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IET Image Processing - 2018 - Sheng - Image splicing detection based on Markov features in discrete octonion cosine

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导读： IET Image Processing Research Article Image splicing detection based on Markov features ...

IET Image Processing

Research Article

Image splicing detection based on Markov features in discrete octonion cosine transform domain

ISSN 17519659 Received on 17th October 2017 Revised 16th April 2018 Accepted on 20th April 2018 EFirst on 5th June 2018 doi: 10.1049/ietipr.2017.1131 www.ietdl.org

Hongda Sheng^1,2, Xuanjing Shen^1,2, Yingda Lyu³

, Zenan Shi^1,2, Shuyang Ma^2,4

1College of Computer Science and Technology, Jilin University, Changchun, People's Republic of China 2Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun, People's Republic of China 3Public Computer Education and Research Center, Jilin University, Changchun, People's Republic of China 4College of Software, Jilin University, Changchun, People's Republic of China

Email: ydlv@jlu.edu.cn

Abstract: To improve the poor robustness and low accuracy of the existing algorithms of image splicing detection, a novel passive image forgery detection method is proposed in this study, which is based on DOCT (discrete octonion cosine transform) and Markov. By introducing the octonion and DOCT, the colour information of six image channels (the RGB model and the HSI model) can be exhaustively extracted, which enhances the robustness of the algorithm. On the issue of improving the detection accuracy, the standard deviation is used to characterise the relationship of the colour information between the parts of DOCT coefficient matrix, and the Kfold crossvalidation is introduced to improve the identification performance of the classifier. The steps of the algorithm are as follows: Firstly, the 8 × 8 block DOCT transform is used to the original image to obtain parts of block DOCT coefficient. Secondly, the standard deviation is used to process the corresponding parts of all blocks of the image. Finally, the Markov feature vector of the DOCT coefficient is extracted and feds to the LIBSVM (a library for support vector machines). When using LIBSVM for classification, Kfold crossvalidation is executed to select the best parameter pairs. The experiment results demonstrate that the algorithm is superior to the other stateoftheart splicing detection methods.

1 Introduction

In today's visual world, digital images have become one of the most common ways to transmit message of our daily lives, due to that they can convey a wide range of information in a compact way. With the rapid development of powerful image editing software, such as ‘PS’, it becomes easier to tamper with digital images without leaving obvious traces. Some criminals use the convenience to tamper with digital images maliciously, causing harmful effects on all sectors of society. Passive image forgery detection method, which determines whether the image has been tampered only by the structural changes of the tampered image, without any prior information, has become the next research direction. In the many means of image tampering, splicing is a fundamental and traditional tampering method, which copies one or more regions from one image and pastes it or them into another image. For example, in 2003, a picture of British soldiers and Iraqi civilians in Iraq War was published in The Los Angeles Times, as shown in Fig. 1c. Actually, it was reported later that this picture was created by merging two different images as shown in Figs. 1a

and b, and the region circled by the red line in Fig. 1c is the tampered region. From Fig. 1, it can be seen that the spliced image is usually a composited image of two or more images. So, there is inevitably inconsistency of image features in the spliced image, which can be the evidence to reveal the splicing tampering. Therefore, there are many effective passive image splicing detection methods. They can be divided into three categories according to the structural changes used by the algorithm. (i) Noisebased image splicing detection methods: they detect the spliced image mainly by the inconsistency of noise of regions of the image. However, these methods can only detect the spliced images with the specified camera or the pre processed spliced images [1–4]. (ii) Lightbased image splicing detection methods: they detect the spliced image mainly by the difference of light direction of regions of the image. If the two images compositing the spliced image have the similar illumination or their illumination environment is unobvious, this method often tends to fail [5–7]. (iii) Pixelbased image splicing detection methods: they distinguish the spliced images and the nature images by the statistical features which can accurately capture structure changes of the spliced image. These methods can be applied to

Fig. 1 Typical example of image splicing (a), (b) Original images, (c) Spliced image

IET Image Process., 2018, Vol. 12 Iss. 10, pp. 18151823 © The Institution of Engineering and Technology 2018 1815

various situations of the spliced images and can get a higher detection rate. Through the above description, in this paper, we focus on the image splicing blind detection based on the statistical features. In most previous algorithms, DCT (discrete cosine transform) is usually used to preprocess the image. Generally speaking, the grey image is processed directly. However, because the DCT can only process one colour channel at a time, the colour image needs to be extracted a colour channel before being processed, which can result in the loss of most of the colour information. In fact, most forgery images are colour images. In order to make use of the colour information, Li et al. [8] extracted the Markov features in QDCT (quaternion discrete cosine transform) domain which uses three channels of images. However, its robustness is poor due to quaternions used by QDCT, which have only one real and three imaginary parts. The octonion has one real part and seven imaginary parts which can represent the information of more colour image channels [9– 12]. Octonions have many applications in the processing of colour images, as for example in colour image edge detection [9], in 2D and 3D signal processing [10], in artificial neural networks, where Octonionic neural networks are used as a computational model [11] and examples can continue. So, in order to improve the robustness, we propose the discrete octonion cosine transform (DOCT) which bases on the principles of octonion and DCT. To improve the detection performance, another key contribution of this paper is that the algorithm uses the standard deviation to process the parts of DOCT coefficient matrix. Finally, the LIBSVM is employed for classification [13, 14]. This paper improves the parameter selection method of the LIBSVM classifier in order to improve the performance of the LIBSVM classifier. The organisation of the paper is as follows. Section 2 gives the research production and existing problems of different splicing detection methods. Section 3 describes the particulars about the proposed technique including preprocessing steps and feature extraction. In Section 4, experimental work is described and the experimental results are discussed and compared. Finally, Section 5 concludes the work and highlights the originality and contribution of this work.

