A generalized ghost detection and segmentation method for double-joint photographic experts group compression

Sepideh Azarianpour; Amir Reza Sadri

doi:10.4103/jmss.JMSS_19_19

₁), the compression history of I can be determined from the difference energy image

Where I (x,y,cc) denotes the intensity of the pixel (x,y) on color channel cc of the image I, in which cc ∈ (R, G, B). The image I_q₂ is the resaved version of image I at quality factor q₂. The above equation would be very sensitive to the image content, meaning that it would be higher in the detailed regions and lower in the smoother regions. To compensate the image content texture, we first calculate the difference in a spatial window and then we normalized the averaged values into interval (0,1), which results in ghost image g using

Where the window size w is typically 16.^[13]

Besides using JPEG ghost, the inconsistencies in quality factor of a double-quantized image can be determined using other techniques. JPEG ghost detection method needs another JPEG quantization to yield I_q₂. However, simpler techniques, for instance, low-pass filtering, window averaging, etc., are able to create image I^̂ similar to I_q₂. As it will be discussed in Section 3, the image I - I^̂ also contains information to separate low- and high-textured parts of the image.

The JPEG ghost detection method of Farid^[13] has the advantage that it works for tampering detection of both high-textured images and low-textured images. However, it still suffers from a number of limitations. One of the fundamental constraints is that this approach only works for C1 (in Section 1). In other words, it does not work for nonaligned DCT grid cases. Second, the method of Farid^[13] needs a manual search for the ghost, instead of an automatic search. As a result, in Farid,^[13] forensic specialist has to make relentless efforts to detect the forged area. As we mentioned in Section 1, a previous literature^[17] has overcome these limitations. Thus, the ideas of Azarian-Pour et al.^[17] are exploited here too.

Proposed Method

The proposed method contains three main steps. In the first and the foremost one, forgery footprints become visible. Tampering details are revealed in this step and they are recognizable with the naked eye, which is known as ghost area. However, to automate the method, in the second step, we extract the precise border of this ghost area throughout a novel segmentation method. In the last step, the classifier assigns the suspicious image to original or tampered group. In other words, in the second and third steps, we just analyze the information given by the first step.

First step: Proposed ghost detection method

To discriminate high-textured regions versus low-textured regions of a given image, first, we separate high-frequency areas and low-frequency ones. The schematic of the first step is illustrated in [Figure 2]. The low-pass filter (LPF) F is applied to image I, yielding Î. Therefore, the image I and its smoothed version, Î, are approximately the same, despite some differences in details. Incidentally, these inconsiderable differences include valuable details for revealing forgery. In this article, we propose eight different smoothing filters and they are compared; the first two filters are

Figure 2: Schematic of the proposed ghost detection method

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Where F₁ and F₂ refer to unweighted and weighted 2D moving average LPFs, described in the spatial domain. The next three filters are described in the frequency domain, by their transfer functions,

These filters, respectively, are fifth-order Butterworth LPF (8), second-order Butterworth LPF (9), and Gaussian LPF (10). The term D (u,v) denotes the distance from the origin of the Fourier transform and D₀= 25 is allocated as the cutoff frequency.

The next three filters originate from discrete wavelet transform which are schematically described in [Figure 3]. First, a 2D wavelet transform is applied to the image. Then, detail bands (H, V, and D) are discarded. Afterward, the reconstruction algorithm (inverse discrete wavelet transform) is applied only to the approximation band. Subsequently, the output will be a smoothed version of image I and at the same size. These filters are numbered as F₆, F₇, and F₈ corresponding to wavelets db1, sym2, and sym8, respectively.

Figure 3: Schematic of low-pass filter F6 using two-dimensional-wavelet decomposition, wavelet type db1. The other two ones, F7 and F8, can be implemented using wavelet types sym2 and sym8, respectively

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We expect that after applying these filters, the low-textured parts of the image are affected much less than the higher quality regions. Hence, the amount of I − Î in each pixel depends on its quality factor. Furthermore, as mentioned in a previous study,^[13] to compensate the image content texture, a spatially averaging and normalizing is also utilized (block diagrams “2D Moving Window Average” and “Normalization” in [Figure 2]. By Substituting I_q2 with I^̂, the equations would be similar to (4) and (5).

