Anti-forensics of contrast enhancement in digital ... - Semantic Scholar
Anti-Forensics of Contrast Enhancement in Digital Images Gang Cao, Yao Zhao, Rongrong Ni, Huawei Tian Institute of Information Science, Beijing Jiaotong University Beijing 100044, China
{06112056, yzhao, rrni, 06120416}@bjtu.edu.cn ABSTRACT
methods concentrate on identifying the content-changing image manipulations including image splicing [1~2] and copy-move [3], which reshape the image content visually and semantically. In the second category, content-preserving image manipulations such as resampling [4, 5], compression [6], contrast enhancement [7~9], blurring [10], sharpening [11] and median filtering [12, 13] are detected or estimated passively [14]. Besides the wide application in the general image processing pipeline, the content-preserving manipulations are often used to conceal visual tampering trail and destroy the forensically significant statistical fingerprints. As a result, blind detection of the content-preserving operations is still significant. Recently, the blind detection and estimation of image contrast enhancement have been concerned extensively. In [7, 8], the blind forensic algorithms for detecting the globally and locally applied contrast enhancement have been proposed. They perform contrast enhancement detection by seeking out unique peak-gap artifacts introduced into an image’s histogram. In the recent paper [9], the authors propose an iterative algorithm to jointly estimate the contrast enhancement mapping used to modify an image and the pixel value histogram of the unenhanced image.
The blind detection of contrast enhancement in digital images has attracted much attention of the forensic analyzers. In this paper, we propose new variants of contrast enhancement operators which are undetectable by the existing contrast enhancement detectors based on the peak-gap artifacts of the pixel graylevel histogram. Local random dithering is introduced into the design of contrast enhancement mapping for removing such artifacts. Effectiveness of the proposed anti-forensic scheme is validated by experimental results on a large image database for various parameter settings. Both detectability and the resulting image quality are evaluated via comparison with the traditional contrast enhancement. The developed anti-forensic techniques could verify the reliability of existing contrast enhancement forensic tools against sophisticated attackers and serve as the targets for developing more reliable and secure forensic techniques.
Categories and Subject Descriptors
I.4 [Image Processing]: Miscellaneous
In contrast with cryptography, multimedia forensics remains an inexact new science without strict security proofs. Although the existing forensic tools are good at uncovering naive manipulations in the scenario without attacks, there is a lack of awareness on their behavior in the practical application. Because little is known about the reliability of forensic techniques against a sophisticated counterfeiter, who is aware of the techniques in detail [15]. Antiforensic is just the technique employed by an image forger to hide or remove the forensically significant manipulation fingerprints, with the aim to deceive the forensic detectors. To the best of our knowledge, currently there are only three anti-forensic techniques: undetectable image resampling [15], synthesis of color filter array pattern [16] and anti-forensic of JPEG compression [17].
General Terms Security.
Keywords
Anti-forensics, digital image forensics, forgery detection, contrast enhancement, undetectable contrast enhancement.
1. INTRODUCTION
A wide variety of multimedia editing softwares, both commercial and open source, are currently available to every computer user. The facility and powerful editing functionality of such softwares makes digital image manipulation become easy and frequent. So the originality, integrity and even authenticity of digital images may suffer destruction. To recover the human’s trust on digital image data, there is an increasing need for developing techniques to detect digital image manipulation in the manner of blind and passive. Image manipulation forensics is just such a technique.
In this paper, we present counter-forensic methods in the form of targeted attacks against the state-of-the-art contrast enhancement forensic algorithms, which have been proposed by M. Stamm and K. J. Ray Liu [7~9]. Local random dithering is introduced into the design of pixel value mapping for removing the histogram peakgap artifacts. Simultaneously, the same visual enhancement effect as that of traditional contrast enhancement is still be preserved. Such an integrated tamper hiding method can be easily tuned to the style of post-processing attack by adding random noise onto the traditional contrast-enhanced image.
In general, prior works on digital image manipulation forensics can be labeled into two categories. In the first category, forensics
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The rest of this paper is organized as follows. Section 2 briefly recalls the basics of contrast enhancement manipulation and the existing contrast enhancement forensics algorithms, followed by the proposed anti-forensic algorithms in Section 3. Performance evaluation results of the proposed attacks are reported in Section 4. Finally we draw the conclusions in Section 5.
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Figure 1. Left: unaltered image and its two gamma correction versions; Right: corresponding histogram of each image.
2. FORENSIC DETECTON OF CONTRAST ENHANCEMENT
the enhanced image can be expressed by the unaltered image’s pixel value histogram hX(x). That is,
hY ( y ) = ∑ hX ( x) l (m( x) = y )
In the prior works [7~9], blind forensic algorithms for detecting and estimating contrast enhancement on digital images have been proposed. In this section, we review such state-of-the-art contrast enhancement detectors.
x∈Ω
where l(·) denotes the indicator function. This equation indicates that each value of hY must equal either a single value of hX, a sum of distinct hX values, or zero. As a consequence, impulsive peaks would occur in hY at y values to which multiple x values were mapped. Similarly, gaps will occur in hY at y values to which no x values were mapped [9]. Such peak and gap artifacts, which can be seen clearly in Fig. 3, would serve as contrast enhancement fingerprints used to identify and estimate contrast enhancement.
Generally, the essence of contrast enhancement manipulation is to apply nonlinear mapping on the pixel values of a digital image. Let Ω = {0, 1, . . . , 255} denote the set of allowable pixel values, each pixel value x∈ Ω in the unaltered image is mapped to a pixel value y∈ Ω in the contrast-enhanced image by the mapping function m, such that
y = m( x ) .
(2)
In ref. [7], the authors exploit the fact that the Fourier transform of an unaltered image’s histogram hX should be strongly low pass, while the sudden peaks and gaps introduced into hY result in a high frequency component. The contrast enhancement detection algorithm proposed in [7] is summarized as follows:
(1)
In practice, m is usually monotonically increasing. It might be gamma correction mapping, namely power law transformation, ‘S’ mapping or other nonstandard form of mapping.
1). Obtain the image’s histogram h(x).
The histogram of an unaltered image hX(x) typically conforms to a smooth envelope. This phenomenon could be caused by many factors, such as CFA interpolation, complex lighting and shading environments, electronic noise in CCD imaging sensors, and the observation that a continuum of colors exist in most real world scenes [9]. However, because the contrast enhancement operation itself alters the pixel values, the pixel value histogram will be affected correspondingly. The histogram hY(y) of pixel values in
2). Calculate g(x) as follows,
g ( x ) = p ( x ) ⋅ h( x )
(3)
where p(x) is a pinch off function for combating the false high frequency effect, which is caused by the high end and low end saturated images.
