values is two, thus, the second derivative is used to detect the periodicity. However, above equations use the video frame pixel values, which are vulnerable to be modified by video compression. Thus, another periodic property, which is resilient to video compression, is required to detect the temporal interpolation. We propose to use motion vector to substitute the frame pixel values for the detection of the temporal interpolation. With an assumption of stationary property with a variance σ2, Eq. 1 can be modified as below:
$$ P O{S}_{frc}(x) = {\displaystyle {\sum}_{k=-\infty}^{\infty } PO{S}_{org}(k) h\left(\frac{x}{\varDelta}- k\right)} $$
(8)
where POSfrc and POSorg denote pixel block position whose pixel blocks are matched. With the identical process presented above, it is shown that the derivative of block position exhibits the periodicity with period of Δ. The most important point is that even frame-rate down-conversion consisting of frame-dropping can be described by this model.

4 Proposed method

From Section 3, we found that the frame-rate conversion introduces a detectable periodic artifact regardless of the type of temporal interpolation. The periodic artifact can be estimated using the pixel block position pairs, and the motion vector is the most proper candidate to matching the pairs. Therefore, begin by assuming that the magnitude of each motion along the motion trajectory is almost constant across a small group of sequential frames in the original video (stationary property). Figure 1 depicts the periodic motion artifact introduced by the frame-rate conversion that uses nearest neighbor interpolation. To detect the motion artifact, we propose a method that is composed of three steps. First, two motions MV1(i, j, t) and MV2(i, j, t) are estimated at each time t. Then, the motions that are not suitable for periodicity detection are removed by motion pruning process. Finally, the periodicity of MA(i, j, t), which is motion artifact, is measured in the frequency domain. The details of the proposed method are described in the following subsections.
Fig. 1

The periodic motion artifact introduced by the temporal up/down resampling that uses nearest neighbor interpolation (t axis represents time index in the resampled video sequences): (a) frame-rate up-conversion (fpsorg =15, fpsfrc =30): zero motions appear due to the frame duplication (dashed frames are interpolated frames using nearest neighbor method); (b) frame-rate down-conversion (fpsorg =15, fpsfrc =10): motion jitters (big motions) appear due to the frame drop (dashed frames are dropped frames using nearest neighbor method)

4.1 Motion estimation

At each time t two different motions MV1(i, j, t) and MV2(i, j, t) are estimated. MV1(i, j, t) stores motions between frames at time t − 1 and t, also, MV2(i, j, t) stores motions between frames at time t and t + 1. To estimate the motions, each frame, whose resolution is M × N, is divided into B × B blocks. Then, the motion for each block centered in (i ⋅ round(B/2), jround(B/2)), where i = 1, …, floor(N/B) and i = 1, …, floor(M/B), is estimated. That is, the resolutions of MV1(i, j, t) and MV2(i, j, t) are floor(M/B) × floor(N/B).

To estimate the motion between frames, the classic optical flow method is considered [2, 16]. The motion between the frames is modeled with a two-parameter translation (2D motion). For the brightness constancy assumption and the robustness to video compression, each video frame is converted to YCbCr color channels; and then, only the Y channel is acquired for the motion estimation. Let f(x, y, t) be the Y channel of the given video sequence, then, the motion MV(i, j, t) = (Δxt, Δyt)T between two consecutive frames is described as follows:
$$ f\left( x, y, t+1\right)\approx f\left( x+\varDelta {x}_t,\ y+\varDelta {y}_t,\ t\right) $$
(9)
where △ xt and △ xt denote the change in pixel position at time t. We can obtain the optimal solution (Δxt, Δxt) by solving the error minimization problem. For more accurate motion estimation, Wang and Farid’s method is employed [13, 26, 27]. Since the motion estimation using optical flow method is limited to small motions due to the Taylor approximation, 3-level image pyramid is used to estimate the large magnitude of the estimated motion [5, 23].

4.2 Motion pruning

The estimated motion vectors are validated before measuring the periodicity of the motion artifact. The consideration for three criterions results in the trajectory map (TM) that stores the motion validity information.

4.2.1 Sum of absolute difference (SAD)

For each motion vector, motion estimation error is tested using SAD measure. Since the estimated motion vector is in sub-pixel precision, SAD is calculated as follows:
$$ SAD = {\displaystyle {\sum}_{x, y\in \varOmega} f\left( x, y, t\right)- f\left( x+ round\left(\varDelta {x}_t\right),\ y+ round\left(\varDelta {y}_t\right), t+\varDelta t\right)} $$
(10)
where f(Δ), Δxt, Δyt, t, and Ω denote Y channel frame, motion vector, time shift, and motion estimation block region, respectively. By thresholding the SAD value, each motion is assessed whether it is valid or not. If the thresholded SAD value is one (i.e., the SAD value is greater than a given threshold), the motion vector is not valid. To validate whether the motions MV1(i, j, t) and MV2(i, j, t) lie on the motion trajectory, the thresholded SAD value map (TSVM) is constructed as follows:
$$ TSVM\left( i, j, t\right)= TSVM1\left( i, j, t\right)\vee TSVM2\left( i, j, t\right) $$
(11)
where TSVM1(i, j, t) and TSVM2(i, j, t) represent the thresholded SAD value, which are calculated using MV1(i, j, t) and MV2(i, j, t), respectively. The corresponding threshold is set as 10 in the proposed method.