Eventually, after normalizing the energy of the difference image, low-textured parts of the image become dark, while higher-quality parts are brighter. In other words, the amount of g is a measure of the quality.

Second step: Proposed multistage segmentation method

In this subsection, we explain our approach for extracting the ghost borders, which is an iterative three-stage algorithm. Then in the next section, segmentation result will be discussed and a classifier decides to assign the image to the original or tampered group.

Our approach for extracting ghost borders is composed of three stages [Figure 4]:

Figure 4: Schematic of the proposed segmentation method

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Stage 1

At first, the ghost image g is partitioned into N nonoverlapped k × k pixel blocks. The effect of parameter k will be discussed later.

Stage 2

The 7D feature vector for each partition is calculated, according to [Table 1]. Image g_i denotes the i^thk × k partition of the image g which is under inspection. The term p_i is the PDF of gray levels of g_i_, which is approximated by the histogram of the image g_i, L is the number of gray levels and j ∈ (1,...,L). Feature numbers 1–4 denote the 1^st–4^th cumulants, that is, average, variance, skewness, and kurtosis.^[26] Feature numbers 5–7 belong to gray-level difference statistics family. They, respectively, represent contrast, angular second moment, and the entropy.^[27]

Table 1: Extracting feature vector for each k × k block

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The term x_i denotes the 7D corresponding feature vector of the i^th partition. The output of this stage will be vector set (x₁, x₂,..., x_N), where N is the total number of partitions.

Stage 3

In this step, the “authenticity label” for each block is obtained using k-means clustering algorithm. The output label would be 1 for singly-quantized or original regions and 0 for doubly quantized or fake regions. The label of the i^th block is denoted by l_i∈ (0, 1). If images I and g are at the size of m × n pixels, then image l will be at the size of

pixels (

denotes the ceiling function). Therefore, it is obvious that the parameter k affects the resolution of the image l.

Choosing parameter k

The parameter k should be chosen in a way that detects the ghost area, as well as maintaining preciseness and resolution. Too great amounts of k result in a low-resolution version of labels [Figure 5]a. It also causes an error in detecting labels. In the case that the forged area is comparatively smaller than block dimensions, the detection error will occur. On the other hand, as depicted in [Figure 5]b, [Figure 5]c, [Figure 5]d, [Figure 5]e, other problems will arise by choosing a small amount of k. The scattering of 0 and 1 labels in the entire image makes the forensics analyzer confused and causes errors in the classification step (the next step of the algorithm). Recalling the image splicing scenario, it is assumed that one part of an image is cut and pasted into another image. Hence, the ideal result of segmentation should have only one connected component. To this end, we develop a new iterative method for choosing the parameter k.

Figure 5: The first row: the results of applying different independent amounts of k, in panel (a), the accuracy of segmentation is very low, as the value of k decreases (panels [b-e]), a more accurate boundary is obtained but scattering and wholes begin to appear. The second row illustrates the procedure of modified k selection. In this approach, as k reduces (transition between panels [f-j]), a higher resolution of the tampered region can be achieved without any wholes and artifacts

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In the first place, k is initialized with a large amount (almost

). In the following iterations, it will be cut in half. At each iteration, segmentation is only applied to the edge blocks. We use the term edge block for each k × k partition, which has at least one adjacent block with a different label, at the previous iteration. Applying the procedure to edge blocks instead of all blocks plays a great role in reducing computational complexity. Furthermore, the labels are not scattered anymore, rather, they are distinctly separate. In this way, the advantages of both cases (large and small amounts of k) are preserved. Moreover, since k has to be cut in half at each iteration, it should be of the form 2^p. [Figure 5]f, [Figure 5]g, [Figure 5]h, [Figure 5]i, [Figure 5]j illustrate the procedure above using the set of parameter k ∈ (64, 32, 16, 8, 4). As it is seen in [Figure 5], it results in a more accurate segmentation in comparison to a noniterative procedure.

