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Revealing the traces of nonaligned double JPEG compression in digital images
Optik - International Journal for Light and Electron Optics 204 (2020) 164196
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Short note
Revealing the traces of nonaligned double JPEG compression in digital images
T
Yujin Zhanga,b,*, Wanqing Songa, Fei Wua, Hua Hana, Lijun Zhanga a
School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China Shanghai Key Laboratory of Integrated Administration Technologies for Information Security, Shanghai Jiao Tong University, Shanghai 200240, China
b
A R T IC LE I N F O
ABS TRA CT
Keywords: Digital image forensics Nonaligned double JPEG compression Quantization artifacts High-order co-occurrence statistics Image-splicing forgery
JPEG standard has been widely applied in many image acquisition devices and image editing tools. Identifying the authenticity of JPEG images is receiving significant attention in image forensics. In many JPEG image splicing forgeries, the forged regions have always experienced the JPEG compression twice with inconsistent block segmentations (hereinafter referred to as nonaligned double JPEG compression). In this paper, an effective method to reveal the traces of the nonaligned double JPEG compression is proposed. The high-order co-occurrence statistics are utilized to model the underlying intra-block and inter-block dependencies of JPEG quantized DCT coefficients. The entropies of the high-order co-occurrence matrices are computed and treated as the discriminative features to identify the presence of nonaligned double JPEG compression. The experiment results have shown that the proposed approach outperforms several existing methods for low resolution (small size) images.
1. Introduction With the rapid increase in image acquisition devices and user-friendly image processing software, it is easy and convenient to synthesize realistic images with the aid of these superior conditions. Against this backdrop, the detection of malicious image forgeries has drawn considerable attention in recent years [1]. JPEG is the most widely used image format on the Internet due to its high efficiency in storage. The identification of forgeries in JPEG images has triggered wide interest among forensic analyzers. It has been a well-recognized fact that JPEG compressed images typically exhibit inherent blocking artifacts. Such intrinsic traces introduced by JPEG compression are conducive to unveiling some possible image forgeries [2]. As a result, revealing the compression history of an image is significant in image forensics. In many JPEG image forgeries, the local manipulated regions have always been compressed by JPEG twice, which are called double JPEG compression. Such phenomena typically occur in two forms, including aligned double JPEG (AD-JPEG) compression [3] (the block dividing of the first and the second JPEG compression is perfectly aligned to each other) and nonaligned double JPEG (NAD-JPEG) compression [5] (also called shifted double JPEG compression [4]). Recently, many forensic approaches working toward the ADJPEG compression scenario have been designed with the fact that ADJPEG compression introduces double quantization effect to a host image [6,7]. These forensics methods are quite effective to expose the traces of AD-JPEG compression. For the case of NAD-JPEG compression, Luo et al. [4] devised a blocking artifact characteristics matrix (BACM) based method to detect the presence of NADJPEG compression. BACM exhibits regular symmetrical shape for a single JPEG compressed images, but such symmetry property is
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Corresponding author at: School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China. E-mail address: [email protected] (Y. Zhang).
https://doi.org/10.1016/j.ijleo.2020.164196 Received 25 February 2019; Received in revised form 23 December 2019; Accepted 7 January 2020 0030-4026/ © 2020 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 204 (2020) 164196
Y. Zhang, et al.
Fig. 1. The generation diagram of an NAD-JPEG compressed image. (a) JPEG compressed image with QF1; (b) NAD-JPEG compressed image with QF2 with a grid shift (x, y).
destroyed to different extent when NAD-JPEG compression is performed. Qu et al. [8] considered the NAD-JPEG compression as noisy convolutive mixing model and tried to handle it by independent component analysis. Similar to that in [4], the presence of NAD-JPEG compression is identified by analyzing the symmetry property of independent value map (IVM). In [5], Bianchi and Piva presented an NAD-JPEG compression identification method based on integer periodicity map (IPM). The statistical artifacts left by NAD-JPEG compression are measured in terms of the uniformity of the min-entropy of the IPM. The IPM detector performs better than the detectors proposed in [4] and [8]. But in general, the aforementioned approaches are still challenging for detecting the presence of NAD-JPEG compression when image patch is small. In this paper, we propose an effective NAD-JPEG compression identification method based on the high-order co-occurrence statistics. The proposed detector can effectively distinguish the NAD-JPEG compressed images from the single JPEG compressed images. In addition, it can more reliably detect the NAD-JPEG compressed images than previous findings for small patch size. We make a comprehensive comparison between the proposed detector and the state-of-the-art detectors investigated at various compression levels to verify the effectiveness of the proposed method. 2. Proposed detection algorithm 2.1. Nonaligned double JPEG compression The NAD-JPEG compression tampering scenario [4] can be described as follows. First, an image patch is cropped from a single JPEG compressed source image with a quality factor QF1 and then pasted onto a single JPEG compressed target image with a quality factor QF2. Finally, the composite image is saved as JPEG format with the quality factor QF2. It is noted that the blocking artifact grids corresponding to the first compression for the forged region are misaligned with that of the second compression with a probability of 63/64. The generation diagram of an NAD-JPEG compressed image is shown in Fig. 1. Suppose f0 is an uncompressed image and f1 is the JPEG compressed version with a quality factor QF1 and a grid shifted by (x , y ) ≠ (0, 0)(x , y ∈ {0, 1, …, 7}) relative to the upper left corner. The compressed image f1 [5] can be formulated as: −1 f1 = Dxy Q1 (Dxy f0 ) + E1 = f0 + R1
(1)
Where Dxy denotes an 8 × 8 block discrete cosine transform (BDCT) with the grid shifted by (x , y ) ≠ (0, 0) relative to the upper left corner, Q1 models quantization and de-quantization processes with JPEG quantization table corresponding to the quality factor QF1, E1 denotes the rounding error and truncating error in JPEG compression and de-compression and R1 stands for the overall error introduced by JPEG compression relative to the image f0 . When the image f1 is compressed with a quality factor QF2 and the block grid aligned with the upper left corner of the image, the NAD-JPEG compressed image f2 [5] can be given by
f2 = f1 + R2
(2)
Where R2 stands for the overall error introduced by JPEG compression relative to the image f1. There exist some underlying dependencies among neighboring quantized BDCT coefficients [9]. In [10], three types of correlations (intra-block correlation, inter-block correlation and sign correlation) among the adjacent quantized BDCT coefficients have been proposed for JPEG steganalysis. Due to the errors generated from double JPEG compression, it is expected that the characteristic traces introduced by NAD-JPEG compression can be reflected in these correlations to certain extent. Inspired by the previous research 2