4.2.2 Motion direction

If the stationary property is assumed, consecutive motions on the motion trajectory need to present small amount of angle difference. Thus, the motion direction map (MDM) is constructed as follows:
$$ M D M\left( i, j, t\right) = \left\{\begin{array}{c}\hfill \begin{array}{cc}\hfill 1,\hfill & \hfill ADA\left( i, j, t\right)>{\tau}_{angle}\hfill \end{array}\hfill \\ {}\hfill \begin{array}{cc}\hfill 0,\hfill & \hfill ADA\left( i, j, t\right)\le {\tau}_{angle}\hfill \end{array}\hfill \end{array}\right. $$
(12)
where ADA(i, j, t) denotes the absolute difference between ∠ MV1(i, j, t) and ∠ MV2(i, j, t). To tolerate small variation in the motion angle, τangle is set as 45°.

4.2.3 Background

Since the background content do not contribute to estimate the motion artifact, the related motions need to be pruned. The object that does not have any motion while three consecutive frames pass is assumed to be the background content. The background map (BM) is constructed as follows:
$$ B M\left( i, j, t\right) = \left\{\begin{array}{c}\hfill \begin{array}{cc}\hfill 1,\hfill & \hfill if\ M V1\left( i, j, t\right)=0\ and\ M V2\left( i, j, t\right)=0\hfill \end{array}\hfill \\ {}\hfill \begin{array}{cc}\hfill 0,\ \hfill & \hfill\ otherwise\hfill \end{array}\hfill \end{array}\right. $$
(13)
After above three criterions are tested, TM is constructed as follows:
$$ T M\left( i, j, t\right)=\neg \left( SAD\left( i, j, t\right)\vee MDM\left( i, j, t\right)\vee BM\left( i, j, t\right)\right) $$
(14)
where ¬ denotes negation bit operation. TM stores the motion validity information. If TM(i, j, t) is non-zero, the corresponding motions are assumed to be on the motion trajectory; otherwise, the corresponding motions are excluded in the periodicity calculation.

4.3 Periodicity detection

Based on the analysis in Section 3, the second derivative of the pixel block position is calculated at each time index t. To simplify the calculation, only the scalar value (magnitude) of the motion vector is used. Since the magnitude of each motion vector is the first derivative, the second derivative is simply defined as the error between |MV2(i, j, t)| and |MV1(i, j, t)|. Furthermore, to enhance this error value, we calculate the normalized error E(i, j, t) as
$$ E\left( i, j, t\right)=\left\{\begin{array}{cc}\hfill \frac{\left| MV2\left( i, j, t\right)\right|-\left| MV1\left( i, j, t\right)\right|}{\left| MV1\left( i, j, t\right)\right|}\hfill & \hfill, \kern0.5em if\ \left| MV1\left( i, j, t\right)\right|\ne 0\hfill \\ {}\hfill 0\hfill & \hfill, \kern0.5em if\ \left| MV1\left( i, j, t\right)\right|=0\hfill \end{array}\right. $$
(15)
Afterwards, with the motion validity information TM(i, j, t), the proposed motion artifact measurement MA(t) is calculated as below:
$$ M A(t) = \frac{1}{{\displaystyle {\sum}_{i, j}} TM\left( i, j, t\right)}{\displaystyle {\sum}_{i, j} E\left( i, j, t\right)\cdot TM\left( i, j, t\right)} $$
(16)

After the calculation at each time index t, one-dimensional array MA(t) is obtained. If an original video is given as an input, the values of MA(t) would be around zeros (stationary property assumption) and non-periodic. On the other hand, if MA(t) is obtained from the frame-rate converted video, it would be periodic and the values on MA(t) that create the periodicity would not be around zero.

The periodicity of MA(t) can be analyzed in the frequency domain. MA(t) is transformed into the frequency domain using Discrete Fourier Transform (DFT). Let the transformed signal be FMA(ξ), then, the peak location is searched. If the magnitude of the peak is at least τmag times greater than the average spectrum magnitude, the input video is claimed as the frame-rate converted video. However, to avoid false positive errors, certain proportions (two percent) from the top and bottom of the normalized frequency domain are trimmed before the peak validation. Figures 2 and 3 present the examples for original and frame-rate converted (nearest neighbor interpolation) videos in spatial and frequency domains, respectively.
Fig. 2

Illustrations of the motion artifacts MA(t) for original and frame-rate converted videos: (a) Original video (‘Bus’) at 30 fps; (b) the frame-rate up converted video from 24 fps to 30 fps using nearest neighbor interpolation; (c) the frame-rate down-converted video from 30 fps to 24 fps using nearest neighbor interpolation