Third step: Proposed classification method

After performing the segmentation task, a criterion is required to conclusively confirm or refute the presence of forgery. More distinct segmented regions can be a decisive proof of tampering, while the similarity between two segmented areas invalidates the segmentation result and represents the authenticity of the image. To this end, we will investigate different statistical measures of the distance between two probability distributions, namely Bhattacharyya distance,^[28] Kullback–Leibler divergence,^[28] symmetric Kullback–Leibler divergence,^[28] and Kolmogorov–Smirnov^[13] statistic. In this step, the distance d between two clusters of the image is calculated. Then, by comparing this criterion with a specific threshold “Th,” the algorithm reports the final authenticity evaluation. The larger distance shows an inherent difference between two segmented areas and confirms the presence of forgery. However, in the case that d< Th, it means that no forgery is detected and the segmentation result is unreliable. One-dimensional Bhattacharyya distance between cluster 0 (the ghost segment) and cluster 1 (the rest of the image), with normal gray-level distributions N (μ_0,σ₀²) and N (μ_1,σ₁²) is given by

Here, both regions are assumed to be normally distributed.

Kullback–Leibler divergence and symmetric Kullback–Leibler divergence are defined as

and

Where P₀(u) and P₁(u) are the probability density functions of segments 0 and 1, respectively, which can be estimated by their corresponding histogram.

Kolmogorov–Smirnov statistic is defined as

Where C₀(u) and C₁(u) are the cumulative distribution functions of segments 0 and 1, respectively. The amount of optimal threshold for each distance criterion will be calculated in Section 4.2. Using this optimal threshold and the best LPF, chosen in Section 4.1, the proposed algorithm is briefly illustrated in [Figure 6]. The first row assumes a composite forged photo combined from two original images in a black box. After performing the three steps, a forgery is detected. In the second row, an original image is analyzed, and at the end, its authenticity is approved.

Figure 6: The procedure of the proposed algorithm for forgery detection on a sample tampered image (upper row) and a sample original image (bottom row)

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Simulation Results

For our simulations, we have utilized the following four standard databases, all of them include original shots of landscapes, people, man-made objects, wildlife, monuments, both indoors and outdoors:

Uncompressed Color Image Database (UCID)^[29] contains 1338 uncompressed raw images of size 512 × 384 pixels, in Tagged Image File Format (TIFF), captured by a Minolta Dimage 5 digital color camera, available for download^[30]
McGill Calibrated Color Image Database, also known as CCID,^[31] encompasses 1152 images in nine different categories. These images were taken by two Nikon Coolpix 5700 digital cameras, called “Pippin” and “Merry.” The images in this database are either the original size 1920 × 2560 pixel images, or scaled down versions at 786 × 576 pixels, with both TIFF and JPEG extension, available for download.^[32] We utilize full-size, TIFF format. Moreover, we removed the 56 repeated items from this database, yielding a total of 1096 unique images.
Never-compressed Color Image Database, in this article called NCID,^[33] consists of 5000 original TIFF raw format digital images of size 640 × 480 pixels, lossless true color and never compressed, bit depth of 24, available for download^[34]
CASIA Tampered Image Detection Evaluation Database version 2.0 contains 7491 authentic and 5123 tampered color images. Their size varies from 240 × 160 to 900 × 600 pixels. Both uncompressed and JPEG compressed images with different quality factors exist in this database, available for download.^[35] We ignore the whole tampered set, because we want to monitor the process of image splicing and be aware of their primary quality factors, for further evaluations.