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Figure 2. Illustrative graph for the graylevel histogram gap (i.e., x = k) removal. (a) Distribution of the primarily mapped values y0 before and after being locally dithered. Here, the pixel number is satisfied from an example image. (b) Local graylevel histogram of the image processed by traditional contrast enhancement and the proposed dithering-based contrast enhancement.
against previous contrast enhancement forensic algorithms [7~9]. The objective of contrast enhancement hiding attack is to make false negative error, or miss, which occurs when the manipulated image is wrongly identified as unaltered image. The regenerated contrast-enhanced images are expected to escape the detection of forensic detectors and keep visually transparent. The transparency requires that the new contrast-enhanced image provides with the same visual effect as that of the traditional contrast enhancement manipulation.
3). Transform g(x) to the Fourier frequency domain, G (ω ) , then obtain the high frequency measure F according to
F=
1 N
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Here the cutoff function β (ω ) used to compute the weight of high frequency component is simply designated as
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From the formula (13), we can find that each bin of the resulting histogram is the weighted summation of all other neighboring bins. Such weight is in inverse proportion to the distance between bins. Consequently, the gap bin hY ( k ) can be filled up and keep smooth with neighboring bins, which can be seen from Fig. 2(b).
(10)
3.2 Postprocessing Attack by Adding Noise
The attack based on the new contrast enhancement mapping in Eq. (9) belongs to the type of integrated. However, it could be easily tuned to the type of postprocessing if the local random dithering acts on the traditionally contrast-enhanced image. That is,
respectively. Without loss of generality, variance of the dithering noise’s distribution can be assigned as
if
+∞
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where i ∈ , j ∈
The extended sets, which include not only the peaks or gaps but also their neighboring pixel values, are denoted by Ψ 'p and Ψ 'g
⎪⎧σ σx = ⎨ 1 ⎪⎩σ 2
(12)
y = round [ m ( x) + nx ] .
(11)
(14)
Here, m(x): Ω → Ω is the same as that defined in the integrated attack. It can also be taken as the traditional contrast enhancement. In fact, nx is just the dithering noise added to the traditionally enhanced image. For attackers, if the employed mapping function has been known previously, nx can be designated as that in the integrated attack. If not, in the case of unknowing the employed mapping function, both the potential peak and gap set have to be searched by applying a simple and strict threshold-based detector. Peaks are identified as certain times greater than the local average magnitude, while gaps are located as times smaller.
where σ 1 and σ 2 are the two selected experiential values and it is essential to make sure that σ 1 ≥ σ 2 . There exists an inherent tradeoff among the dithering intensity, artifacts removal and visual quality. Intenser dithering signifies the better effect for removing histogram peak-gap artifacts, but inferior visual enhancement would be generated comparing with the traditional contrast enhancement. It should be mentioned that nx can also be assigned as a constant, which is invariant with the original pixel value x. In such a scenario, a satisfying but maybe not optimal tradeoff between the peak-gap artifacts removal and the transparency preservation can still be achieved.
As comparing with the integrated attack, the difference for the postprocessing attack is just that the primarily mapped values turn to be integers. Resultingly, such postprocessing attack can also remove the peak-gap artifacts successfully while preserving high enough visual quality.
Next, the reason for successfully removing the peak-gap artifacts by local dithering will be investigated initially. Without loss of generality, we focus on the removal of a specific gap bin, which is illustrated in Fig. 2. Histogram statistic of the primarily mapped values around k ( k∈ Ψ g ) is shown in Fig. 2(a). In the traditional
4. QUANTITATIVE EVALUATION 4.1 Test Data
contrast enhancement, a gap bin would be formed at k because no primarily mapped values fall into the range [ k − 12 , k + 12 ) , which
We compile a database of 693 unaltered photograph images for a quantitative evaluation of the proposed attacks against contrast enhancement forensics. Such images cover on a variety of topics including natural scenes and man-made objects, both indoors and outdoors. These images are captured by several different cameras under default setting, stored in JPEG format and with size from
can also be observed in Fig. 2(b). However, if the local random dithering is introduced onto the primarily mapped values, the mapped values would spread by the form of Gaussian distribution. Specially, suppose the smallest primarily-mapped value above k is
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for evaluating the capability of our proposed attacks to hide the traces of contrast enhancement operation.
1200×900 pixels to 2832×2128 pixels. As in the previous works [7, 8], the green color layer of each photo image is used to form a set of unaltered grayscale images. Correspondingly, the contrastenhanced grayscale images are created by applying the power law transformation, namely gamma correction: γ ⎡ ⎛ x ⎞ ⎤ m ( x) = round ⎢ 255 ⎜ ⎟ ⎥ ⎝ 255 ⎠ ⎦⎥ ⎣⎢
4.4 Quantitative Evaluation of Attacks
To assess the dithering-based integrated attack, we perform the new contrast enhancement on images of the test set according to Eq. (9). Then the generated enhanced images would be detected by the previously trained detector. To ensure the low-complexity of new contrast enhancement operators, we tentatively simplify the selection of dithering noise’s variance and set σ 1 = σ 2 =1 in the following experiments. Even in such a setting, the proposed attacks are to be verified much effective. It should be pointed out that the refined tuning of σ values must be able to improve the attacks’ effect to some extent, at the cost of increasing algorithm complexity. Smaller σ values would fail to remove the histogram peak-gap artifacts while larger values degrade image quality.
(15)
where γ value ranges from 0.5 to 2.0. Additionally, each unaltered image is subjected to S mapping, which is a nonstandard contrast enhancement transformation and displayed in Fig. 3(a).
4.2 Performance Metrics
The performance metrics for the quantitative evaluation of our proposed attacks are twofold. Firstly, the most relevant criterion is the undetectability of the proposed contrast enhancement operator. Contrast-enhanced and unaltered images are labeled as positive (P) and negative (N) samples, respectively. With regard to detection results, we would report true positive rates (TP, the fraction of correctly detected contrast-enhanced images) under different false positive rates (FP, the fraction of incorrectly classified unaltered images). Smaller TP value signifies superior performance for the proposed attacks. Note that the 693 unaltered images are divided into two sets: 1) training set, which is consist of 347 randomly chosen images; 2) test set, including the remaining 346 images. The training set is used to determine the decision threshold τ of contrast enhancement detector. We determined τ empirically for different false positive rate, FP0, by applying the detector to all unaltered images in the training set and their traditional contrast enhancement versions. The test set is employed to evaluate the performance of basic detection schemes and our proposed attacks.