Fig. 3

Illustrations of the Fourier spectrum for ‘Bus’ in Fig. 2. The horizontal axis indicates normalized frequencies

Once the periodicity is estimated, the original frame-rate (fpsorg) can be directly estimated using the position of the peak in the spectrum and the interpolation factor (ω = fpsorg/fpsfrc) [17]:
$$ \omega = n \pm \varDelta f $$
(17)
where Δf and n denote the peak position in the normalized frequency domain and the integer (n -th derivative), respectively. However, when frame-rate down-converted, the periodic artifacts are coincident with those of other frame-rate up-conversion due to aliasing [17]. Thus, the estimation of fpsorg might not be accurate.

5 Experimental results

In this section, the performance of the proposed method is evaluated. The specific settings for the experiments are also provided. Furthermore, the results of the experiments are presented and analyzed. For the experiments, 50 original video sequences, whose format is uncompressed YUV, were collected [7, 11, 25]. The original video set included various types of contents such as sports, news, animation, surveillance, and so on. The resolutions vary from 176 × 144 (CIF) to 1920 × 1080 (full-HD). Since the proposed method is based on the motion vector, fast motion video sequences were also included. Their frame lengths were equal to or less than 300. For the frame-rate conversion, original video sequences were saved using five different frame-rates, which include 15, 20, 24, 25, and 30. Furthermore, each original video was re-saved using H.264/AVC codec. For the robustness test to the video compression, which is commonly conducted before saving the videos, five types of compression factors (100, 90, 80, 70, and 60) were selected and the key frame interval was 20. When the frame-rates were different, the original videos showed different pixel values even though they were compressed using identical compression factor, except uncompressed ones. Therefore, 1300 (50 × 5 × 5 + 50) original videos were prepared. Frame-rate conversion was performed for all pairs (20 combinations) that can be made using fpsorg and fpsfrc. Furthermore, three types of temporal interpolation methods, that is, ‘nearest neighbor interpolation’, ‘bilinear interpolation’ and ‘motion-based interpolation’ methods [9], were used in frame-rate conversion. As a result, 18,000 (50 × 6 × 20 × 3) frame-rate (up/down) converted videos were created for the experiments. The experiments were tested on a PC equipped with Intel i7-2600 (3.4 GHz) CPU, 8 GB of RAM, and MATLAB 2014a.

In the experiments, in order to demonstrate the performance of the proposed method, we compared the proposed method with three different frame-rate conversion detection methods [3, 4, 27]. To provide objective test results, true positive ratios were checked at three different false positive ratios (0, 0.01, and 0.03) for each method. For this purpose, parameter τmag, for the proposed method, was adaptively chosen by changing the false positive error. At 0.01 false positive error ratio, τmag was about 4.31. To measure the performance of Wang and Farid’s method, their second method was used because their first method cannot be applied to progressive video [27]. For the test results, we applied our peak validation to the result (the array of probabilities) of EM algorithm since the authors did not provide a specific measuring tool for the periodicity check. For Bian’s method [4], its first parameter τ1 was set as the authors described. However, the second parameter τ2 was adaptively selected to present true positive ratio at three different false positive ratios. For Bestagini’s method, the max value peak in the frequency domain is selected [3]. Since this decision making is not the threshold-based, our peak validation was used to provide the pairs of false positive error rate and corresponding true positive error rate.

5.1 Frame-rate up-conversion test

In this section, the experiment results for the frame-rate up-conversion are presented. Uncompressed videos and H.264/AVC compressed videos, which were encoded using five different compression factors (Q100, Q90, Q80, Q70, and Q60), were used in the extensive experiments. Table 1 exhibits the detection results for videos that were frame-rate up-converted using nearest neighbor interpolation. The test results in Table 1 demonstrate that the proposed method outperforms the other methods except for the case of converting from 24fps to 25 fps. Most detection methods exhibited the fine detection results. Especially, in the case of converting from 15 fps to 30 fps, most detection methods exhibited the best detection result compared to other frame-rate conversion configurations. Every duplicated frame, which was positioned in right after the original frame, created the strong and periodic artifact signal and it resulted in the highest detection result. However, Bestagini’s method exhibited low detection result in this case. Since the sign information is lost in the calculation of the squared error, which is used in Bestagini’s method, it is difficult to detect the periodicity in this case. For the case of converting from 24 fps to 25 fps, where the interpolation factor ω is close to 1, every detection method exhibited the most degraded performance. Although most detection methods exhibited the fine detection results, Bestagini’s method exhibited the comparatively low detection rate because of non-precise motion estimation and the lack of robustness to video compression.
Table 1

The compared test results for frame-rate up-conversion using ‘nearest neighbor interpolation’

fpsorg

fpsfrc

FPR

Wang and Farid (TPR)

Bian et al. (TPR)