Ultimately, 11704 TIFF and 3221 JPEG authentic images altogether have been exploited, in order to create singly and doubly compressed image sets. According to the image forgery process, as displayed in [Figure 1], JPEG images in different qualities are required to be spliced together. For this purpose, in the first place, all the TIFF images have been compressed in JPEG format, at quality factors of QF = (50, 55., 95), which results in ten different quality sets.

For creating manipulated images, the background is chosen from the group q₁∈ QF and the foreground is chosen from the group q₀∈ QF which is cropped with a random mask and inserted, as the tampered region, in the background. Thus, 100 different spliced sets are constituted, known by pertaining (q₀, q₁) pairs. The crop mask which is employed here is used as the Ground Truth (GT) later, for evaluation of the segmentation results.

All experiments were carried out in MATLAB R2016a using Intel^® Core™ i5-2670QM (3.10GHz) processor and 4GB RAM.

Experimental results of ghost detection and segmentation steps

In addition to the eight smoothing filters defined in Section 3.1, the JPEG recompressor used in a previous study^[13] is utilized here too, for comparing performances. There is no limitation on our proposed filters, but for Farid's method, the two following constraints are necessary:

The parameter of double quantization, q₂, should be almost equal to low-quality factor to discriminate the ghost
The DCT grids of the tampered region of I and the JPEG compressor should be aligned.

Although we have no prior knowledge about q₂ and possible shifting in DCT grids, we use the approaches of Azarian-Pour et al.^[17] in order to overcome these limitations. Ultimately, nine different smoothing filters are compared and the best one is employed for the next section, in which we choose the best distance criterion and analyze the result of the classifier. To this end, 500 forged images are randomly chosen from the manipulated dataset. Each manipulated image is processed by the ghost detection step, using nine different smoothing filters. Afterward, the iterative segmentation method is applied to the ghost output.

In each case by comparing the final segmentation result and GT, the values of true positives (TPs), true negatives (TNs), false positives, and false negatives are obtained. It is obvious that reporting these values for each image or in the average form is not helpful. Instead, we use accuracy, precision, specificity, and sensitivity defined in Theodoridis and Koutroumbas study.^[28]

These criteria are averaged over the 500 above-mentioned images and displayed in [Table 2], along with the average run time in terms of seconds.

Table 2: Average segmentation results for nine different filters

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In the results of [Table 2], the best values of accuracy, specificity, sensitivity, and precision are displayed in boldface. It is seen that the Gaussian LPF shows the best performance overall. Thus, for further simulations, F₅(u,v) = e^{−D2(u, v)/2D02}, D₀= 25, is used as the smoothing filter. [Figure 7] shows two examples of segmentation of the forged area, using F₅ as the smoothing filter.

Figure 7: Final segmentation results on two different forged images. (a) Spliced image using quality factor 85 (forged area) and 90 (background image). (b) Green area: Singly compressed, red area: doubly compressed. (c) Spiced image using 95 (forged area) and 85 (background image). (d) Green area: singly compressed, red area: doubly compressed

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Experimental results of the classification step

The final classification step is a simple thresholding on the distance measure. Thus, the values of the threshold, Th, for each type of distance must be determined. For this purpose, we applied the steps 1 and 2 of the proposed method on 10,000 original and 10,000 tampered images. As a result, the segmented area is obtained. Then, using formulae (11–14), the distance between two areas is calculated. We set Th in a way which minimizes the classification error rate on this set of images. It occurs when P (e|Original) = P (e|Forged). The values of optimum Th and the minimum resulted error rate are displayed in [Table 3].

Table 3: Optimum threshold and minimum error rate for each distance measure

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Due to the significant performance and accuracy of Kolmogorov–Smirnov statistic [Table 3], the classification task is performed by using this criterion.

For reporting the final results, a comprehensive simulation is performed. First, 10,000 authentic images are randomly chosen from the ten different quality groups, each one containing 1000 images. On the other hand, 10,000 tampered images are chosen from the 10 × 10 = 100 different quality groups, each one containing 100 images. The result of simulation is reported in [Table 4]. For the authentic images, the percentage of true detection (TN rate) versus quality factor is displayed and for the tampered ones, the percentage of true detection (TP rate) versus both q₀ and q₁ is depicted.