The high frequency metric F for each enhanced image is shown in Fig. 4(b). Such feature values happen to fall into the range of unaltered images, which reveals that the enhanced and unaltered images are not distinguishable. The detection results are shown in Fig. 5(a)~(b). Comparing with the baseline results, much lower detection rate is gained and adjacent to random guess. That just proves the undetectability of the proposed contrast enhancement based on integrated local dithering. With respect to visual quality, Fig. 5(c) reports PSNR results to measure the visual discrepancy between dithering-based enhanced images and the corresponding traditionally enhanced ones. On the average, PSNR for gamma correction and ‘S’ mapping achieve as highly as 46.7 dB and 47.5 dB, respectively. Good transparency can be got by the ditheringbased contrast enhancement. In the same way, the experiments for assessing the postprocessing type of attack are also done. The detection results are shown in Fig. 6. It shows that the contrast enhancement based on adding noise is difficult to be detected. In comparison with the contrast enhancement based on integrated dithering, higher detection ratio occurs for gamma correction γ = 1.2 ~ 2.0 and ‘S’ mapping but is still adjacent to random guess. Besides, the corresponding PSNR metric keeps above 46 dB. Such results can verify the reliability of the postprocessing attack based on adding noise.
Any attack algorithm against image manipulation forensics should be assessed not only by undetectability, but also by the amount of image degradation relative to the traditional manipulated version. The common image-quality metric PSNR is utilized to assess the visual impact of the proposed contrast enhancement operators. Specifically, PSNR between the new enhanced image and that without dithering is measured. We have noted that other metric such as wPSNR could also be adopted alternatively [15]. Since PSNR metric is prone to reflect the objective discrepancy, it will be priorly used in the following experiments.
Both images and histograms for different contrast enhancement operations on an example image are plotted in Fig. 7. Histograms of the images, which are enhanced by the integrated ditheringbased contrast enhancement, are smooth enough to resemble those of traditional contrast enhancement operations. In conclusion, the successfulness of the two proposed attacks against the existing contrast enhancement forensic techniques can be verified by both the low detection performance and high PSNR metric.
4.3 Baseline Detection Results
To verify the validity of original contrast enhancement detection schemes [7~8], the detection is performed on 346 images of the test set and their different contrast-enhanced versions. The cutoff parameter in Eq. (5) takes c = 7π / 8 , which is adopted in [7~8]. The high frequency metric F computed from each test sample is shown in Fig. 4(a). We can find that feature values of enhanced images are much higher than those of unaltered ones, respectively distributing in the range of 1000~10000 and 30~100.
4.5 Application to Forgery Making
Detection results for the locally applied contrast enhancement on practical forgery images are shown in Fig. 8. The F-Map records the high frequency metric of each 200×200 unoverlapped image block. As shown in Fig. 8(a), the untouched forgery image is spliced by two photos. However, contrast enhancement is needed to be employed due to the mismatching of color contrast between the ‘gate’ and ‘wall’ regions.
Detection results for traditional contrast enhancement operations are reported in Fig. 3(b). We can see that the contrast-enhanced images have been classified accurately. The detection algorithm performs extremely well against all gamma values and the ‘S’ mapping. In each case, TP exceeds 0.99 when FP0≥0.07. Such results confirm the much reliable detection for a wide range of operation parameters. As a result, Fig. 3(b) may serve as reference
If the traditional contrast enhancement is done, the computed FMap would present obvious inconsistency. As shown in subfigure
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(c) and (d), metric values on the enhanced region, namely ‘gate’ region, are much higher than those on the other regions. In terms of such abnormity, the employed traditional contrast enhancement would be detected.
International Conf. on Acoustics, Speech and Signal Processing, Taipei, 2009. [4] A. C. Popescu and H. Farid, “Exposing digital forgeries by detecting traces of resampling,” IEEE Trans. on Signal Processing, vol. 53, no. 2, pp.758-767, 2005.
On the contrary, if the dithering-based contrast enhancement is performed, the computed F-Map would behave as the untouched forgery image. That can be seen from subfigure (b) and (e), where low and continuous F values distribute on the whole image region. Consequently, the dithering-based contrast enhancement can’t be detected by the previous forensics methods. In such a scenario, PSNR between the retouched forgery image and the traditionally enhanced image can still be gained as highly as 56.6 dB. From such illustrative results, it can be concluded that the ditheringbased contrast enhancement can be used to create image forgeries which couldn’t be detected by the locally contrast enhancement forensic detector [8].
[5] B. Mahdian and S. Saic, “Blind authentication using periodic properties of interpolation,” IEEE Trans. on Information Forensics and Security, vol. 3, no. 3, pp.529–538, 2008. [6] Z. Fan and R. L. Queiroz, “Identification of bitmap compression history: JPEG detection and quantizer estimation,” IEEE Trans. on Image Processing, vol. 12, no. 2, pp. 230– 235, 2003. [7] M. Stamm and K. J. R. Liu, “Blind forensics of contrast enhancement in digital images,” in International Conf. on Image Processing, San Diego, 2008. [8] M. Stamm and K. J. R. Liu, “Forensic detection of image tampering using intrinsic statistical fingerprints in histograms,” in Proc. APSIPA Annual Summit and Conference, Sapporo, 2009.
5. CONCLUSION
As targeted anti-forensic techniques, two kinds of untraditional contrast enhancement methods have been proposed as targeted attacks against the state-of-the-art contrast enhancement forensic algorithms. In order to remove the histogram peak-gap artifacts, local random dithering is integrated into the design of contrast enhancement mapping. The histogram of the resulting enhanced image, which is subjected to the integrated attack, is proved to be smooth by brief theoretical reasoning and illustrative simulation results. The postprocessing type of attack is proposed by adding noise to the image enhanced by traditional contrast enhancement operations. Such an attack method can be applied in the case of unknowing the primary mapping function.