2 Related works

Recently, many passive image splicing detection methods have been proposed, especially methods based on the statistical features. Since our algorithm is based on Markov features in DOCT domain, related works are concerned only with some methods associated with the DCT and the Markov feature.

2.1 Review of related works

Due to the DCT and the Markov feature incisively capture the correlation between image pixels, many methods utilise the DCT [15] and the Markov feature [16–19]. In DCT domain, the correlation between adjacent coefficients can less reflect the image content and retain more noncontent information (splicing information). The Markov transition probability features can reveal the dependencies between adjacent pixels after the image has been tampered. The correlation between the coefficients is valid for the method. He and Huang et al. extracted Markov features in DCT and DWT (discrete wavelet transform) domain, and the accuracy was up to 93.42% on the Columbia image dataset [17]. They achieved 89.76% accuracy on CASIA V2.0. Although the paper proved the validity of the Markov feature, its detection rate was too low. Zhang et al. [20] proposed an image tamper detection method based on local binary patterns (LBPs) of DCT coefficient. The high dimensionality of feature space was reduced using PCA (principal component analysis). The technique was evaluated on the Columbia image splicing detection dataset, the accuracy is 89.93%. The paper combined the DCT and LBP features for the first time, but its detection rate was still not ideal. Alahmadi et al. [15] proposed an image forgery forensics technique using the local binary pattern and the DCT. The

algorithm took the chrominance channel of the YCbCr colour space of the input image and used LBP to model the texture variation in each block of the chrominance channel. Then, the algorithm used DCT to convert the LBP code blocks to the frequency domain. Finally, the mean and standard deviation of corresponding DCT coefficients of all blocks were fed to the SVM classifier. The method achieved 97, 97.5, and 97.77% accuracies on CASIA V1.0, CASIA V2.0 [21], and Columbia database, respectively. Although the algorithm has achieved good performance, it cannot use all the information of the three colour channels. Zhang et al. [22] extracted the expanded Markov features in DCT domain and Contourlet transform domain. The Contourlet transform domain was used to process colour images, and the method obtained a detection accuracy of 94.10 and 96.69% on Columbia database and IFSTC database [23–26]. This article had a certain treatment for the detection of colour images, but its detection rate was not high. Li et al. [8] extracted the expanded Markov features in QDCT domain. They chose SVM [27] to classification. The method obtained the accuracies of 95.217 and 92.38% on CASIA V1.0 and CASIA V2.0, respectively. The paper used all the information of all colour channels, but its detection rate was not high and the robustness of the postprocessing image was poor. All of the above algorithms used the image splicing forensics model as shown in Fig. 2. All the shortcomings of the above algorithm can be summarised as the following points. (i) The detection performance of the algorithm is poor, and the accuracy is not high. (ii) The robustness of the algorithm is poor, especially for postprocessing images.

2.2 Key contribution of this paper

To overcome the shortcomings mentioned above, this paper provides a novel passive image splicing detection method based on the Markov features and the DOCT. The contributions of the work can be summarised as follows.

i. In the period of the pretreatment, the steps of DOCT were proposed and used in the algorithm. The DOCT can process six channels of colour images simultaneously, which can enhance the robustness of the algorithm. ii. When extracting the feature vector, the standard deviation is applied to show the relationship of the information between the DOCT coefficient matrix. The features obtained have a better ability to represent image splicing information. iii. The Kfolding crossvalidation is applied to select parameter pairs in the final step of classifying using LIBSVM. LIBSVM has better classification performance.

3 Proposed approach

In this section, the whole framework of the proposed algorithm is introduced. Then we present the technology involved in the algorithm and give the implementation steps of each technology. That is, how to transform the image into DOCT domain, extract the intrablock Markov features and the interblock Markov features [17] in DOCT domain and classify the Markov features using LIBSVM.

3.1 Algorithm framework

In this work, the Markov features are extracted in DOCT domain, and the LIBSVM is used to classify the spliced images and natural images. The outline for calculating these features for a given colour image is shown in Fig. 3. Compared to other algorithms, octonion and DOCT are firstly introduced into the algorithm in this paper. Unlike earlier work, e.g. [8], we use LIBSVM classifier, and the K fold crossvalidation is applied to improve the classification performance of LIBSVM. Firstly, in order to reduce the complexity of DOCT, the image needs to be blocked before DOCT. In this paper, the original image is segmented to nonoverlapping 8 × 8 image blocks, and the specific experiment is discussed in Section 4.3. The DOCT is applied to each image block.