Optik - International Journal for Light and Electron Optics 204 (2020) 164196
Y. Zhang, et al.
results [9] and [10], a forensic method of NAD-JPEG compression based on high-order statistics is investigated in this paper. Different from some existing methods which only use the first order statistics, the third order co-occurrence statistics are adopted to characterize all three types of correlations for detecting the presence of NAD-JPEG compression, effectively capturing more discriminative information. 2.2. Third order Co-occurrence Let I be a 2-D quantized BDCT coefficient array, the normalized third order co-occurrence matrices [11] along four directions are given by
Jh (m1, m2 , m3) = |{(i, j )|Ii + k − 1, j = mk , k= 1, 2, 3}|/ Nh Jv (m1, m2 , m3) = |{(i, j )|Ii, j + k − 1 = mk , k= 1, 2, 3}|/ Nv Jd (m1, m2 , m3) = |{(i, j )|Ii + k − 1, j + k − 1 = mk , k= 1, 2, 3}|/ Nd J-d (m1, m2 , m3) = |{(i, j )|Ii + k − 1, j − k + 1 = mk , k= 1, 2, 3}|/ N−d
(3)
Where mk ∈ { −T , −T + 1, …, 0, …, T − 1, T }, k = 1, 2, 3,T is a pre-determined positive integer value, |⋅| denotes the cardinality, the subscript h, v, d and -d represent the horizontal direction, the vertical direction, the main diagonal direction and the minor diagonal direction, and Nh, Nυ, Nd and N−d are the normalization factors associated with the co-occurrences in corresponding directions, respectively. Each co-occurrence matrix in Eq. (3) has (2T + 1)3 elements. In the subsequent experiments, T is empirically set to 1 for making a trade-off between detection accuracy and computational complexity. 2.3. Feature extraction For an NAD-JPEG compressed image, the grid shift corresponding to the first compression may have 63 possible cases but only one real scenario. Since the quality factor that corresponds to the second compression is known for the given JPEG image, motivated by the steganalysis of YASS [9], we can use a JPEG quantizer at the image to quantize all the shifted versions of the image. Due to double quantization artifacts [3,7,9], the third order co-occurrence statistics calculated from the BDCT domain corresponding to the block segmentation in accordance with that of the first compression should exhibit variations between the NAD-JPEG compressed images and the single JPEG compressed ones. It is noted that the luminance channel of a color JPEG image is only considered for feature construction. This is mainly because image chrominance sub-sampling for JPEG compression will introduce interpolation noise in chroma channels. In view of the analysis above, the proposed feature extraction procedure is summarized as follows: 1) Get the quantized BDCT coefficient array I with size M1× N1 and the current quantization table TQF2 of the luminance channel from the head files of the given JPEG image, and then de-compress I to spatial domain. Denote the spatial array as Φ = [Φm, n], where Φm, n represents the (m,n)-th 8 × 8 sub-block in Φ , defined as
Φm, n = D−1 (Im, n ⊗ TQF2) Where, 1 ≤ m ≤ r1, 1 ≤ n ≤ s1, r1 = ⌊M1 8⌋ s1 = ⌊N1 8⌋, operator.
(4)
D−1
models the inverse 8 × 8 block DCT and ⊗ is the Hadamard product
1) Calculate the shifted spatial version of Φ according to a grid shift (x , y ) (x , y ∈ {0, 1, ⋯, 7}) . Divide the resulting shifted spatial array into non-overlapping 8 × 8 blocks, denoted by Ψ x , y = [Ψux,,vy], where the superscript (x, y) denotes the grid shift and the subscript (u, v) is the index of 8 × 8 sub-block. x,y 2) Quantize Ψ x , y with TQF2 to get the quantized BDCT coefficient array Ω x , y = [Ωux,,vy], where Ωu,v can be expressed as
Ωux,,vy = D (Ψux,,vy ⊙ TQF2)
(5)
Where, D models the 8 × 8 block DCT and ⊙ is an entry-by- entry division operator. 1) Round all the elements in Ω x , y and calculate the third order co-occurrences along four directions (denoted by Jhx , y , Jvx , y , Jdx , y and J−xd, y ) by using Eq. (3) to represent the intra-block correlation and sign correlation among adjacent quantized BDCT coefficients. 2) Perform the row block scanning pattern and the column block scanning pattern [10] on Ω x , y to get two arrays, denoted by Θrx , y and Θcx , y , respectively. Calculate the third order co-occurrences of Θrx , y and Θcx , y along vertical direction by using Eq. (3) to represent the inter-block correlation and sign correlation among adjacent coefficients, denoted by Jrvx, y and Jcvx, y , respectively. 3) Calculate the entropies of the third order co-occurrence matrices generated from steps 4) and 5), For a specific grid shift (x , y ) ( x , y ∈ {0, 1, 2, ⋯, 7} ) and specific direction α (α ∈ {h, v, d, −d, rv, cv}) , the resulting feature can be formulated as
Fαx , y = − ∑ ∑ ∑ Jαx , y (i, j, k ) log2 Jαx , y (i, j, k ) i
j
(6)
k
1) Loop through steps 2) to 6) for all the grid shifts and concatenate all these entropies to form the final feature set. The dimension of 3
Optik - International Journal for Light and Electron Optics 204 (2020) 164196
Y. Zhang, et al.
Fig. 2. Distributions of the proposed features extracted from the single JPEG compressed Lena image and the NAD-JPEG compressed version for the quality factor pair (a) {QF1, QF2} = {50, 70} and (b) {QF1, QF2} = {50, 90}, respectively.