Bestagini et al. (TPR)

Proposed method (TPR)

15

20

0.00

0.90

1.00

0.73

1.00

0.01

0.90

1.00

0.73

1.00

0.03

0.92

1.00

0.74

1.00

24

0.00

0.94

0.99

0.73

1.00

0.01

0.94

1.00

0.74

1.00

0.03

0.94

1.00

0.75

1.00

25

0.00

1.00

1.00

0.68

1.00

0.01

1.00

1.00

0.68

1.00

0.03

1.00

1.00

0.71

1.00

30

0.00

1.00

1.00

0.16

1.00

0.01

1.00

1.00

0.16

1.00

0.03

1.00

1.00

0.17

1.00

20

24

0.00

0.66

0.97

0.64

1.00

0.01

0.68

0.97

0.64

1.00

0.03

0.72

0.97

0.64

1.00

25

0.00

0.76

0.97

0.67

1.00

0.01

0.76

0.97

0.67

1.00

0.03

0.78

0.99

0.69

1.00

30

0.00

0.96

1.00

0.75

1.00

0.01

0.96

1.00

0.75

1.00

0.03

0.96

1.00

0.76

1.00

24

25

0.00

0.00

0.78

0.15

0.67

0.01

0.00

0.78

0.15

0.69

0.03

0.00

0.83

0.16

0.73

30

0.00

0.78

0.97

0.67

1.00

0.01

0.78

0.97

0.67

1.00

0.03

0.82

0.98

0.68

1.00

25

30

0.00

0.66

0.96

0.64

1.00

0.01

0.68

0.96

0.64

1.00

0.03

0.72

0.97

0.64

1.00

Six types (‘Uncompressed’, ‘Q100’, ‘Q90’, ‘Q80’, ‘Q70’, ‘Q60’) compression factors are used in video encoding

Table 2 presents the performance for frame-rate up-conversion that uses the bilinear interpolation method. Compared to Table 1, the overall test results were degraded. The pixel value changes by interpolation made the motion estimation less accurate, which led to the performance degradation of the proposed method. However, it still exhibited the acceptable detection rate and outperformed other methods. Bian’s method exhibited the poor performance for the bilinear interpolation because its quantization process prevented it from detectin the periodicity of the SSIM sequence.
Table 2

The compared test results for frame-rate up-conversion using ‘bilinear interpolation’

fpsorg

fpsfrc

FPR

Wang and Farid (TPR)

Bian et al. (TPR)

Bestagini et al. (TPR)

Proposed method (TPR)

15

20

0.00

0.64

0.06

0.70

0.85

0.01

0.64

0.08

0.70

0.86

0.03

0.68

0.08

0.70

0.86

24

0.00

0.78

0.12

0.70

0.98

0.01

0.78

0.14

0.71

0.98

0.03

0.80

0.14

0.72

0.98

25

0.00

0.80

0.16

0.70

1.00

0.01

0.80

0.16

0.70

1.00

0.03

0.80

0.18

0.71

1.00

30

0.00

0.94

0.12

0.77

0.77

0.01

0.94

0.12

0.77

0.78

0.03

0.94

0.14

0.78

0.82

20

24

0.00

0.64

0.08

0.73

0.68

0.01

0.64

0.08

0.73

0.69

0.03

0.72

0.10

0.74

0.70

25

0.00

0.68

0.08

0.72

0.76

0.01

0.68

0.10

0.73

0.76

0.03

0.70

0.12

0.74

0.77

30

0.00

0.78

0.12

0.75

0.95

0.01

0.78

0.12

0.76

0.95

0.03

0.80

0.14

0.77

0.96

24

25

0.00

0.34

0.02

0.16

0.32

0.01

0.36

0.02

0.16

0.34

0.03

0.42

0.02

0.17

0.36

30

0.00

0.68

0.08

0.72

0.76

0.01

0.68

0.10

0.72

0.76

0.03

0.70

0.12

0.74

0.77

25

30

0.00

0.64

0.08

0.72

0.67

0.01

0.66

0.08

0.73

0.69

0.03

0.72

0.10

0.73

0.70

Six types (‘Uncompressed’, ‘Q100’, ‘Q90’, ‘Q80’, ‘Q70’, ‘Q60’) compression factors are used in video encoding

Table 3 presents the performance for frame-rate up-conversion that uses the motion-based interpolation method. Compared to Table 1 and 2, every detection method excluding Bestagini’s method and the proposed method exhibited severely low detection results. The basic mechanism for those methods is not appropriate for the motion-based interpolation. Bestagini’s method exhibited low detection results considering that it was designed to detect motion-based interpolated video sequences. The motion compensation of the motion-based frame-rate conversion and the light of the consideration of wrongly estimated motions lowered the performance. The proposed method was less affected by motion compensation since the motion compensation changes pixel values but not pixel locations; it outperformed other methods. However, since the periodic signal was not strong enough, the proposed method required more frames to present proper results compared to other detection methods.
Table 3