[9] M. Stamm and K. J. R. Liu, “Forensic estimation and reconstruction of a contrast enhancement mapping,” in International Conf. on Acoustics, Speech and Signal Processing, Dallas, Texas, USA, 2010. [10] D. Hsiao and S. Pei, “Detecting digital tampering by blur estimation,” 1st International Workshop on Systematic Approaches to Digital Forensic Engineering, Washington, 2005. [11] G. Cao, Y. Zhao and R. Ni, “Detection of image sharpening based on histogram aberration and ringing artifacts,” in International Conf. on Multimedia and Expo, New York, 2009.
Lastly, the two proposed anti-forensic schemes are justified by plentiful experimental results on a large digital photograph image database for various parameter settings. Both undetectability and excellent visual quality have been manifested by comparing the test results with traditional contrast enhancement manipulations. The developed anti-forensic techniques examine the reliability of existing contrast enhancement forensic tools and could serve as targets for developing more secure forensic techniques.
[12] M. Kirchner and J. Fridrich, “On detection of median filtering in digital images,” SPIE Electronic Imaging: Security, Steganography, and Watermarking of Multimedia Contents, pp. 754110-754110-12, San Jose, CA, USA, 2010. [13] G. Cao, Y. Zhao and R. Ni, “Forensic detection of median filtering in digital images,” in International Conf. on Multimedia and Expo, Singapore, 2010.
6. ACKNOWLEDGMENTS
This paper is supported in part by National 973 program (No. 20 06CB303104), National Natural Science Foundation of China (No. 60702013, No. 60776794), Beijing Natural Science Foundation (No. 4073038).
[14] W.-H. Chuang, A. Swaminathan and M. Wu, “Tampering identification using empirical frequency response,” in International Conf. on Acoustics, Speech and Signal Processing, Taipei, 2009.
7. REFERENCES
[15] M. Kirchner and R. Böhme, “Hiding traces of resampling in digital images,” IEEE Trans. on Information Forensics and Security, vol. 3, no. 4, pp.582-592, 2008.
[1] Y.-F. Hsu and S.-F. Chang, “Image splicing detection using camera response function consistency and automatic segmentation,” in International Conf. on Multimedia and Expo, Beijing, 2007.
[16] M. Kirchner and R. Böhme, “Synthesis of color filter array pattern in digital images,” in Proc. SPIE-IS&T Electronic Imaging: Media Forensics and Security, Feb. 2009, vol. 7254.
[2] W. Chen, Y. Q. Shi and W. Su, “Image splicing detection using 2-D phase congruency and statistical moments of characteristic function,” SPIE Electronic Imaging: Security, Steganography, and Watermarking of Multimedia Contents, San Jose, CA, USA, 2007.
[17] M. Stamm, S. Tjoa, W. S. Lin and K. J. Ray Liu, “Antiforensic of JPEG compression,” in International Conf. on Acoustics, Speech and Signal Processing, pp. 1694-1697, Dallas, Texas, USA, 2010.
[3] S. Bayram, H. T. Sencar and N. Memon, “An efficient and robust method for detecting copy-move forgery,” in
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Figure 7. Detect contrast enhancement on an example image. The first column shows the original image and the images enhanced by traditional contrast enhancement. The third column shows the images enhanced by the integrated dithering-based contrast enhancement. Histogram and high frequency metric of each image are displayed adjacently on the right side.
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(d)
(e) Figure 8. Detect locally applied contrast enhancement on a forgery image. (a) The untouched spliced image. The middle ‘gate’ and bilateral ‘wall’ are cut from two different photos and resized. (b) F -Map for each 200×200 unoverlapped block of (a). (c) The spliced image retouched by traditional gamma correction γ =1.5 on the ‘gate’ region of (a). (d) F -Map of (c). (e) F -Map of the spliced image which is retouched by the integrated dithering-based contrast enhancement on the ‘gate’ region of (a). PSNR between this spliced image and (c) is 56.6 dB.
34
{06112056, yzhao, rrni, 06120416}@bjtu.edu.cn ABSTRACT
methods concentrate on identifying the content-changing image manipulations including image splicing [1~2] and copy-move [3], which reshape the image content visually and semantically. In the second category, content-preserving image manipulations such as resampling [4, 5], compression [6], contrast enhancement [7~9], blurring [10], sharpening [11] and median filtering [12, 13] are detected or estimated passively [14]. Besides the wide application in the general image processing pipeline, the content-preserving manipulations are often used to conceal visual tampering trail and destroy the forensically significant statistical fingerprints. As a result, blind detection of the content-preserving operations is still significant. Recently, the blind detection and estimation of image contrast enhancement have been concerned extensively. In [7, 8], the blind forensic algorithms for detecting the globally and locally applied contrast enhancement have been proposed. They perform contrast enhancement detection by seeking out unique peak-gap artifacts introduced into an image’s histogram. In the recent paper [9], the authors propose an iterative algorithm to jointly estimate the contrast enhancement mapping used to modify an image and the pixel value histogram of the unenhanced image.
The blind detection of contrast enhancement in digital images has attracted much attention of the forensic analyzers. In this paper, we propose new variants of contrast enhancement operators which are undetectable by the existing contrast enhancement detectors based on the peak-gap artifacts of the pixel graylevel histogram. Local random dithering is introduced into the design of contrast enhancement mapping for removing such artifacts. Effectiveness of the proposed anti-forensic scheme is validated by experimental results on a large image database for various parameter settings. Both detectability and the resulting image quality are evaluated via comparison with the traditional contrast enhancement. The developed anti-forensic techniques could verify the reliability of existing contrast enhancement forensic tools against sophisticated attackers and serve as the targets for developing more reliable and secure forensic techniques.
Categories and Subject Descriptors
I.4 [Image Processing]: Miscellaneous
In contrast with cryptography, multimedia forensics remains an inexact new science without strict security proofs. Although the existing forensic tools are good at uncovering naive manipulations in the scenario without attacks, there is a lack of awareness on their behavior in the practical application. Because little is known about the reliability of forensic techniques against a sophisticated counterfeiter, who is aware of the techniques in detail [15]. Antiforensic is just the technique employed by an image forger to hide or remove the forensically significant manipulation fingerprints, with the aim to deceive the forensic detectors. To the best of our knowledge, currently there are only three anti-forensic techniques: undetectable image resampling [15], synthesis of color filter array pattern [16] and anti-forensic of JPEG compression [17].
General Terms Security.
Keywords
Anti-forensics, digital image forensics, forgery detection, contrast enhancement, undetectable contrast enhancement.