the final feature set is 6 × 8 × 8 = 384. To preliminarily validate the discriminative ability of the proposed features, Fig. 2 shows the distributions of features extracted from the single JPEG compressed Lena image and the NAD-JPEG compressed version by using the proposed feature extraction procedure for two {QF1,QF2} pairs (i.e., {50,70} and {50,90}). It is observed from Fig. 2 that the constructed feature can effectively distinguish NAD-JPEG compression from single JPEG compression. 3. Experimental results 3.1. Experimental setup In order to evaluate the proposed NAD-JPEG compression detector and to compare it with several existing detectors in various compression scenarios, two image databases widely used in image forensics, i.e. UCID [12] and NRCS [13], are adopted to measure their accuracy. All the original images with TIFF format in the databases above are uncompressed and with the size of 384 × 512 and 1500 × 2100, respectively. In our experiment, 5000 original images are selected from the aforementioned two databases, and the quality factors QF1 and QF2 are selected from 50 to 90 with a step of 10 for evaluation. For a specific {QF1, QF2} pair, the following datasets are constructed: 1) The NAD-JPEG compressed dataset (denoted by ηNAD): JPEG compression with QF1 is first performed on each TIFF image. Then, image patches with three sizes, i.e. 64 × 64, 128 × 128 and 256 × 256 are cropped from each de-compressed image with random grid shifts (x, y) ≠ (0, 0) (x , y ∈ {0, 1, 2, ⋯, 7}) and saved as JPEG format with QF2 to construct ηNAD. 2) The single JPEG compressed dataset (denoted by ηS): Image patches with three sizes are first extracted from each TIFF image, respectively. Then, each image patch is saved in JPEG format with QF2 to construct ηS. Note that each pair of single JPEG compressed image patch and NAD-JPEG compressed image patch has the same image content for the same patch size similar to that in Qu’s [8]. When the datasets above are constructed, 5 × 5×3 = 75 training-testing pairs are prepared for classification. For a specific patch size and a specific {QF1, QF2} pair, there are 5000 NAD-JPEG compressed image patches and 5000 single JPEG compressed image patches in the datasets above. 3.2. Classification For the proposed method, the NAD-JPEG compression detection is considered as a binary classification task. C-SVM [14] with 4
Optik - International Journal for Light and Electron Optics 204 (2020) 164196
Y. Zhang, et al.
Table 1 Average Detection Accuracy with Various Values of QF1 and QF2 and Various Patch size. The Values a/b/c/d Represent the Average Detection Accuracy by A) the BACM Detector, B) the IVM Detector, C) the IPM Detector, and D) the proposed Detector, Respectively. The Best Accuracies among the Four Methods Investigated are Highlighted in Bold. (a)
PATCH SIZE OF
64 × 64
QF2 QF1
50
60
70
80
90
50 60 70 80 90
52.60/50.40/50.81/57.02 51.76/50.78/49.98/54.57 51.01/50.20/50.31/52.61 50.41/49.98/50.35/49.77 50.90/50.47/49.53/50.34
51.92/51.37/53.42/70.94 51.46/50.28/52.24/57.82 50.79/50.76/51.86/54.31 50.26/50.34/50.97/51.49 50.26/49.79/50.02/50.30
57.44/52.30/61.97/98.94 53.91/50.74/56.13/83.70 51.91/50.07/51.36/57.91 50.14/50.40/50.18/53.50 50.63/50.07/49.97/50.38
61.42/56.22/70.05/99.73 58.92/54.93/63.02/99.64 55.64/52.97/61.21/96.25 52.03/50.95/52.01/60.65 50.54/50.49/50.19/50.53
67.76/64.28/77.41/99.76 65.61/63.17/72.03/99.74 62.47/60.52/65.01/99.72 58.99/55.84/60.11/99.76 53.48/50.83/50.93/63.89
(b)
PATCH SIZE OF
128 × 128
QF2 QF1
50
60
70
80
90
50 60 70 80 90
52.85/52.92/54.03/66.92 52.06/51.01/51.98/62.18 50.59/50.32/51.39/57.65 50.88/49.72/50.07/52.03 50.12/50.63/49.87/50.48
54.74/54.39/55.88/88.72 53.97/51.88/51.44/67.47 52.75/51.12/50.72/62.15 50.94/50.23/50.61/53.92 50.18/50.32/49.29/50.73
63.47/56.66/68.03/99.84 57.71/55.16/59.98/97.01 53.11/53.16/54.05/69.49 51.66/50.94/50.82/60.19 50.49/50.72/50.01/50.90
71.04/62.46/78.33/99.90 66.25/59.57/70.91/99.89 59.92/55.64/64.59/99.57 53.51/53.09/52.87/73.72 50.22/50.25/52.17/54.33
80.67/73.54/86.96/99.93 77.09/72.63/79.84/99.91 72.88/69.46/78.63/99.90 65.87/62.77/68.65/99.92 55.33/52.78/53.72/79.54
(c)
PATCH SIZE OF
256 × 256
QF2 QF1
50
60
70
80
90
50 60 70 80 90
56.27/57.46/60.06/83.71 53.89/54.88/52.46/77.59 51.56/51.05/51.31/69.55 50.50/50.22/51.03/55.87 50.49/49.70/50.53/50.87
60.27/59.87/64.81/97.83 57.27/57.76/57.98/84.60 53.56/53.63/52.71/77.57 52.20/50.59/51.41/61.26 50.59/49.60/50.31/51.71
71.99/64.71/71.55/99.95 62.66/61.49/63.62/99.59 57.28/57.45/58.03/86.57 53.51/51.76/51.97/76.16 50.17/49.57/50.49/53.17
82.69/71.78/86.93/99.96 77.17/69.50/71.98/99.96 67.50/64.50/69.87/99.87 58.14/57.18/59.34/88.94 51.46/50.75/51.05/61.17
89.67/82.92/94.06/99.98 87.39/81.73/88.64/99.99 83.19/78.73/82.98/99.97 76.46/71.49/72.05/99.97 58.04/54.84/53.99/92.98