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Secondly, the real and imaginary parts of the DOCT coefficient matrix are processed by the standard deviation, and the DOCT coefficient matrix of the entire original colour image can be acquired. Finally, the intrablock Markov feature and the interblock Markov feature of the DOCT coefficient matrix is extracted and fed to the LIBSVM.

3.2 Discrete octonion cosine transform

In this section, we recall some basic properties of the octonion and introduce the definition and the step of the DOCT.

3.2.1 Definition and multiplication rule of octonion: Compared with the quaternion used in Li et al. [8], octonion matrix of the image has a real part and seven imaginary parts and can simultaneously represent the colour information of six image

channels. In this paper, the RGB model and the HSI model are selected. The RGB model is inevitable. The HSI model is chosen because it completely reflects the basic attributes of human perception of colour, and human perception of the colour of the results of onetoone correspondence. Based on the above discussion, the inconsistency of adjacent pixels of six colour channels are captured by the octonion at the same time, the robustness of the algorithm is enhanced. Quaternion could be regarded as the generalisation of complex number, it includes a real part component and three imaginary part components [8]. A quaternion can be constructed by two complex numbers. Octonion could be regarded as the generalisation of quaternion, it includes a real part component and seven imaginary part components. The octonion with zero real part is pure octonion and the octonion with a unit module is called unit octonion. According to the Cayley–Dickson theorem, the pair of quaternions can be used to represent the octonion [28]:

Fig. 2 Existing image splicing forensics model

Fig. 3 System design of the proposed algorithm, the calculation of transition probability matrix in four directions (Dir_1 = DH, DV, GH and GV, Dir_2 = ED and GD, Dir_3 = EM and GM)

IET Image Process., 2018, Vol. 12 Iss. 10, pp. 18151823 © The Institution of Engineering and Technology 2018 1817

o = r0 + r1e1 + r2e2 + r3e3 + r4e4 + r5e5 + r6e6 + r7e7 q1 = r0 + r1e1 + r2e2 + r3e3 q2 = r4 + r5e1 + r6e2 + r7e3 o = q1 + q2e4

(1)

where o is the octonion, and the q1 and q2 are quaternions. The multiplication rules of the octonion are shown in Table 1.

3.2.2 DOCT: According to the fundamental principles and steps [8, 29, 30] of QDCT, combining with the nature of DOCT, the specific algorithm of DOCT is presented in this study. The DOCT formula is shown in

o(u, v) = α(u)α(v) ∑ x = 0

M −1

∑

y = 0

N −1 uo × ho(x, y) × H(u, v, x, y) (2)

where ho(x, y) is a twodimensional M × N octonion matrix. x and y indicate the location of pixels in rows and columns in the matrix, and M and N represent the dimensions of the rows and columns of the image matrix. uo is the unit pure octonion, and uo 2 = 1. The other parameter pairs are shown in

α(u) =

M ^,u = 0

2 M ^,otherwise , α(v) =

N ^,v = 0

2 N ^,otherwise

H(u, v, x, y) = cos^πu⁽²^x^{+ 1)}2M cos^πv⁽²^y^{+ 1)}2N

(3)

The steps of the algorithm of the DOCT are as follows:

i. The original colour image is divided into nonoverlapping 8 × 8 blocks. Six colour components of R, G, B, H, S, and I of blocked images are utilised to represents the six imaginary parts of the octonion matrix, and the remaining real and imaginary parts are zero:

ho(x, y) = f R(x, y)e2 + f G(x, y)e3 + f B(x, y)e4 + f H(x, y)e5 + f S(x, y)e6 + f I(x, y)e7

(4)

ii. uo is the unit pure octonion with zero real part and unit module, and it satisfies uo 2 = 1:

uo = u2e2 + u3e3 + u4e4 + u5e5 + u6e6 + u7e7

where u2 = u3 = u4 = u5 = u6 = u7 = 6 6

(5)

iii. uo and ho(x, y) are used to substitute the DOCT formula. In the process of substitution, the DCT formula is introduced to simplify the DOCT formula. Formulae (15)–(23) are obtained and are shown in the Appendix.

Through the above steps, the DOCT coefficient matrix of each block is obtained. In [8], the square root is used to process a real part and three imaginary parts of the QDCT coefficient matrix,

which ignores the relationship between the parts of the QDCT coefficient matrix (each channel of the image model). In this algorithm, the standard deviation is used to capture the relationship between a real part and seven imaginary parts of the DOCT coefficient matrix. In Section 4, it is proved by experiments that this improvement can effectively improve the detection rate. Finally, all calculated matrices need to reassemble according to the site of blocking, thus an 8 × 8 blocked DOCT matrix F of the original colour image can be acquired.