1. INTRODUCTION
A wide variety of multimedia editing softwares, both commercial and open source, are currently available to every computer user. The facility and powerful editing functionality of such softwares makes digital image manipulation become easy and frequent. So the originality, integrity and even authenticity of digital images may suffer destruction. To recover the human’s trust on digital image data, there is an increasing need for developing techniques to detect digital image manipulation in the manner of blind and passive. Image manipulation forensics is just such a technique.
In this paper, we present counter-forensic methods in the form of targeted attacks against the state-of-the-art contrast enhancement forensic algorithms, which have been proposed by M. Stamm and K. J. Ray Liu [7~9]. Local random dithering is introduced into the design of pixel value mapping for removing the histogram peakgap artifacts. Simultaneously, the same visual enhancement effect as that of traditional contrast enhancement is still be preserved. Such an integrated tamper hiding method can be easily tuned to the style of post-processing attack by adding random noise onto the traditional contrast-enhanced image.
In general, prior works on digital image manipulation forensics can be labeled into two categories. In the first category, forensics
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The rest of this paper is organized as follows. Section 2 briefly recalls the basics of contrast enhancement manipulation and the existing contrast enhancement forensics algorithms, followed by the proposed anti-forensic algorithms in Section 3. Performance evaluation results of the proposed attacks are reported in Section 4. Finally we draw the conclusions in Section 5.
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Figure 1. Left: unaltered image and its two gamma correction versions; Right: corresponding histogram of each image.
2. FORENSIC DETECTON OF CONTRAST ENHANCEMENT
the enhanced image can be expressed by the unaltered image’s pixel value histogram hX(x). That is,
hY ( y ) = ∑ hX ( x) l (m( x) = y )
In the prior works [7~9], blind forensic algorithms for detecting and estimating contrast enhancement on digital images have been proposed. In this section, we review such state-of-the-art contrast enhancement detectors.
x∈Ω
where l(·) denotes the indicator function. This equation indicates that each value of hY must equal either a single value of hX, a sum of distinct hX values, or zero. As a consequence, impulsive peaks would occur in hY at y values to which multiple x values were mapped. Similarly, gaps will occur in hY at y values to which no x values were mapped [9]. Such peak and gap artifacts, which can be seen clearly in Fig. 3, would serve as contrast enhancement fingerprints used to identify and estimate contrast enhancement.
Generally, the essence of contrast enhancement manipulation is to apply nonlinear mapping on the pixel values of a digital image. Let Ω = {0, 1, . . . , 255} denote the set of allowable pixel values, each pixel value x∈ Ω in the unaltered image is mapped to a pixel value y∈ Ω in the contrast-enhanced image by the mapping function m, such that
y = m( x ) .
(2)
In ref. [7], the authors exploit the fact that the Fourier transform of an unaltered image’s histogram hX should be strongly low pass, while the sudden peaks and gaps introduced into hY result in a high frequency component. The contrast enhancement detection algorithm proposed in [7] is summarized as follows:
(1)
In practice, m is usually monotonically increasing. It might be gamma correction mapping, namely power law transformation, ‘S’ mapping or other nonstandard form of mapping.
1). Obtain the image’s histogram h(x).
The histogram of an unaltered image hX(x) typically conforms to a smooth envelope. This phenomenon could be caused by many factors, such as CFA interpolation, complex lighting and shading environments, electronic noise in CCD imaging sensors, and the observation that a continuum of colors exist in most real world scenes [9]. However, because the contrast enhancement operation itself alters the pixel values, the pixel value histogram will be affected correspondingly. The histogram hY(y) of pixel values in
2). Calculate g(x) as follows,
g ( x ) = p ( x ) ⋅ h( x )
(3)
where p(x) is a pinch off function for combating the false high frequency effect, which is caused by the high end and low end saturated images.
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Figure 2. Illustrative graph for the graylevel histogram gap (i.e., x = k) removal. (a) Distribution of the primarily mapped values y0 before and after being locally dithered. Here, the pixel number is satisfied from an example image. (b) Local graylevel histogram of the image processed by traditional contrast enhancement and the proposed dithering-based contrast enhancement.
against previous contrast enhancement forensic algorithms [7~9]. The objective of contrast enhancement hiding attack is to make false negative error, or miss, which occurs when the manipulated image is wrongly identified as unaltered image. The regenerated contrast-enhanced images are expected to escape the detection of forensic detectors and keep visually transparent. The transparency requires that the new contrast-enhanced image provides with the same visual effect as that of the traditional contrast enhancement manipulation.
3). Transform g(x) to the Fourier frequency domain, G (ω ) , then obtain the high frequency measure F according to
F=
1 N
β (ω )G (ω ) . ∑ ω
(4)
Here the cutoff function β (ω ) used to compute the weight of high frequency component is simply designated as
⎧⎪ 1 ⎪⎩ 0
β (ω ) = ⎨
ω ≥c ω 1 ⎬ ⎭
∑
⎫ l ( y0 ∈ [ y − 12 , y + 12 )) = 0 ⎬ . ⎭
x∈Ω
x∈Ω
hY (k + i ) =
round [ m0 ( x) ] ∈ {Ψ 'p ∪ Ψ 'g }
else
X
j =−∞
(
( xg + j ) ∫
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g
) dt
(13)
and
Gt m0 ( xg + j ), σ x 2
g
)=
1 2πσ xg
⎡ ( t − m ( x + j ) )2 ⎤ 0 g ⎥. exp ⎢ − 2 ⎢ ⎥ 2σ x g ⎣ ⎦
From the formula (13), we can find that each bin of the resulting histogram is the weighted summation of all other neighboring bins. Such weight is in inverse proportion to the distance between bins. Consequently, the gap bin hY ( k ) can be filled up and keep smooth with neighboring bins, which can be seen from Fig. 2(b).
(10)
3.2 Postprocessing Attack by Adding Noise
The attack based on the new contrast enhancement mapping in Eq. (9) belongs to the type of integrated. However, it could be easily tuned to the type of postprocessing if the local random dithering acts on the traditionally contrast-enhanced image. That is,
respectively. Without loss of generality, variance of the dithering noise’s distribution can be assigned as
if
+∞
∑h
where i ∈ , j ∈
The extended sets, which include not only the peaks or gaps but also their neighboring pixel values, are denoted by Ψ 'p and Ψ 'g
⎪⎧σ σx = ⎨ 1 ⎪⎩σ 2
(12)
y = round [ m ( x) + nx ] .