The compared test results for frame-rate up-conversion using ‘motion-based interpolation’

fpsorg

fpsfrc

FPR

Wang and Farid (TPR)

Bian et al. (TPR)

Bestagini et al. (TPR)

Proposed method (TPR)

15

20

0.00

0.19

0.03

0.30

0.97

0.01

0.20

0.05

0.31

0.98

0.03

0.21

0.08

0.35

0.98

24

0.00

0.21

0.00

0.45

0.96

0.01

0.22

0.00

0.45

0.96

0.03

0.22

0.00

0.45

0.96

25

0.00

0.23

0.00

0.44

0.95

0.01

0.24

0.00

0.44

0.97

0.03

0.24

0.00

0.46

0.97

30

0.00

0.25

0.12

0.48

0.94

0.01

0.25

0.12

0.49

0.94

0.03

0.25

0.13

0.49

0.94

20

24

0.00

0.06

0.00

0.44

0.91

0.01

0.06

0.00

0.44

0.91

0.03

0.07

0.00

0.45

0.92

25

0.00

0.11

0.01

0.44

0.94

0.01

0.11

0.01

0.46

0.94

0.03

0.12

0.03

0.46

0.94

30

0.00

0.23

0.01

0.41

0.99

0.01

0.23

0.02

0.41

0.99

0.03

0.23

0.03

0.43

0.99

24

25

0.00

0.00

0.00

0.07

0.44

0.01

0.00

0.00

0.07

0.44

0.03

0.00

0.00

0.07

0.49

30

0.00

0.11

0.01

0.40

0.94

0.01

0.11

0.01

0.40

0.94

0.03

0.11

0.03

0.40

0.94

25

30

0.00

0.06

0.05

0.44

0.91

0.01

0.06

0.06

0.44

0.91

0.03

0.06

0.07

0.45

0.92

Six types (‘Uncompressed’, ‘Q100’, ‘Q90’, ‘Q80’, ‘Q70’, ‘Q60’) compression factors are used in video encoding

Figure 4 compares the test results at each different level of compression factors. The detection results depicted in Fig. 4 were sampled when the FPR was 0.01. The average detection rate of the proposed method was about 88% (97%, 78%, and 90% for nearest neighbor, bilinear interpolation, and motion-based interpolation methods). Bian’s method and the proposed method exhibited the robustness against H.264/AVC compression in case of the nearest neighbor interpolation was used to convert the frame-rates. However, Wang and Farid’s method and Bestagini’s method presented lower detection results along the compression factor decreases. In case of bilinear interpolation, every detection method was affected by the change of the compression factor. It is because the bilinear interpolation process creates the high-frequency contents, which is easily quantized by lossy video compression, in the interpolated frames.
Fig. 4

Detection accuracies for frame-rate up-converted videos at the different compression factors (The corresponding false positive rates are 0.01)

5.2 Frame-rate down-conversion test

In this section, the experiment results for the frame-rate down-conversion are presented. Table 4, 5 and 6 present the performance for frame-rate down-converted videos. Before analyzing the test results, the case of the frame-rate conversion from 30 fps to 15 fps is considered. This frame-rate conversion does not introduce any temporal artifact. More specifically, when the interpolation factor ω is an integer, no further interpolation process is done; only frame dropping is done. As a result, the detector cannot distinguish the frame-rate converted videos from the original videos. Indeed, the corresponding test results in Table 4, 5, and 6 exhibits zero detection rates at zero false positive ratio.
Table 4

The compared test results for frame-rate down conversion using ‘nearest neighbor interpolation’

fpsorg

fpsfrc

FPR

Wang and Farid (TPR)

Bian et al. (TPR)

Bestagini et al. (TPR)

Proposed method (TPR)

30

25

0.00

0.00

0.00

0.54

0.98

0.01

0.00

0.00

0.54

0.98

0.03

0.00

0.00

0.54

0.99

24

0.00

0.00

0.00

0.45

0.99

0.01

0.00

0.00

0.46

0.99

0.03

0.00

0.00

0.46

1.00

20

0.00

0.00

0.00

0.10

1.00

0.01

0.00

0.00

0.12

1.00

0.03

0.00

0.00

0.12

1.00

15

0.00

0.00

0.00

0.00

0.00

0.01

0.00

0.00

0.00

0.00

0.03

0.00

0.00

0.00

0.00

25

24

0.00

0.00

0.00

0.12

0.67

0.01

0.00

0.00

0.13

0.68

0.03

0.00

0.02

0.15

0.70

20

0.00

0.00

0.00

0.45

0.99

0.01

0.00

0.00

0.46

0.99

0.03

0.00

0.02

0.46

0.99

15

0.00

0.00

0.00

0.46

0.99

0.01

0.00

0.00

0.46

0.99

0.03

0.00

0.02

0.49

0.99

24

20

0.00

0.00

0.00

0.54

0.98

0.01

0.00

0.00

0.54

0.98

0.03

0.02

0.00

0.54

0.98

15

0.00

0.00

0.00

0.16

0.99

0.01

0.00

0.00

0.16

0.99

0.03

0.00

0.00

0.16

0.99

20

15

0.00

0.00

0.00

0.43

1.00

0.01

0.00

0.00

0.43

1.00

0.03

0.00

0.00

0.43

1.00

Six types (‘Uncompressed’, ‘Q100’, ‘Q90’, ‘Q80’, ‘Q70’, ‘Q60’) compression factors are used in video encoding. The frame-rate down conversion from 30 fps to 15 fps does not leave any temporal interpolation artifact