3.3 Markov features in DOCT domain

After the DOCT, the information of each channel of the image is integrated, and a matrix of the same size as the original image matrix is obtained. Then, the Markov features are used to capture the artefacts caused by splicing. The steps to extract the Markov features in DOCT domain are as follows:

i. Firstly, 8 × 8 block DOCT is applied to the original image following Part 3.4 (denote the obtained arrays by F). ii. All the DOCT coefficients F are rounded to the nearest integer and took absolute value (denote the obtained arrays by S). iii. The difference matrix is used to decrease the correlation of the image content, highlight the impact of the splicing operation on the original image. The intrablock difference arrays in horizontal, vertical, main diagonal, and antidiagonal directions are calculated for the array S (denote the obtained arrays as EH, EV, ED, and EM, respectively). Where u and v denote the coordinates in the corresponding matrices

EH(u, v) = S(u, v) −S(u + 1, v)

EV(u, v) = S(u, v) −S(u, v + 1)

ED(u, v) = S(u, v) −S(u + 1, v + 1)

EM(u, v) = S(u + 1, v) −S(u, v + 1)

(6)

The interblock difference arrays in horizontal, vertical, main diagonal, and antidiagonal directions are calculated for the array S (denote the obtained arrays GH, GV, GD, and GM, respectively). Where u and v denote the coordinates in the corresponding matrices:

GH(u, v) = S(u, v) −S(u + 8, v)

GV(u, v) = S(u, v) −S(u, v + 8)

GD(u, v) = S(u, v) −S(u + 8, v + 8)

GM(u, v) = S(u + 8, v) −S(u, v + 8)

(7)

iv. In order to reduce the dimension of the feature and the complexity, threshold processing on the difference arrays is performed. The proposed algorithm introduces a threshold T (T∈N+). If an element of EH (or EV, ED, EM, GH, GV, GD, and GM) is either larger than T or smaller than −T, it will be represented by T or −T correspondingly, applying (8)

Table 1 Multiplication rules in octonion × 1 e1 e2 e3 e4 e5 e6 e7 1 1 e1 e2 e3 e4 e5 e6 e7 e1 e1 −1 e3 −e2 e5 −e4 −e7 e6 e2 e2 −e3 −1 e1 e6 e7 −e4 −e5 e3 e3 e2 −e1 −1 e7 −e6 e5 −e4 e4 e4 −e5 −e6 −e7 −1 e1 e2 e3 e5 e5 e4 −e7 e6 −e1 −1 −e3 e2 e6 e6 e7 e4 −e5 −e2 e3 −1 −e1 e7 e7 −e6 e5 e4 −e3 −e2 e1 −1

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xnew =

T, xold ≥T

−T, xold ≤−T

xold otherwise

(8)

v. According to the stochastic process theory, the transition probability matrix can be used to characterise the Markov stochastic process. The horizontal, vertical, main diagonal, and antidiagonal transition probability matrices of EH, EV, ED, EM, GH, GV, GD, and GM are calculated by applying (24)–(35) in the Appendix (denote the obtained arrays as T1hh, T1hv, T1vh, T1vv, T1dd, T1aa, T2hh, T2hv, T2vh, T2vv, T2dd, and T2aa, respectively):

where i, j ∈{ −T, −T + 1, …, 0, …, T −1, T}, Su and Sv denote the dimensions of the original source image. δ( ⋅) = 1 only when its arguments are satisfied, otherwise δ( ⋅) = 0.

3.4 LIBSVM and Kfold crossvalidation

There are many classification methods of binary classification problem, such as random forest [31], support vector machine (SVM) methods, deep learning and so on. While simultaneously maximising the geometric margin between two different classes, SVM can minimise the empirical classification error [8]. Compared with other classifiers, SVM can get a very good performance by simply adjusting the parameters, and the LIBSVM is a library for SVM. In this paper, the LIBSVM is introduced to classify the spliced images and natural images. In previous papers, in the selection of parameter pairs, the LIBSVM uses only fixed parameters pairs. However, for LIBSVM classifiers, there are different most suitable parameter pairs for different datasets. In our algorithm, the Kfold crossvalidation is utilised to select parameter pairs. The best parameter pairs c and g are obtained by the Kfold crossvalidation based on the characteristics of the dataset. The contribution of Kfold crossvalidation to the algorithm is given in Section 4. The steps of using LIBSVM are as follows: Firstly, the dataset are normalised according to the requirements of the LIBSVM. Secondly, the LIBSVM choose the RBF (radial basis function) kernel, and the Kfold crossvalidation is used to select the best parameter pairs c and g. Finally, the training model is used to test the test data to get the classification results. In step (i), some data do not need to be normalised because the data is already in the range that we specify. In our algorithm, as for the image dataset, 5/6 authentic images and 5/6 spliced images of the image dataset are considered as the training set, then remaining 1/6 of the authentic and spliced images of the image dataset are as the testing set. In step (ii), the basic steps to use the Kfold crossvalidation are as follows:

i. The training set of an image dataset is divided into k non intersecting subsets, and each time k − 1 data as training data, and another piece of data as test data. ii. The training data and the given parameter pairs are used to establish a regression model, then the test data is utilised to get the mean square error (MSE) for this set of parameter pairs. iii. After repeated K times, the average of the MSE obtained after k iterations are used to estimate the expected generalisation error. iv. According to the expected generalisation error, a set of optimal parameter pairs is selected.

4 Experimental results

The proposed work is experimented by Matlab R2013a on the hardware platform of a PC with a 4G duo core processor. LIBSVM is used to classify the authentic images and spliced images with the kernel function of RBF. The threshold T is selected as T = 4 to obtain 972dimensional feature vector.