(11)
(14)
Here, m(x): Ω → Ω is the same as that defined in the integrated attack. It can also be taken as the traditional contrast enhancement. In fact, nx is just the dithering noise added to the traditionally enhanced image. For attackers, if the employed mapping function has been known previously, nx can be designated as that in the integrated attack. If not, in the case of unknowing the employed mapping function, both the potential peak and gap set have to be searched by applying a simple and strict threshold-based detector. Peaks are identified as certain times greater than the local average magnitude, while gaps are located as times smaller.
where σ 1 and σ 2 are the two selected experiential values and it is essential to make sure that σ 1 ≥ σ 2 . There exists an inherent tradeoff among the dithering intensity, artifacts removal and visual quality. Intenser dithering signifies the better effect for removing histogram peak-gap artifacts, but inferior visual enhancement would be generated comparing with the traditional contrast enhancement. It should be mentioned that nx can also be assigned as a constant, which is invariant with the original pixel value x. In such a scenario, a satisfying but maybe not optimal tradeoff between the peak-gap artifacts removal and the transparency preservation can still be achieved.
As comparing with the integrated attack, the difference for the postprocessing attack is just that the primarily mapped values turn to be integers. Resultingly, such postprocessing attack can also remove the peak-gap artifacts successfully while preserving high enough visual quality.
Next, the reason for successfully removing the peak-gap artifacts by local dithering will be investigated initially. Without loss of generality, we focus on the removal of a specific gap bin, which is illustrated in Fig. 2. Histogram statistic of the primarily mapped values around k ( k∈ Ψ g ) is shown in Fig. 2(a). In the traditional
4. QUANTITATIVE EVALUATION 4.1 Test Data
contrast enhancement, a gap bin would be formed at k because no primarily mapped values fall into the range [ k − 12 , k + 12 ) , which
We compile a database of 693 unaltered photograph images for a quantitative evaluation of the proposed attacks against contrast enhancement forensics. Such images cover on a variety of topics including natural scenes and man-made objects, both indoors and outdoors. These images are captured by several different cameras under default setting, stored in JPEG format and with size from
can also be observed in Fig. 2(b). However, if the local random dithering is introduced onto the primarily mapped values, the mapped values would spread by the form of Gaussian distribution. Specially, suppose the smallest primarily-mapped value above k is
28
for evaluating the capability of our proposed attacks to hide the traces of contrast enhancement operation.
1200×900 pixels to 2832×2128 pixels. As in the previous works [7, 8], the green color layer of each photo image is used to form a set of unaltered grayscale images. Correspondingly, the contrastenhanced grayscale images are created by applying the power law transformation, namely gamma correction: γ ⎡ ⎛ x ⎞ ⎤ m ( x) = round ⎢ 255 ⎜ ⎟ ⎥ ⎝ 255 ⎠ ⎦⎥ ⎣⎢
4.4 Quantitative Evaluation of Attacks
To assess the dithering-based integrated attack, we perform the new contrast enhancement on images of the test set according to Eq. (9). Then the generated enhanced images would be detected by the previously trained detector. To ensure the low-complexity of new contrast enhancement operators, we tentatively simplify the selection of dithering noise’s variance and set σ 1 = σ 2 =1 in the following experiments. Even in such a setting, the proposed attacks are to be verified much effective. It should be pointed out that the refined tuning of σ values must be able to improve the attacks’ effect to some extent, at the cost of increasing algorithm complexity. Smaller σ values would fail to remove the histogram peak-gap artifacts while larger values degrade image quality.
(15)
where γ value ranges from 0.5 to 2.0. Additionally, each unaltered image is subjected to S mapping, which is a nonstandard contrast enhancement transformation and displayed in Fig. 3(a).
4.2 Performance Metrics
The performance metrics for the quantitative evaluation of our proposed attacks are twofold. Firstly, the most relevant criterion is the undetectability of the proposed contrast enhancement operator. Contrast-enhanced and unaltered images are labeled as positive (P) and negative (N) samples, respectively. With regard to detection results, we would report true positive rates (TP, the fraction of correctly detected contrast-enhanced images) under different false positive rates (FP, the fraction of incorrectly classified unaltered images). Smaller TP value signifies superior performance for the proposed attacks. Note that the 693 unaltered images are divided into two sets: 1) training set, which is consist of 347 randomly chosen images; 2) test set, including the remaining 346 images. The training set is used to determine the decision threshold τ of contrast enhancement detector. We determined τ empirically for different false positive rate, FP0, by applying the detector to all unaltered images in the training set and their traditional contrast enhancement versions. The test set is employed to evaluate the performance of basic detection schemes and our proposed attacks.
The high frequency metric F for each enhanced image is shown in Fig. 4(b). Such feature values happen to fall into the range of unaltered images, which reveals that the enhanced and unaltered images are not distinguishable. The detection results are shown in Fig. 5(a)~(b). Comparing with the baseline results, much lower detection rate is gained and adjacent to random guess. That just proves the undetectability of the proposed contrast enhancement based on integrated local dithering. With respect to visual quality, Fig. 5(c) reports PSNR results to measure the visual discrepancy between dithering-based enhanced images and the corresponding traditionally enhanced ones. On the average, PSNR for gamma correction and ‘S’ mapping achieve as highly as 46.7 dB and 47.5 dB, respectively. Good transparency can be got by the ditheringbased contrast enhancement. In the same way, the experiments for assessing the postprocessing type of attack are also done. The detection results are shown in Fig. 6. It shows that the contrast enhancement based on adding noise is difficult to be detected. In comparison with the contrast enhancement based on integrated dithering, higher detection ratio occurs for gamma correction γ = 1.2 ~ 2.0 and ‘S’ mapping but is still adjacent to random guess. Besides, the corresponding PSNR metric keeps above 46 dB. Such results can verify the reliability of the postprocessing attack based on adding noise.
Any attack algorithm against image manipulation forensics should be assessed not only by undetectability, but also by the amount of image degradation relative to the traditional manipulated version. The common image-quality metric PSNR is utilized to assess the visual impact of the proposed contrast enhancement operators. Specifically, PSNR between the new enhanced image and that without dithering is measured. We have noted that other metric such as wPSNR could also be adopted alternatively [15]. Since PSNR metric is prone to reflect the objective discrepancy, it will be priorly used in the following experiments.