radial basis function (RBF) kernel is selected as the classifier. For a specific training-testing condition, 40 % of the positive samples (NAD-JPEG compressed image patches) and 40 % of the negative ones (single JPEG compressed image patches) are randomly picked out to train the SVM, and the remaining samples are used for evaluation. Five-fold cross-validation on the training set is performed to get the optimal kernel parameters of the SVM classifier in the multiplicative grid (C , γ )ε{(2i , 2 j)|i, jεZ , −10 ≤ i, j ≤ 10)} . In the stage of classification, the above training-testing procedure is repeated thirty times to reduce the performance variations caused by random selections of training samples. The average detection accuracy is recorded to evaluate the performance of the proposed method. 3.3. Detection of NAD-JPEG compression To validate the effectiveness of the proposed method, three state-of-the-art methods, i.e., the BACM-based method [4], the IVMbased method [8], and the IPM-based method [5], are utilized for performance comparison on the constructed dataset. For the proposed detector and the BACM detector and the IVM detector, a specific SVM is trained with the extracted features to distinguish the NAD-JPEG compressed image patches from the single JPEG compressed ones. For the IPM detector, the optimal thresholds are achieved by an exhaustive search to identify the presence of NAD-JPEG compression. The average detection accuracies of the proposed detector and other three detectors for three patch sizes are summarized in Table 1 . It is shown from these tables that the patch size and the difference in quality factor between the first and the second compression (i.e. ΔQ=QF2-QF1) have a major influence on the performance of the investigated detectors. The following observation can be made by taking a closer look at these tables: 1) The higher value of ΔQ results in higher detection accuracy. The main reason for this is that the first compression with a lower quality factor will generate more compression artifacts. Meanwhile, it is easier to identify the presence of NAD-JPEG compression when the second compression is executed via a higher quality factor due to the less distortion to the image. 2) For a specific ΔQ, larger patch size leads to better detection performance. Since all these NAD-JPEG compression detectors investigated are based on statistical models, larger patch size results in better statistical performance, which makes the presence of NAD-JPEG compression easier to be captured. 3) Among all these detectors, the proposed detector performs better than other three state-of-the-art detectors in general especially when patch size is small, which indicates that the proposed detector is capable of capturing the traces introduced by NAD-JPEG compression more effectively and is more robust in various JPEG compression scenarios.
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Optik - International Journal for Light and Electron Optics 204 (2020) 164196
Y. Zhang, et al.
4. Conclusions In this paper, we have proposed a high-order-statistics based scheme to identify the presence of NAD-JPEG compression. Due to double quantization artifacts, statistical features extracted from the neighboring quantized BDCT coefficients corresponding to the block segmentation in accordance with that of the first compression exhibit variations between the NAD-JPEG compressed images and the single JPEG compressed ones, leaving detectable traces. The third order co- occurrence statistics are adopted to characterize three types of correlations of quantized BDCT coefficients for NAD-JPEG compression identification. We have conducted a series of experiments at various compression levels and various patch sizes to evaluate the performance of the algorithms. Experiment results have shown that the proposed method can more reliably identify the presence of NAD-JPEG compression than existing three methods, especially when image patch is small. Future research will focus on the estimation of the quality factor of the first compression for tampering detection and location more intelligently. In addition, this research can also be combined with many disciplines, such as criminal investigation, artificial intelligence [15–18], fault analysis [19–23], and so on. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work is mainly funded by the Natural Science Foundation of Shanghai (grant no. 17ZR1411900), the National Natural Science Foundation of China (grant no. 51705307), the Key Project of Science and Technology Commission of Shanghai Municipality (grant no. 18511101600), the Opening Project of Shanghai Key Laboratory of Integrated Administration Technologies for Information Security (grant no. AGK2015006), the Founding Program for the Cultivation of Young University Teachers of Shanghai (grant no. ZZGCD15090), and the Research Start-up Foundation of Shanghai University of Engineering Science (grant no. 2016-56). References [1] X. Zhao, S. Wang, S. Li, J. Li, Passive image-splicing detection by a 2-d noncausal Markov model, IEEE Trans. Circuits Syst. Video Technol. 25 (2) (2015) 185–199. [2] B. Li, T.-T. Ng, X. Li, S. Tan, J. Huang, Revealing the trace of high-quality JPEG compression through quantization noise analysis, IEEE Trans. Inf. Forensics Secur. 