4.1 Image datasets

The proposed algorithm is evaluated using two image datasets: CASIA TIDE V1.0 and CASIA TIDE V2.0 (CASIA Tampered Image Detection Evaluation Database version 1.0 and 2.0). Their detailed information is listed in Table 2 [32]. In order to demonstrate the experimental images more intuitively, Fig. 4 shows some sample images selected from the above two datasets. When experimenting on CASIA V1.0, the average value of 10 repeating independent tests is selected to be the experimental result. When testing on CASIA V2.0, the experiment is run only one time. During the training, the authentic images and the spliced images in the training set are randomly selected from the image database, and the remaining images are used to test the trained model. The above practices ensure the fairness of the experiment. In order to evaluate the performance of the proposed algorithm, all the experiments and comparisons are tested on the dataset mentioned above and the same classifier.

4.2 Evaluating indicator

The performance indicators Accuracy and ROC (receiver operating characteristic) curve are used to evaluate the experimental results. The Accuracy can be calculated by

Accuracy = (TP + TN) (TP + FP + TN + FN) ^{× 100%}(9)

where TP (true positive) is the number of authentic images classified as authentic ones; FN (false negative) is the number of authentic images classified as tampered ones; TN (true negative) is the number of tampered images classified as tampered ones; and FP (false positive) is the number of tampered images classified as authentic ones. The ROC curve is also an important indicator of a comprehensive evaluation algorithm. The horizontal axis of the ROC curve is FPR (false positive rate) and the vertical axis is TPR (true positive rate). TPR indicates the probability that the authentic images are identified as authentic ones. TNR (true negative rate) indicates the probability that the tampered images are identified to have been tampered, as shown in (10)–(12). The value of AUC is the area under the ROC curve. The AUC is equal to the probability that a classifier will rank a randomly chosen positive instance higher than a randomly chosen negative one. The larger the value of AUC, the algorithm platforms better:

TPR = TP (TP + FN) (10)

TNR = TN (TN + FP) (11)

FPR = 1 −TNR (12)

4.3 Choice of size of blocks

In principle, the entire image can be DOCT transform, but the overall approach is poor performance due to the different levels of detail in different parts of the image [33]. To select the appropriate size of blocks, the following two points should be considered. If

Table 2 Detailed information of CASIA TIDE V1.0 and CASIA TIDE V2.0 Dataset No. of images Image type Image size Authentic Tampered Total CASIA V1.0 800 921 1721 Jpg 384 × 256, 256 × 384 CASIA V2.0 7491 5123 12,614 Jpg, tif, bmp 240 × 160–900 × 600

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size is too small, an image will be divided into more image blocks to be processed. Although the processing time of each image block decreases, the complexity of the algorithm increases due to the increase in the number of image blocks. Since the size of each image block is too small, the ability of DOCT transform is limited. On the other hand, if size is too large, due to the above analysis, we know that the complexity of the algorithm will be reduced. Due to the size of each image block is too large, DOCT transform has a good decorrelation, which reduces the detection rate of the algorithm. The relationship between the number of image blocks and size n × n of the image block is expressed as shown in (13). Suppose the dimension of the original image is Su × Sv:

numbers = Su × Sv ÷ (n × n) (13)

Thus three values of size are tested on CASIA V1.0, the corresponding experimental results are shown in Table 3. From Table 3 it can be seen that, when the size of blocks is 8 × 8, the algorithm achieves the highest detection rate and the complexity is acceptable. In addition, most papers [8, 22, 33] using the DCT transform and QDCT transform use size 8 × 8. So, taking into account the fairness of comparison with other algorithm and the performance of the algorithm, size 8 × 8 is chosen in this work.

4.4 Choice of threshold T

The threshold T is used to reduce the dimension when extracting the Markov features. To select the appropriate threshold T, the following two points should be considered. If threshold T is too small, the dimension of the Markov feature is so small that it cannot completely capture the change in the correlation of the pixels brought by splicing. On the other hand, if threshold T is too large, the dimension will be too large to reduce the complexity of the algorithm. The relationship between the Dim (dimension) and the threshold T is expressed as shown in

Dim = (2T + 1) × (2T + 1) × 12 (14)

Thus three values of T are tested on CASIA V1.0, the corresponding experimental results are shown in Table 4. From Table 4 it can be seen that, when T = 5, although the Accuracy of the algorithm is as high as 99.06%, the feature dimension and feature extraction time and feature classification time are the highest. Therefore, considering the complexity of the algorithm, the threshold T is not selected as 5. When T = 3, although the feature dimension and feature extraction time and feature classification time are the least, the accuracy of the algorithm is only 98.233%, which is the lowest of the three thresholds. When T = 4, the performance of all aspects of the algorithm is good. In addition, most papers [8, 17, 22] using the Markov feature use a threshold T = 4. If T chooses 3 or 5, the difference in accuracy due to the difference in T will affect the fairness of the comparison experiment. So, for the reasons stated above, T = 4 is chosen in this work.