Table 5

The compared test results for frame-rate down conversion using ‘bilinear interpolation’

fpsorg

fpsfrc

FPR

Wang and Farid (TPR)

Bian et al. (TPR)

Bestagini et al. (TPR)

Proposed method (TPR)

30

25

0.00

0.36

0.03

0.42

0.44

0.01

0.36

0.03

0.43

0.44

0.03

0.38

0.06

0.43

0.44

24

0.00

0.24

0.03

0.34

0.44

0.01

0.24

0.03

0.34

0.45

0.03

0.26

0.03

0.35

0.46

20

0.00

0.36

0.01

0.55

0.31

0.01

0.36

0.01

0.55

0.32

0.03

0.38

0.01

0.57

0.32

15

0.00

0.00

0.00

0.00

0.00

0.01

0.00

0.00

0.00

0.00

0.03

0.00

0.00

0.00

0.00

25

24

0.00

0.32

0.02

0.48

0.15

0.01

0.32

0.02

0.50

0.15

0.03

0.34

0.02

0.51

0.20

20

0.00

0.24

0.03

0.34

0.43

0.01

0.24

0.03

0.34

0.44

0.03

0.26

0.03

0.34

0.46

15

0.00

0.14

0.01

0.41

0.50

0.01

0.14

0.01

0.41

0.50

0.03

0.16

0.02

0.41

0.51

24

20

0.00

0.36

0.03

0.42

0.44

0.01

0.36

0.03

0.43

0.44

0.03

0.38

0.05

0.43

0.44

15

0.00

0.14

0.01

0.32

0.62

0.01

0.14

0.01

0.32

0.62

0.03

0.14

0.01

0.33

0.63

20

15

0.00

0.26

0.01

0.46

0.55

0.01

0.28

0.01

0.47

0.56

0.03

0.30

0.02

0.47

0.64

Six types (‘Uncompressed’, ‘Q100’, ‘Q90’, ‘Q80’, ‘Q70’, ‘Q60’) compression factors are used in video encoding. The frame-rate down conversion from 30 fps to 15 fps does not leave any temporal interpolation artifact

Table 6

The compared test results for frame-rate down conversion using ‘motion-based interpolation’

fpsorg

fpsfrc

FPR

Wang and Farid (TPR)

Bian et al. (TPR)

Bestagini et al. (TPR)

Proposed method (TPR)

30

25

0.00

0.08

0.00

0.32

0.92

0.01

0.12

0.00

0.33

0.92

0.03

0.12

0.00

0.33

0.93

24

0.00

0.08

0.00

0.32

0.92

0.01

0.12

0.00

0.33

0.92

0.03

0.12

0.00

0.33

0.93

20

0.00

0.00

0.00

0.15

0.72

0.01

0.00

0.00

0.15

0.72

0.03

0.00

0.00

0.16

0.72

15

0.00

0.00

0.00

0.00

0.00

0.01

0.00

0.00

0.00

0.00

0.03

0.00

0.00

0.00

0.00

25

24

0.00

0.00

0.00

0.34

0.56

0.01

0.00

0.00

0.34

0.56

0.03

0.00

0.00

0.35

0.61

20

0.00

0.09

0.00

0.33

0.92

0.01

0.12

0.00

0.33

0.92

0.03

0.12

0.00

0.33

0.93

15

0.00

0.00

0.01

0.21

0.73

0.01

0.00

0.01

0.21

0.73

0.03

0.00

0.02

0.22

0.74

24

20

0.00

0.00

0.00

0.28

0.92

0.01

0.00

0.00

0.29

0.92

0.03

0.02

0.00

0.30

0.92

15

0.00

0.00

0.00

0.17

0.82

0.01

0.00

0.00

0.17

0.82

0.03

0.00

0.00

0.18

0.83

20

15

0.00

0.00

0.00

0.06

0.84

0.01

0.00

0.00

0.06

0.85

0.03

0.00

0.00

0.07

0.88

Six types (‘Uncompressed’, ‘Q100’, ‘Q90’, ‘Q80’, ‘Q70’, ‘Q60’) compression factors are used in video encoding. The frame-rate down conversion from 30 fps to 15 fps does not leave any temporal interpolation artifact

As analyzed in the previous subsection, the frame-rate conversion that uses nearest neighbor interpolation exhibits the higher detection rates for the proposed method. The remarkable point in Table 4 is that only the proposed method exhibited the acceptable test results (over than 95%). For the bilinear interpolation test, Bestagini’s method exhibited best detection results. The designs of the other methods are not suitable to detect the frame-rate down-conversion because the dropped frames (including ‘bilinear interpolation’) do not introduce the correlations between adjacent frames. Their test results are considerably degraded compared with those of the frame-rate up-conversion. The proposed method also exhibited degraded performance for bilinear interpolation.