10 (3) (2015) 558–573. [3] B. Li, Y.Q. Shi, J. Huang, Detecting doubly compressed JPEG images by using mode based first digit features, Proc. IEEE Multimedia Signal Processing Workshop (2008) 730–735. [4] W. Luo, Z. Qu, J. Huang, G. Qiu, A novel method for detecting cropped and recompressed image block, Proc. Int. Conf. Acoustics, Speech, and Signal Processing (2007) 217–220. [5] T. Bianchi, A. Piva, Detection of nonaligned double JPEG compression based on integer periodicity maps, IEEE Trans. Inf. Forensics Secur. 7 (2) (2012) 842–848. [6] F. Huang, J. Huang, Y.Q. Shi, Detecting double JPEG compression with the same quantization matrix, IEEE Trans. Inf. Forensics Secur. 5 (4) (2010) 848–856. [7] Z. Lin, J. He, X. Tang, C.K. Tang, Fast, automatic and fine-grained tampered JPEG image detection via DCT coefficient analysis, Pattern Recognit. 42 (11) (2009) 2492–2501. [8] Z. Qu, W. Luo, J. Huang, A convolutive mixing model for shifted double JPEG compression with application to passive image authentication, Proc. ICASSP (2008) 1661–1664. [9] B. Li, J. Huang, Y.Q. Shi, Steganalysis of YASS, IEEE Trans. Inf. Forensics Secur. 4 (3) (2009) 369–382. [10] F. Huang, B. Li, J. Huang, Universal JPEG steganalysis based on microscopic and macroscopic calibration, Proc. ICIP (2008) 2068–2071. [11] J. Fridrich, J. Kodovsky, Rich models for steganalysis of digital images, IEEE Trans. Inf. 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Short note
Revealing the traces of nonaligned double JPEG compression in digital images
T
Yujin Zhanga,b,*, Wanqing Songa, Fei Wua, Hua Hana, Lijun Zhanga a
School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China Shanghai Key Laboratory of Integrated Administration Technologies for Information Security, Shanghai Jiao Tong University, Shanghai 200240, China
b
A R T IC LE I N F O
ABS TRA CT
Keywords: Digital image forensics Nonaligned double JPEG compression Quantization artifacts High-order co-occurrence statistics Image-splicing forgery
JPEG standard has been widely applied in many image acquisition devices and image editing tools. Identifying the authenticity of JPEG images is receiving significant attention in image forensics. In many JPEG image splicing forgeries, the forged regions have always experienced the JPEG compression twice with inconsistent block segmentations (hereinafter referred to as nonaligned double JPEG compression). In this paper, an effective method to reveal the traces of the nonaligned double JPEG compression is proposed. The high-order co-occurrence statistics are utilized to model the underlying intra-block and inter-block dependencies of JPEG quantized DCT coefficients. The entropies of the high-order co-occurrence matrices are computed and treated as the discriminative features to identify the presence of nonaligned double JPEG compression. The experiment results have shown that the proposed approach outperforms several existing methods for low resolution (small size) images.
1. Introduction With the rapid increase in image acquisition devices and user-friendly image processing software, it is easy and convenient to synthesize realistic images with the aid of these superior conditions. Against this backdrop, the detection of malicious image forgeries has drawn considerable attention in recent years [1]. JPEG is the most widely used image format on the Internet due to its high efficiency in storage. The identification of forgeries in JPEG images has triggered wide interest among forensic analyzers. It has been a well-recognized fact that JPEG compressed images typically exhibit inherent blocking artifacts. Such intrinsic traces introduced by JPEG compression are conducive to unveiling some possible image forgeries [2]. As a result, revealing the compression history of an image is significant in image forensics. In many JPEG image forgeries, the local manipulated regions have always been compressed by JPEG twice, which are called double JPEG compression. Such phenomena typically occur in two forms, including aligned double JPEG (AD-JPEG) compression [3] (the block dividing of the first and the second JPEG compression is perfectly aligned to each other) and nonaligned double JPEG (NAD-JPEG) compression [5] (also called shifted double JPEG compression [4]). Recently, many forensic approaches working toward the ADJPEG compression scenario have been designed with the fact that ADJPEG compression introduces double quantization effect to a host image [6,7]. These forensics methods are quite effective to expose the traces of AD-JPEG compression. For the case of NAD-JPEG compression, Luo et al. [4] devised a blocking artifact characteristics matrix (BACM) based method to detect the presence of NADJPEG compression. BACM exhibits regular symmetrical shape for a single JPEG compressed images, but such symmetry property is
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Corresponding author at: School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China. E-mail address: [email protected] (Y. Zhang).
https://doi.org/10.1016/j.ijleo.2020.164196 Received 25 February 2019; Received in revised form 23 December 2019; Accepted 7 January 2020 0030-4026/ © 2020 Elsevier GmbH. All rights reserved.
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Fig. 1. The generation diagram of an NAD-JPEG compressed image. (a) JPEG compressed image with QF1; (b) NAD-JPEG compressed image with QF2 with a grid shift (x, y).