Table 4: Percentage of true detection rate, for different quality images

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Moreover, for better illustration, the sensitivity of the tampered images is plotted versus △ q = |q₀− q₁| in [Figure 8]. At the end, the F₁ score defined Theodoridis and Koutroumbas^[28] as

Figure 8: Sensitivity of composite forged images versus △ q = |q₀− q₁|

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is calculated, respectively, for UCID, NCID, CCID, and CASIA databases. Actually, F₁ is a measure of the accuracy of a test. It considers both precision and sensitivity of the test to compute the score.

The final results of our proposed method are shown in [Table 5], compared to the six state-of-the-art methods. The results of Li's method,^[36] Milani's method,^[37] Dong's method,^[38] and Taimori's method^[39] are previously quoted.^[39] In summary, the method used in a previous study^[36] is based on extracting alternate current (AC) mode features from the first digit of DCT coefficients which is inspired by Benford's law. Milani etal. used a highly accurate approach based on the same feature set in Milani et al.,^[37] using Markov transition probability matrix. Dong et al.^[38] used quantized AC modes based on texture features. They exploited PCA algorithm for dimensionality reduction and SVM for training the classifier. The method of Taimori et al.^[39] also used PCA and SVM accordingly for feature selection and classification. We also add the results of Azarian-Pour et al.,^[17] which is based on a similar method to Farid^[13] and is modified to be compatible with both aligned and nonaligned DCT grids. Finally, the performance of Yang et al.^[23] has been compared which is based on the DCT coefficients with the same frequency which yield the direction effect. Again PCA and SVM are exploited for feature selection and classification. As it can be seen in [Table 5], in most cases, our method outperforms other methods, more particularly, in terms of sensitivity.

Table 5: Performance metrics of our proposed method, compared to five other methods

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Conclusion

In composite tampered images, often discrepancies in different parts of the image could lead forensic specialists to detect forgery. Low-quality factor in the JPEG compression scheme distinctly affects high-frequency texture in the image. Tracing these inconsistencies, we are able to estimate which regions do not originally belong to the image under inspection. In this article, we proposed a fully automatic method for detecting JPEG recompression based on separating low-frequency parts from high-frequency ones. It has been demonstrated that after applying a LPF, the low-textured parts of the image are affected less than high-quality regions. Hence, the difference (ghost image) in each pixel reveals inconsistencies in quality factor. Motivated by this observation, the new algorithm provides a procedure for constructing a method for forensic analyses of digital images which does not fail in the not aligned DCT grids cases. We also proposed a new segmentation method. Although we have used it for ghost detection purpose, this technique can be applied to other fields for performing segmentation tasks.

Financial support and sponsorship

None.

Conflicts of interest

There are no conflicts of interest.

Biographies

Sepideh Azarianpour is a 2^nd year PhD student in biomedical engineering department at Case Western Reserve University, Ohio, USA. She joined the Center of Computational Imaging and Personalized Diagnostics (CCIPD) in 2018. She earned her M.Sc. degree in electrical engineering at Sharif University of Technology, Tehran, Iran, and her B.Sc. degree in electrical engineering at Isfahan University of Technology, Isfahan, Iran. She pursues her research in developing, evaluating and applying novel quantitative methods for identifying sub-visual image features and employing them in different artificial intelligence applications.

Email: [email protected]

Amir Reza Sadri was born in Isfahan, Iran. He received the B.Sc. degree in electrical engineering from the Department of Electrical Engineering, University of Kashan, Kashan, Iran and the M.Sc. degree in electrical engineering from Isfahan University of Technology, Isfahan, Iran, in 2012. His research interests include medical image analysis, system identification and software developing

Email: [email protected]

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Figures

[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8]

Tables

[Table 1], [Table 2], [Table 3], [Table 4], [Table 5]