4.5 Contribution of Kfold crossvalidation

Unlike the specified parameter pairs provided by the classifier in [8], the Kfold crossvalidation is used in this work to determine the optimal parameter pairs c and g. To illustrate the effect of K fold crossvalidation in the algorithm, we compare the detection rate of the algorithm using the specified parameter pairs provided by LIBSVM with the algorithm using the Kfold crossvalidation. The statistical results of Accuracy are shown in Fig. 5. Form Fig. 5 it can be seen that the Accuracy of the algorithm using Kfold crossvalidation is 98.7755%, which is significantly higher than 95.6268% of the algorithm using fixed parameter pairs. This illustrates that the Kfold crossvalidation can enhance the classification ability of the classifier.

Fig. 4 Sample images selected from CASIA TIDE V1.0 and CASIA TIDE V2.0 Table 3 Classification results of the proposed algorithm with different size of blocks on CASIA TIDE V1.0 Size Feature extraction time, s Accuracy, % 4 × 4 1030 84.4315 8 × 8 768 98.7755 16 × 16 699 93.9359

Table 4 Classification results of the proposed algorithm with different threshold T on CASIA TIDE V1.0 T Dim Feature extraction time, s Feature classification time, s Accuracy, %

3 588 140 313 98.2333 4 972 227 525 98.7755 5 1452 326 762 99.0617

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4.6 Contribution of standard deviation

In the QDCT proposed in [8], the real and the imaginary parts of the QDCT coefficient matrix are computed by the square root. After QDCT or DOCT, each real or imaginary part of the coefficient matrix of QDCT or DOCT can roughly represent the statistical change of the spliced image. Therefore, this paper considers that the use of standard deviation means that the dispersion between data is more efficient for the algorithm than using the square root to represent the mean of the data. The algorithms with square root and standard deviation are tested, respectively, on CASIA V1.0. The statistical results of Accuracy are shown in Fig. 6. From Fig. 6 it can be observed that, as we analysed, the use of standard deviations is much better than using square roots. Finally, the algorithm with standard deviation can achieve higher Accuracy (98.7755%).

4.7 Contribution of DOCT

In [8], the Markov feature in QDCT domain is used to classify authentic images and spliced images, and a superior detection rate is obtained. However, QDCT does not guarantee the robustness to the postprocessing image. Considering the fact that the spliced image may undergo some postprocessing operations, such as Gaussian Blur and White Gaussian Noise, DOCT is introduced to improve the robustness of the algorithm. Therefore, the experiments are conducted to evaluate the robustness of the algorithm on CASIA V1.0.

i. Gaussian blur: Gaussian blur with window size of w = 3, and standard deviation of σ = 0.1 to all the images on CASIA v1.0. ii. White Gaussian noise: White Gaussian noise with mean of m = 0 and variance of v = 0.00001 is added to all the images on CASIA v1.0.

The comparative experiment is based on the above image dataset, and the statistical results are shown in Fig. 7. From Fig. 7 it can be seen that our algorithm can stronger resist Gaussian blur and white Gaussian noise, with the Accuracy of 82.9155 and 82.2741%, respectively. This shows that DOCT can contribute to improving the robustness of the algorithm.

4.8 Comparison with other algorithms

Fig. 8 shows the ROC curves and AUC values of the algorithm. According to Section 4.2, AUC values and ROC curves are related to TPR and TNR, which are the important index to measure the performance of the algorithm. The data in Fig. 8 demonstrate that the proposed algorithm platforms well enough to distinguish the spliced images and the authentic images. To evaluate the algorithm comprehensively, the algorithm is compared with the following three stateoftheart image splicing detection methods. (i) The algorithm of Alahmadi et al.[15]: It has a very good classification effect among the recently proposed algorithms. (ii) The algorithm in [8]: the quaternion is introduced and the Markov feature is extracted in the QDCT domain to classify spliced images and original images, which has a similar principle to our work. (iii) The algorithm of He et al. [17]: The Markov feature is extracted for the first time in DCT domain and DWT domain. To ensure the fairness of the results of different algorithms, the above algorithms are experimented based on the same image databases of CASIA V1.0 and CASIA V2.0 and in the same experimental environment. The results of the comparison experiments are shown in Table 5. Through these results, it can be seen that the proposed algorithm is superior to the existing algorithms with the Accuracy of 98.7755 and 97.59%, respectively, on CASIA V1.0 and CASIA V2.0. This shows that the algorithm contributes to the research work of image splicing forensics.

Fig. 5 Effects of Kfold crossvalidation on the detection accuracy (%) using CASIA v1.0

Fig. 6 Effects of the standard deviation on the detection accuracy (%) using CASIA v1.0

Fig. 7 Effects of DOCT on the detection accuracy (%) using post processed CASIA v1.0

Fig. 8 ROC curves for the proposed algorithm using CASIA V1.0 and CASIA V2.0

IET Image Process., 2018, Vol. 12 Iss. 10, pp. 18151823 © The Institution of Engineering and Technology 2018 1821

5 Conclusion

In order to improve the detection rate and robustness of the image splicing detection algorithm, the expanded Markov features are extracted in DOCT domain in this study. The experimental results show that the algorithm platforms well with Accuracy of 98.7755 and 97.59% on CASIA V1.0 and CASIA V2.0, respectively, and it also has good robustness to the two postprocessing operations. The main contributions of this work are as follows:

• Relative to the QDCT in [8], the DOCT can simultaneously manipulate data consisting of six image channels, which enhances the robustness of the algorithm. • Through the experimental results, there are two innovations that can improve the detection rate of the algorithm: (i) The standard deviation is used to capture the relationship of colour information in the image. (ii) The Kfold crossvalidation is introduced to select the most appropriate parameter pairs, which can enhance the performance of the classifier.