destroyed to different extent when NAD-JPEG compression is performed. Qu et al. [8] considered the NAD-JPEG compression as noisy convolutive mixing model and tried to handle it by independent component analysis. Similar to that in [4], the presence of NAD-JPEG compression is identified by analyzing the symmetry property of independent value map (IVM). In [5], Bianchi and Piva presented an NAD-JPEG compression identification method based on integer periodicity map (IPM). The statistical artifacts left by NAD-JPEG compression are measured in terms of the uniformity of the min-entropy of the IPM. The IPM detector performs better than the detectors proposed in [4] and [8]. But in general, the aforementioned approaches are still challenging for detecting the presence of NAD-JPEG compression when image patch is small. In this paper, we propose an effective NAD-JPEG compression identification method based on the high-order co-occurrence statistics. The proposed detector can effectively distinguish the NAD-JPEG compressed images from the single JPEG compressed images. In addition, it can more reliably detect the NAD-JPEG compressed images than previous findings for small patch size. We make a comprehensive comparison between the proposed detector and the state-of-the-art detectors investigated at various compression levels to verify the effectiveness of the proposed method. 2. Proposed detection algorithm 2.1. Nonaligned double JPEG compression The NAD-JPEG compression tampering scenario [4] can be described as follows. First, an image patch is cropped from a single JPEG compressed source image with a quality factor QF1 and then pasted onto a single JPEG compressed target image with a quality factor QF2. Finally, the composite image is saved as JPEG format with the quality factor QF2. It is noted that the blocking artifact grids corresponding to the first compression for the forged region are misaligned with that of the second compression with a probability of 63/64. The generation diagram of an NAD-JPEG compressed image is shown in Fig. 1. Suppose f0 is an uncompressed image and f1 is the JPEG compressed version with a quality factor QF1 and a grid shifted by (x , y ) ≠ (0, 0)(x , y ∈ {0, 1, …, 7}) relative to the upper left corner. The compressed image f1 [5] can be formulated as: −1 f1 = Dxy Q1 (Dxy f0 ) + E1 = f0 + R1
(1)
Where Dxy denotes an 8 × 8 block discrete cosine transform (BDCT) with the grid shifted by (x , y ) ≠ (0, 0) relative to the upper left corner, Q1 models quantization and de-quantization processes with JPEG quantization table corresponding to the quality factor QF1, E1 denotes the rounding error and truncating error in JPEG compression and de-compression and R1 stands for the overall error introduced by JPEG compression relative to the image f0 . When the image f1 is compressed with a quality factor QF2 and the block grid aligned with the upper left corner of the image, the NAD-JPEG compressed image f2 [5] can be given by
f2 = f1 + R2
(2)
Where R2 stands for the overall error introduced by JPEG compression relative to the image f1. There exist some underlying dependencies among neighboring quantized BDCT coefficients [9]. In [10], three types of correlations (intra-block correlation, inter-block correlation and sign correlation) among the adjacent quantized BDCT coefficients have been proposed for JPEG steganalysis. Due to the errors generated from double JPEG compression, it is expected that the characteristic traces introduced by NAD-JPEG compression can be reflected in these correlations to certain extent. Inspired by the previous research 2
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results [9] and [10], a forensic method of NAD-JPEG compression based on high-order statistics is investigated in this paper. Different from some existing methods which only use the first order statistics, the third order co-occurrence statistics are adopted to characterize all three types of correlations for detecting the presence of NAD-JPEG compression, effectively capturing more discriminative information. 2.2. Third order Co-occurrence Let I be a 2-D quantized BDCT coefficient array, the normalized third order co-occurrence matrices [11] along four directions are given by
Jh (m1, m2 , m3) = |{(i, j )|Ii + k − 1, j = mk , k= 1, 2, 3}|/ Nh Jv (m1, m2 , m3) = |{(i, j )|Ii, j + k − 1 = mk , k= 1, 2, 3}|/ Nv Jd (m1, m2 , m3) = |{(i, j )|Ii + k − 1, j + k − 1 = mk , k= 1, 2, 3}|/ Nd J-d (m1, m2 , m3) = |{(i, j )|Ii + k − 1, j − k + 1 = mk , k= 1, 2, 3}|/ N−d
(3)
Where mk ∈ { −T , −T + 1, …, 0, …, T − 1, T }, k = 1, 2, 3,T is a pre-determined positive integer value, |⋅| denotes the cardinality, the subscript h, v, d and -d represent the horizontal direction, the vertical direction, the main diagonal direction and the minor diagonal direction, and Nh, Nυ, Nd and N−d are the normalization factors associated with the co-occurrences in corresponding directions, respectively. Each co-occurrence matrix in Eq. (3) has (2T + 1)3 elements. In the subsequent experiments, T is empirically set to 1 for making a trade-off between detection accuracy and computational complexity. 2.3. Feature extraction For an NAD-JPEG compressed image, the grid shift corresponding to the first compression may have 63 possible cases but only one real scenario. Since the quality factor that corresponds to the second compression is known for the given JPEG image, motivated by the steganalysis of YASS [9], we can use a JPEG quantizer at the image to quantize all the shifted versions of the image. Due to double quantization artifacts [3,7,9], the third order co-occurrence statistics calculated from the BDCT domain corresponding to the block segmentation in accordance with that of the first compression should exhibit variations between the NAD-JPEG compressed images and the single JPEG compressed ones. It is noted that the luminance channel of a color JPEG image is only considered for feature construction. This is mainly because image chrominance sub-sampling for JPEG compression will introduce interpolation noise in chroma channels. In view of the analysis above, the proposed feature extraction procedure is summarized as follows: 1) Get the quantized BDCT coefficient array I with size M1× N1 and the current quantization table TQF2 of the luminance channel from the head files of the given JPEG image, and then de-compress I to spatial domain. Denote the spatial array as Φ = [Φm, n], where Φm, n represents the (m,n)-th 8 × 8 sub-block in Φ , defined as
Φm, n = D−1 (Im, n ⊗ TQF2) Where, 1 ≤ m ≤ r1, 1 ≤ n ≤ s1, r1 = ⌊M1 8⌋ s1 = ⌊N1 8⌋, operator.