Figure 5 compares the test results at each different level of compression factors. The detection results depicted in Fig. 5 were sampled when the FPR was 0.01. Bian’s method and the proposed method exhibited the robustness against H.264/AVC compression when the nearest neighbor interpolation was used to convert the frame-rates. However, Wang and Farid’s method and Bestagini’s method presented lower detection results along the compression factor decreases.
Fig. 5

Detection accuracies for frame-rate down-converted videos at the different compression factors (The corresponding false positive rates are 0.01 and the case of converting frame-rate from 30 fps to 15 fps is excluded)

It is also interesting to analyze how the frame length affects the detection results. Figure 6 exhibits the average detection rate along the frame length increases for each detection method when the original fps was 20. In most cases, the proposed method outperformed other methods and required minimum number of frame to reach the maximum detection ratio. Although the proposed model accommodates the frame dropping, the frame-rate down-conversion test required more frames than the frame-rate up-conversion test to reach maximum detection ratio. For nearest neighbor frame-rate conversion, most detection methods were possible to reach the maximum detection results with small number of frames. In case of bilinear frame-rate conversion, more frames were required to reach the maximum detection ratio.
Fig. 6

Detection accuracies analysis for different temporal window size

5.3 Processing time test

In this subsection, the processing time of each method is compared. Table. 7 describes the processing time of each method. To avoid the slow loop operations of MATLAB, most of core algorithms were implemented using C++ and MEX-compiled. Wang and Farid’s method was the fastest method among the comparing methods considering only the algorithm computation time. However, their method required the considerable amount of memory since every frame should be loaded for the computation. It made their method operate slowest considering the whole processes, including video frame loading, when full-HD resolution video was on the examination. The proposed method required much time to estimate the motions between frames. To reduce the processing time, the frames whose resolution was larger than 4CIF (704 x 480) size were resized to CIF size. Since the proposed method uses the motion vectors, the detection rate degradation due to resizing was not considerable. About 4% of true positive ratio at 0.01 false positive was degraded. Since SSIM is the most time consuming part of Bian’s method, the input video resolution affected the processing time. Since Bestagini’s method uses motion vector, the processing time was comparable with the proposed method.
Table 7

Processing time (in second) comparison (100 frames were used and frame loading was excluded)

 

Wang and Farid

Bian et al.

Bestagini et al.

Proposed

4CIF resolution

2.4

4.9

26.1

29.1

Full-HD resolution

5.9

126.0

323.1

331.1

6 Conclusion

In this paper, we presented a method to assess if a video has been frame-rate converted. Video frame-rate conversion is one of the most common temporal domain operations in video tampering. To accommodate three types of temporal interpolation methods, which is mandatory for frame-rate conversion, we proposed a model and the periodic artifact on the motion trajectories were analyzed. The proposed method estimates the motion vectors according to the motion trajectories. Afterwards, the periodicity of the estimated motion artifacts is assessed. The proposed method demonstrated its performance through the extensive experiments on frame-rate converted videos. Furthermore, by comparing the test results with other frame-rate conversion detection methods, the superiority of the proposed method was exhibited. Especially, for the frame-rate is down-converted using nearest interpolation, only the proposed method presented the detection rate over than 95%. Moreover, the test results proved that the proposed method is even valid on small number of frames, which allows the proposed method to be used as a possible tool for frame copy and paste forgery. However, the further consideration for the bilinear interpolation in temporal domain is required. Our future work will include the further investigation on the robustness in frame-rate down-conversion and bilinear interpolation.

Notes

Acknowledgements

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. 2016R1A2B2009595), and by the Institute for Information & communications Technology Promotion (IITP) grant funded by the Korean government (MSIP) (No.R0126-16-1024, Managerial Technology Development and Digital Contents Security of 3D Printing based on Micro Licensing Technology).