Both images and histograms for different contrast enhancement operations on an example image are plotted in Fig. 7. Histograms of the images, which are enhanced by the integrated ditheringbased contrast enhancement, are smooth enough to resemble those of traditional contrast enhancement operations. In conclusion, the successfulness of the two proposed attacks against the existing contrast enhancement forensic techniques can be verified by both the low detection performance and high PSNR metric.
4.3 Baseline Detection Results
To verify the validity of original contrast enhancement detection schemes [7~8], the detection is performed on 346 images of the test set and their different contrast-enhanced versions. The cutoff parameter in Eq. (5) takes c = 7π / 8 , which is adopted in [7~8]. The high frequency metric F computed from each test sample is shown in Fig. 4(a). We can find that feature values of enhanced images are much higher than those of unaltered ones, respectively distributing in the range of 1000~10000 and 30~100.
4.5 Application to Forgery Making
Detection results for the locally applied contrast enhancement on practical forgery images are shown in Fig. 8. The F-Map records the high frequency metric of each 200×200 unoverlapped image block. As shown in Fig. 8(a), the untouched forgery image is spliced by two photos. However, contrast enhancement is needed to be employed due to the mismatching of color contrast between the ‘gate’ and ‘wall’ regions.
Detection results for traditional contrast enhancement operations are reported in Fig. 3(b). We can see that the contrast-enhanced images have been classified accurately. The detection algorithm performs extremely well against all gamma values and the ‘S’ mapping. In each case, TP exceeds 0.99 when FP0≥0.07. Such results confirm the much reliable detection for a wide range of operation parameters. As a result, Fig. 3(b) may serve as reference
If the traditional contrast enhancement is done, the computed FMap would present obvious inconsistency. As shown in subfigure
29
(c) and (d), metric values on the enhanced region, namely ‘gate’ region, are much higher than those on the other regions. In terms of such abnormity, the employed traditional contrast enhancement would be detected.
International Conf. on Acoustics, Speech and Signal Processing, Taipei, 2009. [4] A. C. Popescu and H. Farid, “Exposing digital forgeries by detecting traces of resampling,” IEEE Trans. on Signal Processing, vol. 53, no. 2, pp.758-767, 2005.
On the contrary, if the dithering-based contrast enhancement is performed, the computed F-Map would behave as the untouched forgery image. That can be seen from subfigure (b) and (e), where low and continuous F values distribute on the whole image region. Consequently, the dithering-based contrast enhancement can’t be detected by the previous forensics methods. In such a scenario, PSNR between the retouched forgery image and the traditionally enhanced image can still be gained as highly as 56.6 dB. From such illustrative results, it can be concluded that the ditheringbased contrast enhancement can be used to create image forgeries which couldn’t be detected by the locally contrast enhancement forensic detector [8].
[5] B. Mahdian and S. Saic, “Blind authentication using periodic properties of interpolation,” IEEE Trans. on Information Forensics and Security, vol. 3, no. 3, pp.529–538, 2008. [6] Z. Fan and R. L. Queiroz, “Identification of bitmap compression history: JPEG detection and quantizer estimation,” IEEE Trans. on Image Processing, vol. 12, no. 2, pp. 230– 235, 2003. [7] M. Stamm and K. J. R. Liu, “Blind forensics of contrast enhancement in digital images,” in International Conf. on Image Processing, San Diego, 2008. [8] M. Stamm and K. J. R. Liu, “Forensic detection of image tampering using intrinsic statistical fingerprints in histograms,” in Proc. APSIPA Annual Summit and Conference, Sapporo, 2009.
5. CONCLUSION
As targeted anti-forensic techniques, two kinds of untraditional contrast enhancement methods have been proposed as targeted attacks against the state-of-the-art contrast enhancement forensic algorithms. In order to remove the histogram peak-gap artifacts, local random dithering is integrated into the design of contrast enhancement mapping. The histogram of the resulting enhanced image, which is subjected to the integrated attack, is proved to be smooth by brief theoretical reasoning and illustrative simulation results. The postprocessing type of attack is proposed by adding noise to the image enhanced by traditional contrast enhancement operations. Such an attack method can be applied in the case of unknowing the primary mapping function.
[9] M. Stamm and K. J. R. Liu, “Forensic estimation and reconstruction of a contrast enhancement mapping,” in International Conf. on Acoustics, Speech and Signal Processing, Dallas, Texas, USA, 2010. [10] D. Hsiao and S. Pei, “Detecting digital tampering by blur estimation,” 1st International Workshop on Systematic Approaches to Digital Forensic Engineering, Washington, 2005. [11] G. Cao, Y. Zhao and R. Ni, “Detection of image sharpening based on histogram aberration and ringing artifacts,” in International Conf. on Multimedia and Expo, New York, 2009.
Lastly, the two proposed anti-forensic schemes are justified by plentiful experimental results on a large digital photograph image database for various parameter settings. Both undetectability and excellent visual quality have been manifested by comparing the test results with traditional contrast enhancement manipulations. The developed anti-forensic techniques examine the reliability of existing contrast enhancement forensic tools and could serve as targets for developing more secure forensic techniques.
[12] M. Kirchner and J. Fridrich, “On detection of median filtering in digital images,” SPIE Electronic Imaging: Security, Steganography, and Watermarking of Multimedia Contents, pp. 754110-754110-12, San Jose, CA, USA, 2010. [13] G. Cao, Y. Zhao and R. Ni, “Forensic detection of median filtering in digital images,” in International Conf. on Multimedia and Expo, Singapore, 2010.
6. ACKNOWLEDGMENTS
This paper is supported in part by National 973 program (No. 20 06CB303104), National Natural Science Foundation of China (No. 60702013, No. 60776794), Beijing Natural Science Foundation (No. 4073038).
[14] W.-H. Chuang, A. Swaminathan and M. Wu, “Tampering identification using empirical frequency response,” in International Conf. on Acoustics, Speech and Signal Processing, Taipei, 2009.
7. REFERENCES
[15] M. Kirchner and R. Böhme, “Hiding traces of resampling in digital images,” IEEE Trans. on Information Forensics and Security, vol. 3, no. 4, pp.582-592, 2008.
[1] Y.-F. Hsu and S.-F. Chang, “Image splicing detection using camera response function consistency and automatic segmentation,” in International Conf. on Multimedia and Expo, Beijing, 2007.
[16] M. Kirchner and R. Böhme, “Synthesis of color filter array pattern in digital images,” in Proc. SPIE-IS&T Electronic Imaging: Media Forensics and Security, Feb. 2009, vol. 7254.