(4)
D−1
models the inverse 8 × 8 block DCT and ⊗ is the Hadamard product
1) Calculate the shifted spatial version of Φ according to a grid shift (x , y ) (x , y ∈ {0, 1, ⋯, 7}) . Divide the resulting shifted spatial array into non-overlapping 8 × 8 blocks, denoted by Ψ x , y = [Ψux,,vy], where the superscript (x, y) denotes the grid shift and the subscript (u, v) is the index of 8 × 8 sub-block. x,y 2) Quantize Ψ x , y with TQF2 to get the quantized BDCT coefficient array Ω x , y = [Ωux,,vy], where Ωu,v can be expressed as
Ωux,,vy = D (Ψux,,vy ⊙ TQF2)
(5)
Where, D models the 8 × 8 block DCT and ⊙ is an entry-by- entry division operator. 1) Round all the elements in Ω x , y and calculate the third order co-occurrences along four directions (denoted by Jhx , y , Jvx , y , Jdx , y and J−xd, y ) by using Eq. (3) to represent the intra-block correlation and sign correlation among adjacent quantized BDCT coefficients. 2) Perform the row block scanning pattern and the column block scanning pattern [10] on Ω x , y to get two arrays, denoted by Θrx , y and Θcx , y , respectively. Calculate the third order co-occurrences of Θrx , y and Θcx , y along vertical direction by using Eq. (3) to represent the inter-block correlation and sign correlation among adjacent coefficients, denoted by Jrvx, y and Jcvx, y , respectively. 3) Calculate the entropies of the third order co-occurrence matrices generated from steps 4) and 5), For a specific grid shift (x , y ) ( x , y ∈ {0, 1, 2, ⋯, 7} ) and specific direction α (α ∈ {h, v, d, −d, rv, cv}) , the resulting feature can be formulated as
Fαx , y = − ∑ ∑ ∑ Jαx , y (i, j, k ) log2 Jαx , y (i, j, k ) i
j
(6)
k
1) Loop through steps 2) to 6) for all the grid shifts and concatenate all these entropies to form the final feature set. The dimension of 3
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Fig. 2. Distributions of the proposed features extracted from the single JPEG compressed Lena image and the NAD-JPEG compressed version for the quality factor pair (a) {QF1, QF2} = {50, 70} and (b) {QF1, QF2} = {50, 90}, respectively.
the final feature set is 6 × 8 × 8 = 384. To preliminarily validate the discriminative ability of the proposed features, Fig. 2 shows the distributions of features extracted from the single JPEG compressed Lena image and the NAD-JPEG compressed version by using the proposed feature extraction procedure for two {QF1,QF2} pairs (i.e., {50,70} and {50,90}). It is observed from Fig. 2 that the constructed feature can effectively distinguish NAD-JPEG compression from single JPEG compression. 3. Experimental results 3.1. Experimental setup In order to evaluate the proposed NAD-JPEG compression detector and to compare it with several existing detectors in various compression scenarios, two image databases widely used in image forensics, i.e. UCID [12] and NRCS [13], are adopted to measure their accuracy. All the original images with TIFF format in the databases above are uncompressed and with the size of 384 × 512 and 1500 × 2100, respectively. In our experiment, 5000 original images are selected from the aforementioned two databases, and the quality factors QF1 and QF2 are selected from 50 to 90 with a step of 10 for evaluation. For a specific {QF1, QF2} pair, the following datasets are constructed: 1) The NAD-JPEG compressed dataset (denoted by ηNAD): JPEG compression with QF1 is first performed on each TIFF image. Then, image patches with three sizes, i.e. 64 × 64, 128 × 128 and 256 × 256 are cropped from each de-compressed image with random grid shifts (x, y) ≠ (0, 0) (x , y ∈ {0, 1, 2, ⋯, 7}) and saved as JPEG format with QF2 to construct ηNAD. 2) The single JPEG compressed dataset (denoted by ηS): Image patches with three sizes are first extracted from each TIFF image, respectively. Then, each image patch is saved in JPEG format with QF2 to construct ηS. Note that each pair of single JPEG compressed image patch and NAD-JPEG compressed image patch has the same image content for the same patch size similar to that in Qu’s [8]. When the datasets above are constructed, 5 × 5×3 = 75 training-testing pairs are prepared for classification. For a specific patch size and a specific {QF1, QF2} pair, there are 5000 NAD-JPEG compressed image patches and 5000 single JPEG compressed image patches in the datasets above. 3.2. Classification For the proposed method, the NAD-JPEG compression detection is considered as a binary classification task. C-SVM [14] with 4
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Table 1 Average Detection Accuracy with Various Values of QF1 and QF2 and Various Patch size. The Values a/b/c/d Represent the Average Detection Accuracy by A) the BACM Detector, B) the IVM Detector, C) the IPM Detector, and D) the proposed Detector, Respectively. The Best Accuracies among the Four Methods Investigated are Highlighted in Bold. (a)
PATCH SIZE OF
64 × 64
QF2 QF1
50
60
70
80
90
50 60 70 80 90
52.60/50.40/50.81/57.02 51.76/50.78/49.98/54.57 51.01/50.20/50.31/52.61 50.41/49.98/50.35/49.77 50.90/50.47/49.53/50.34
51.92/51.37/53.42/70.94 51.46/50.28/52.24/57.82 50.79/50.76/51.86/54.31 50.26/50.34/50.97/51.49 50.26/49.79/50.02/50.30
57.44/52.30/61.97/98.94 53.91/50.74/56.13/83.70 51.91/50.07/51.36/57.91 50.14/50.40/50.18/53.50 50.63/50.07/49.97/50.38
61.42/56.22/70.05/99.73 58.92/54.93/63.02/99.64 55.64/52.97/61.21/96.25 52.03/50.95/52.01/60.65 50.54/50.49/50.19/50.53
67.76/64.28/77.41/99.76 65.61/63.17/72.03/99.74 62.47/60.52/65.01/99.72 58.99/55.84/60.11/99.76 53.48/50.83/50.93/63.89
(b)
PATCH SIZE OF
128 × 128
QF2 QF1
50
60
70
80
90
50 60 70 80 90
52.85/52.92/54.03/66.92 52.06/51.01/51.98/62.18 50.59/50.32/51.39/57.65 50.88/49.72/50.07/52.03 50.12/50.63/49.87/50.48
54.74/54.39/55.88/88.72 53.97/51.88/51.44/67.47 52.75/51.12/50.72/62.15 50.94/50.23/50.61/53.92 50.18/50.32/49.29/50.73