From the above, the proposed algorithm for image splicing detection research has a certain theoretical and more practical significance. In the future, we will attention the application of deep learning in image splicing detection field to reduce the complexity of the algorithm and strengthen the detection rate of the algorithm.

6 Acknowledgments

This research is supported by the National Natural Science Foundation of China (61672259, 61602203), and Outstanding Young Talent Foundation of Jilin Province (20170520064JH).

7 References

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hyperspectral image classification’, Neural Comput. Appl., 2017, 35d1, (4), pp. 1–10 [15] Alahmadi, A., Hussain, M., Aboalsamh, H., et al.: ‘Passive detection of image forgery using DCT and local binary pattern’, Signal Image Video Processing, 2016, 11, (1), pp. 1–8 [16] Zhao, X., Wang, S., Li, S., et al.: ‘Passive imagesplicing detection by a 2D Noncausal Markov model’, IEEE Trans. Circuits Syst. Video Technol., 2015, 25, (2), pp. 185–199 [17] He, Z., Lu, W., Sun, W., et al.: ‘Digital image splicing detection based on Markov features in DCT and DWT domain’, Pattern Recognit., 2012, 45, (12), pp. 4292–4299 [18] ElAlfy, E.S.M., Qureshi, M.A.: ‘Combining spatial and DCT based Markov features for enhanced blind detection of image splicing’, Pattern Anal. Appl., 2015, 18, (3), pp. 713–723 [19] Hashmi, M.F., Keskar, A.G.: ‘Image forgery authentication and classification using hybridization of HMM and SVM classifier’, Int. J. Sec. Appli., 2015, 9, (4), pp. 125–140 [20] Zhang, Y., Zhao, C., Pi, Y., et al.: ‘Revealing image splicing forgery using local binary patterns of DCT coefficients’, Commun., Signal Process. Syst., 2012, 202, pp. 181–189 [21] Dong, J., Wang, W., Tan, T.: ‘CASIA image tampering detection evaluation database’. IEEE China Summit & Int. Conf. Signal and Information Processing, Beijing, China, 2013, pp. 422–426 [22] Zhang, Q., Lu, W., Weng, J.: ‘Joint image splicing detection in DCT and contourlet transform domain’, J. Vis. Commun. Image Represent., 2016, 40, pp. 449–458 [23] Cozzolino, D., Gragnaniello, D., Verdoliva, L.: ‘Image forgery localization through the fusion of camerabased, featurebased and pixelbased techniques’. IEEE Int. Conf. Image Processing, Paris, France, 2015, pp. 5302–5306 [24] Verdoliva, L., Cozzolino, D., Poggi, G.: ‘A featurebased approach for image tampering detection and localization’. IEEE Int. Workshop Information Forensics and Security, Atlanta, USA, 2015, pp. 149–154 [25] Wang, D.P., Gao, T., Yang, F.: ‘A forensic algorithm against median filtering based on coefficients of image blocks in frequency domain’, Multimedia Tools Applications, 2018, 4, pp. 1–17 [26] Isaac, M.M., Wilscy, M.: ‘Multiscale local Gabor phase quantization for image forgery detection’, Multimedia Tools Applications, 2017, 76, (24), pp. 1–22 [27] Chapelle, O.: ‘Training a support vector machine in the primal’, Neural Comput., 2007, 19, (5), p. 1155 [28] Łukasz Błaszczyk, , Snopek, K.M.: ‘Octonion Fourier transform of real valued functions of three variables selected properties and examples’, Signal Process., 2017, 136, pp. 29–37 [29] Feng, W., Hu, B.: ‘Quaternion discrete cosine transform and its application in color template matching’. Congress on IEEE Image and Signal Processing, Sanya, China, 2008, pp. 252–256 [30] Wang, R., Lu, W., Xiang, S., et al.: ‘Digital image splicing detection based on Markov features in QDCT and QWT domain’, 2017, arXiv:1708.08245 [31] Zhu, L., Wu, M., Wan, X., et al.: ‘Image recognition of rapeseed pests based on random forest classifier’, Int. J. Inf. Technol. Web Eng., 2017, 12, (3), pp. 1–10 [32] Shen, X., Shi, Z., Chen, H.: ‘Splicing image forgery detection using textural features based on the grey level cooccurrence matrices’, IET Image Process., 2017, 11, (1), pp. 44–53 [33] Doulamis, N., Doulamis, A., Kalogeras, D., et al.: ‘Low bitrate coding of image sequences using adaptive regions of interest’, IEEE Trans. Circuits Syst. Video Technol., 1998, 8, (8), pp. 928–934

8 Appendix

o(u, v) = o0(u, v) + o1(u, v)e1 + o2(u, v)e2 + o3(u, v)e3 +o4(u, v)e4 + o5(u, v)e5 + o6(u, v)e6 + o7(u, v)e7