[2] W. Chen, Y. Q. Shi and W. Su, “Image splicing detection using 2-D phase congruency and statistical moments of characteristic function,” SPIE Electronic Imaging: Security, Steganography, and Watermarking of Multimedia Contents, San Jose, CA, USA, 2007.
[17] M. Stamm, S. Tjoa, W. S. Lin and K. J. Ray Liu, “Antiforensic of JPEG compression,” in International Conf. on Acoustics, Speech and Signal Processing, pp. 1694-1697, Dallas, Texas, USA, 2010.
[3] S. Bayram, H. T. Sencar and N. Memon, “An efficient and robust method for detecting copy-move forgery,” in
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(a) r = 0.5 r = 0.6 r = 0.7 r = 0.8 r = 0.9 r = 1.2 r = 1.4 r = 1.6 r = 1.8 r = 2.0 S mapping
700 600
F
500 400 300 200 100 0
0
100
200
300 400 Image No.
(b) Figure 4. Distribution of the high frequency metric F. (a) for unaltered images and their traditionally contrast-enhanced versions; (b) for the integrated dithering-based enhanced images.
31
1 0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
TP
TP
1 0.9
0.4 0.3
0.3
r = 0.5 r = 0.6 r = 0.7 r = 0.8 r = 0.9
0.2 0.1 0
r = 1.2 r = 1.4 r = 1.6 r = 1.8 r = 2.0 S mapping in Fig. 3(a)
0.4
0
0.2
0.4
FP0
0.6
0.8
0.2 0.1 0
1
0
0.2
0.4
(a)
FP0
0.6
0.8
1
(b) Maximum PSNR for gamma mapping Minimum PSNR for gamma mapping PSNR for S mapping displayed in Fig. 3(a)
48.4 48.2 48
PSNR
47.8 47.6 47.4 47.2 47 46.8 46.6 46.4
0
50
100
150 200 Image No.
250
300
350
(c) Figure 5. Results for assessing the integrated attack. (a) Detection results for γ = 0.5 ~ 0.9 ; (b) Detection results for γ = 1.2 ~ 2.0 ; (c) PSNR between the dithering-based enhanced image and the corresponding traditionally enhanced image.
1 0.9 0.8 0.7
r = 0.5 r = 0.6 r = 0.7 r = 0.8 r = 0.9 r = 1.2 r = 1.4 r = 1.6 r = 1.8 r = 2.0 S mapping in Fig.3(a)
TP
0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.2
0.4
FP0
0.6
0.8
1
Figure 6. Detection results for assessing the postprocessing attack.
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0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0
γ = 0.7
0
50
100
150
200
250
0.04
0.04
0.035
0.035
0.03
0.03
0.025
0.025
0.02
0.02
0.015
0.015
0.01
0.01
0.005
0.005
0
0
50
100
150
200
250
0
0.04
0.04
0.035
0.035
0.03
0.03
0.025
0.025
0.02
0.02
0.015
0.015
0.01
0.01
0.005
0.005
0
γ = 1.4
0
50
100
150
200
250
0
0.04
0.04
0.035
0.035
0.03
0.03
0.025
0.025
0.02
0.02
0.015
0.015
0.01
0.01
0.005
0.005
0
0
50
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250
0
0
50
100
150
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250
0
50
100
150
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250
0
50
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200
250
Figure 7. Detect contrast enhancement on an example image. The first column shows the original image and the images enhanced by traditional contrast enhancement. The third column shows the images enhanced by the integrated dithering-based contrast enhancement. Histogram and high frequency metric of each image are displayed adjacently on the right side.
(a)
33
0
0
0
0
0
0
0
3
2
2
4
4
3
2
3
3
3
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
5
6
13
6
7
7
5
7
6
7
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
5
8
4
4
4
13
7
13
4
4
4
0
0
0
0
0
0
0
2
2
1
3
4
4
7
5
4
5
4
7
6
7
6
7
8
9
7
4
4
5
3
1
1
3
5
4
6
6
6
5
4
5
5
5
5
4
6
7
6
5
4
7
4
7
5
4
4
4
5
5
7
7
6
5
5
5
8
7
6
5
7
6
9
11
5
5
5
6
5
8
6
5
5
4
7
6
5
5
7
3
9
4
6
7
7
10
3
7
17
21
5
4
7
6
5
7
3
5
6
4
8
6
(b)
(c) 0
0
0
0
0
0
0
4
8
7
11
18
11
10
15
10
8
11
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
53
32
33
46
34
33
33
25
40
50
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
42
88
98
101
65
75
117
92
70
21
4
0
0
0
0
0
0
0
2
2
1
3
4
4
7
11
39
35
26
30
35
35
29
32
48
29
7
4
4
5
3
1
1
3
5
4
6
6
6
5
4
8
32
27
47
47
52
53
45
31
40
27
4
7
5
4
4
4
5
5
7
7
6
5
5
5
8
10
41
32
52
61
260
231
56
81
89
113
5
8
6
5
5
4
7
6
5
5
7
3
9
4
6
7
40
44
87
50
222
281
50
51
67
81
5
7
3
5
6
4
8
6
0
0
0
0
0
0
0
4
14
14
10
9
13
13
11
11
12
12
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
5
3
4
5
6
5
6
5
4
6
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
8
10
7
8
4
7
10
3
12
6
4
0
0
0
0
0
0
0
2
2
1
3
4
4
7
8
4
4
6
6
5
5
8
4
5
5
7
4
4
5
3
1
1
3
5
4
6
6
6
5
4
6
6
4
7
9
7
5
6
5
7
4
4
7
5
4
4
4
5
5
7
7
6
5
5
5
8
6
7
6
8
6
5
11
7
4
5
3
5
8
6
5
5
4
7
6
5
5
7
3
9
4
6
7
8
4
4
8
13
5
7
12
4
6
5
7
3
5
6
4
8
6
(d)
(e) Figure 8. Detect locally applied contrast enhancement on a forgery image. (a) The untouched spliced image. The middle ‘gate’ and bilateral ‘wall’ are cut from two different photos and resized. (b) F -Map for each 200×200 unoverlapped block of (a). (c) The spliced image retouched by traditional gamma correction γ =1.5 on the ‘gate’ region of (a). (d) F -Map of (c). (e) F -Map of the spliced image which is retouched by the integrated dithering-based contrast enhancement on the ‘gate’ region of (a). PSNR between this spliced image and (c) is 56.6 dB.
34