63.47/56.66/68.03/99.84 57.71/55.16/59.98/97.01 53.11/53.16/54.05/69.49 51.66/50.94/50.82/60.19 50.49/50.72/50.01/50.90
71.04/62.46/78.33/99.90 66.25/59.57/70.91/99.89 59.92/55.64/64.59/99.57 53.51/53.09/52.87/73.72 50.22/50.25/52.17/54.33
80.67/73.54/86.96/99.93 77.09/72.63/79.84/99.91 72.88/69.46/78.63/99.90 65.87/62.77/68.65/99.92 55.33/52.78/53.72/79.54
(c)
PATCH SIZE OF
256 × 256
QF2 QF1
50
60
70
80
90
50 60 70 80 90
56.27/57.46/60.06/83.71 53.89/54.88/52.46/77.59 51.56/51.05/51.31/69.55 50.50/50.22/51.03/55.87 50.49/49.70/50.53/50.87
60.27/59.87/64.81/97.83 57.27/57.76/57.98/84.60 53.56/53.63/52.71/77.57 52.20/50.59/51.41/61.26 50.59/49.60/50.31/51.71
71.99/64.71/71.55/99.95 62.66/61.49/63.62/99.59 57.28/57.45/58.03/86.57 53.51/51.76/51.97/76.16 50.17/49.57/50.49/53.17
82.69/71.78/86.93/99.96 77.17/69.50/71.98/99.96 67.50/64.50/69.87/99.87 58.14/57.18/59.34/88.94 51.46/50.75/51.05/61.17
89.67/82.92/94.06/99.98 87.39/81.73/88.64/99.99 83.19/78.73/82.98/99.97 76.46/71.49/72.05/99.97 58.04/54.84/53.99/92.98
radial basis function (RBF) kernel is selected as the classifier. For a specific training-testing condition, 40 % of the positive samples (NAD-JPEG compressed image patches) and 40 % of the negative ones (single JPEG compressed image patches) are randomly picked out to train the SVM, and the remaining samples are used for evaluation. Five-fold cross-validation on the training set is performed to get the optimal kernel parameters of the SVM classifier in the multiplicative grid (C , γ )ε{(2i , 2 j)|i, jεZ , −10 ≤ i, j ≤ 10)} . In the stage of classification, the above training-testing procedure is repeated thirty times to reduce the performance variations caused by random selections of training samples. The average detection accuracy is recorded to evaluate the performance of the proposed method. 3.3. Detection of NAD-JPEG compression To validate the effectiveness of the proposed method, three state-of-the-art methods, i.e., the BACM-based method [4], the IVMbased method [8], and the IPM-based method [5], are utilized for performance comparison on the constructed dataset. For the proposed detector and the BACM detector and the IVM detector, a specific SVM is trained with the extracted features to distinguish the NAD-JPEG compressed image patches from the single JPEG compressed ones. For the IPM detector, the optimal thresholds are achieved by an exhaustive search to identify the presence of NAD-JPEG compression. The average detection accuracies of the proposed detector and other three detectors for three patch sizes are summarized in Table 1 . It is shown from these tables that the patch size and the difference in quality factor between the first and the second compression (i.e. ΔQ=QF2-QF1) have a major influence on the performance of the investigated detectors. The following observation can be made by taking a closer look at these tables: 1) The higher value of ΔQ results in higher detection accuracy. The main reason for this is that the first compression with a lower quality factor will generate more compression artifacts. Meanwhile, it is easier to identify the presence of NAD-JPEG compression when the second compression is executed via a higher quality factor due to the less distortion to the image. 2) For a specific ΔQ, larger patch size leads to better detection performance. Since all these NAD-JPEG compression detectors investigated are based on statistical models, larger patch size results in better statistical performance, which makes the presence of NAD-JPEG compression easier to be captured. 3) Among all these detectors, the proposed detector performs better than other three state-of-the-art detectors in general especially when patch size is small, which indicates that the proposed detector is capable of capturing the traces introduced by NAD-JPEG compression more effectively and is more robust in various JPEG compression scenarios.
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4. Conclusions In this paper, we have proposed a high-order-statistics based scheme to identify the presence of NAD-JPEG compression. Due to double quantization artifacts, statistical features extracted from the neighboring quantized BDCT coefficients corresponding to the block segmentation in accordance with that of the first compression exhibit variations between the NAD-JPEG compressed images and the single JPEG compressed ones, leaving detectable traces. The third order co- occurrence statistics are adopted to characterize three types of correlations of quantized BDCT coefficients for NAD-JPEG compression identification. We have conducted a series of experiments at various compression levels and various patch sizes to evaluate the performance of the algorithms. Experiment results have shown that the proposed method can more reliably identify the presence of NAD-JPEG compression than existing three methods, especially when image patch is small. Future research will focus on the estimation of the quality factor of the first compression for tampering detection and location more intelligently. In addition, this research can also be combined with many disciplines, such as criminal investigation, artificial intelligence [15–18], fault analysis [19–23], and so on. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work is mainly funded by the Natural Science Foundation of Shanghai (grant no. 17ZR1411900), the National Natural Science Foundation of China (grant no. 51705307), the Key Project of Science and Technology Commission of Shanghai Municipality (grant no. 18511101600), the Opening Project of Shanghai Key Laboratory of Integrated Administration Technologies for Information Security (grant no. 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