(15)

where

o0(u, v) = −u2 × DCT(f R) −u3 × DCT(f G) −u4 × DCT(f B)

−u5 × DCT(f H) −u6 × DCT(f S) −u7 × DCT(f I) (16)

o1(u, v) = −u2 × DCT(f G) + u3 × DCT(f R) −u4 × DCT(f H)

+u5 × DCT(f B) + u6 × DCT(f I) −u7 × DCT(f S) (17)

o2(u, v) = −u4 × DCT(f S) −u5 × DCT(f I) + u6 × DCT(f B)

+u7 × DCT(f H) (18)

o3(u, v) = −u4 × DCT(f I) + u5 × DCT(f S) −u6 × DCT(f H)

+u7 × DCT(f B) (19)

o4(u, v) = u2 × DCT(f S) + u3 × DCT(f I) −u6 × DCT(f R)

−u7 × DCT(f G) (20)

Table 5 Results of the comparison experiments Method Accuracy, % CASIA V1.0 CASIA V2.0 proposed method 98.7755 97.59 Alahmadi et al. [15] 97.00 97.50 Li and Ma et al. [8] 95.958 92.377 He et al. [17] — 89.75

o5(u, v) = u2 × DCT(f I) −u3 × DCT(f S) + u6 × DCT(f G)

−u7 × DCT(f R) (21)

o6(u, v) = −u2 × DCT(f B) + u3 × DCT(f H) + u4 × DCT(f R)

−u5 × DCT(f G) (22)

o7(u, v) = −u2 × DCT(f H) −u3 × DCT(f B) + u4 × DCT(f G)

+u5 × DCT(f R) (23)

T1hh(i, j) = ^∑^u^{= 1}Su −2 ∑v = 1 Sv δ(EH(u, v) = i, EH(u + 1, v) = j)

∑u = 1 Su −2 ∑v = 1 Sv δ(EH(u, v) = i)

(24)

T1hv(i, j) = ^∑^u^{= 1}Su −1 ∑v = 1 Sv −1δ(EH(u, v) = i, EH(u, v + 1) = j)

∑u = 1 Su −1 ∑v = 1 Sv −1δ(EH(u, v) = i)

(25)

T1vh(i, j) = ^∑^u^{= 1}Su −1 ∑v = 1 Sv −1δ(EV(u, v) = i, EV(u + 1, v) = j)

∑u = 1 Su −1 ∑v = 1 Sv −1δ(EV(u, v) = i)

(26)

T1vv(i, j) = ^∑^u^{= 1}Su ∑v = 1 Sv −2δ(EV(u, v) = i, EV(u, v + 1) = j)

∑u = 1 Su ∑v = 1 Sv −2δ(EV(u, v) = i)

(27)

T1dd(i, j) = ^∑^u^{= 1}Su −2 ∑v = 1 Sv −2δ(ED(u, v) = i, ED(u + 1, v + 1) = j)

∑u = 1 Su −2 ∑v = 1 Sv −2δ(ED(u, v) = i)

(28)

T1aa(i, j) = ^∑^u^{= 1}Su −2 ∑v = 1 Sv −2δ(EM(u + 1, v) = i, EM(u, v + 1) = j)

∑u = 1 Su −2 ∑v = 1 Sv −2δ(EM(u, v) = i)

(29)

T2hh(i, j) = ^∑^u^{= 1}Su −16 ∑v = 1 Sv δ(GH(u, v) = i, GH(u + 8, v) = j)

∑u = 1 Su −16 ∑v = 1 Sv δ(GH(u, v) = i)

(30)

T2hv(i, j) = ^∑^u^{= 1}Su −8 ∑v = 1 Sv −8δ(GH(u, v) = i, GH(u + 8, v) = j)

∑u = 1 Su −8 ∑v = 1 Sv −8δ(GH(u, v) = i)

(31)

T2vh(i, j) = ^∑^u^{= 1}Su ∑v = 1 Sv −16δ(GV(u, v) = i, GV(u, v + 8) = j)

∑u = 1 Su ∑v = 1 Sv −16δ(GV(u, v) = i)

(32)

T2vv(i, j) = ^∑^u^{= 1}Su −8 ∑v = 1 Sv −8δ(GV(u, v) = i, GV(u + 8, v) = j)

∑u = 1 Su −8 ∑v = 1 Sv −8δ(GV(u, v) = i)

(33)

T2dd(i, j) = ^∑^u^{= 1}Su −16 ∑v = 1 Sv −16δ(GD(u, v) = i, GD(u + 8, v + 8) = j)

∑u = 1 Su −16 ∑v = 1 Sv −16δ(GD(u, v) = i)

(34)

T2aa(i, j) = ^∑^u^{= 1}Su −16 ∑v = 1 Sv −16δ(GM(u + 8, v) = i, GM(u, v + 8) = j)

∑u = 1 Su −16 ∑v = 1 Sv −16δ(GM(u, v) = i)

(35)

IET Image Processing - 2018 - Sheng - Image splicing detection based on Markov features in discrete octonion cosine

Image splicing detection based on Markov features in discrete octonion cosine transform domain

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