References

  1. 1.
    Ascenoso J, Brites C, Pereira F (2005) Improving frame interpolation with spatial motion smoothing for pixel domain distributed video coding. In: 5th EURASIP Conference on Speech and Image Processing, Multimedia communications and Sevices, pp. 1-6. CiteseerGoogle Scholar
  2. 2.
    Barron JL, Fleet DJ, Beauchemin SS (1994) Performance of optical flow techniques. Int J Comput Vis 12(1):43–77CrossRefGoogle Scholar
  3. 3.
    Bestagini P, Battaglia S, Milani S, Tagliasacchi M, Tubaro S (2013) Detection of temporal interpolation in video sequences. 2013 I.E. Int Conf Acoustics, Speech Signal Process: 3033–3037. doi 10.1109/ICASSP.2013.6638215
  4. 4.
    Bian S, Luo W, Huang J (2014) Detecting video frame-rate up-conversion based on periodic properties of inter-frame similarity. Multimed Tools Appl 72(1):437–451CrossRefGoogle Scholar
  5. 5.
    Bouguet JY (2013) Pyramidal implementation of the lucas kanade feature tracker description of the algorithm. Cit’e en: 69Google Scholar
  6. 6.
    Castagno R, Hassvisto P, Ramponi G (1996) A method for motion adaptive frame rate up-conversion. Circ Syst Video Technol, IEEE Trans 6(5):436–446CrossRefGoogle Scholar
  7. 7.
    Center for image processing research sequences. URL http://www.cipr.rpi.edu/resource/sequences/. (last access: Oct. 2015)
  8. 8.
    Chen M, Fridrich J, Goljan M, Luka’ˇs J (2007) Source digital camcorder identification using sensor photo response non-uniformity. In: Electronic Imaging 2007, pp. 65,051G– 65,051G. International Society for Optics and PhotonicsGoogle Scholar
  9. 9.
    Choi BD, Han JW, Kim CS, Ko SJ (2007) Motion-compensated frame interpolation using bilateral motion estimation and adaptive overlapped block motion compensation. Circ Syst Video Technol, IEEE Trans 17(4):407–416CrossRefGoogle Scholar
  10. 10.
    Choi BT, Lee SH, Ko SJ (2000) New frame rate up-conversion using bi-directional motion estimation. Consumer Electro, IEEE Trans 46(3):603–609CrossRefGoogle Scholar
  11. 11.
    Dash dataset at itec/alpen-adria-universita¨t klagenfurt. URL http://www-itec.uni-klu.ac.at/dash/?page_id=207. (last access: Oct. 2015)
  12. 12.
    Farid H (2009) Image forgery detection. Sign Process Mag, IEEE 26(2):16–25CrossRefGoogle Scholar
  13. 13.
    Farid H, Simoncelli EP (2004) Differentiation of discrete multidimensional signals. Imag Process, IEEE Trans 13(4):496–508MathSciNetCrossRefGoogle Scholar
  14. 14.
    Fridrich J (2009) Digital image forensics. Sign Process Mag, IEEE 26(2):26–37CrossRefGoogle Scholar
  15. 15.
    Gallagher AC (2005) Detection of linear and cubic interpolation in jpeg compressed images. In: Computer and Robot Vision, 2005. Proc 2nd Can Conf: 65–72. IEEEGoogle Scholar
  16. 16.
    Horn B (1986) Robot vision. MIT pressGoogle Scholar
  17. 17.
    Kirchner M (2008) Fast and reliable resampling detection by spectral analysis of fixed linear predictor residue. Proc 10th ACM Workshop Multimed Sec: 11–20. ACMGoogle Scholar
  18. 18.
    Luka’ˇs J, Fridrich J (2003) Estimation of primary quantization matrix in double compressed jpeg images. Proc Digit Forensic Res Workshop: 5–8Google Scholar
  19. 19.
    Mahdian B, Saic S (2007) On periodic properties of interpolation and their application to image authentication. In: Information Assurance and Security, 2007. IAS 2007. Third Int Symp: 439–446. IEEEGoogle Scholar
  20. 20.
    Milani S, Fontani M, Bestagini P, Barni M, Piva A, Tagliasacchi M, Tubaro S (2012) An overview on video forensics. APSIPA Trans Sign Inform Process 1:e2CrossRefGoogle Scholar
  21. 21.
    Paul RT (2011) Review of robust video watermarking techniques. IJCA Special Issue Computat Sci 3:90–95Google Scholar
  22. 22.
    Popescu AC, Farid H (2005) Statistical tools for digital forensics. In: Information Hiding, pp. 128–147. SpringerGoogle Scholar
  23. 23.
    Simoncelli EP (1999) Bayesian multi-scale differential optical flowGoogle Scholar
  24. 24.
    Stamm MC, Lin WS, Liu K (2012) Temporal forensics and anti-forensics for motion compensated video. Inform Forensics Sec, IEEE Trans 7(4):1315–1329CrossRefGoogle Scholar
  25. 25.
    Video trace library yuv video sequences. URL http://trace.eas.asu.edu/yuv/. (last access: Oct. 2015)
  26. 26.
    Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. Imag Process, IEEE Trans 13(4):600–612CrossRefGoogle Scholar
  27. 27.
    Wang W, Farid H (2007) Exposing digital forgeries in interlaced and deinterlaced video. Inform Forensics Sec, IEEE Trans 2(3):438–449CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Agency for Defense DevelopmentYusong-Gu DaejoenSouth Korea
  2. 2.School of ComputingKAISTYusong-Gu DaejoenSouth Korea

Personalised recommendations