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On Image Forgery Detection Using Two Dimensional Discrete Cosine Transform and Statistical Moments
Available online at www.sciencedirect.com
ScienceDirect Procedia Computer Science 70 (2015) 130 – 136
4th International Conference on Eco-friendly Computing and Communication Systems, ICECCS 2015
On Image Forgery Detection Using Two Dimensional Discrete Cosine Transform and Statistical Moments Rajeev Kaushika , Rakesh Kumar Bajajb,∗, Jimson Mathewc b Jaypee
a Gyan Bharti Institute of Technology, Meerut, Uttar Pradesh, PIN- 250 103, INDIA University of Information Technology, Waknaghat, Solan, Himachal Pradesh, PIN-173234, INDIA c University of Bristol, Bristol, UK
Abstract In the present communication, we propose a new approach for detecting copy-move forgery in digital images using statistical moments and two dimensional discrete cosine transform. We first slide a window centered around every pixel of the suspicious image, then each window is passed through two dimensional discrete cosine transform (2D − DCT ) to obtain the quantized coefficient matrix. The low dimensional statistical feature vector of each quantized coefficient matrix is obtained and arranged in a feature matrix F. The columns of F contain 4 - statistical features, i.e., mean Me, variance Var, third order moment skewness S k and fourth order moment kurtosis Kr obtained from the quantized coefficient matrix. In order to make similar windows adjacent, the feature matrix F is lexicographically sorted using radix sort. Finally, a copy-move forgery detection is performed using the adjacent pairs of feature vectors. It has also been observed that the proposed method has the lower dimension feature vector with lower computational complexity. c 2015 2015The TheAuthors. Authors. Published by Elsevier © Published by Elsevier B.V. B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Organizing Committee of ICECCS 2015. Peer-review under responsibility of the Organizing Committee of ICECCS 2015 Keywords: Copy-Move Image Forgery; Discrete Cosine Transform; Statistical Moments; Feature Matrix; Euclidean Distance.
1. Introduction The authenticity of a digital image can be used as an evidence or as an important resource of information in image processing. Due to availability of various powerful editing software as well as sophisticated digital cameras, digital image forgery has become more and more popular in image manipulation, where a part of the image is copied and pasted on another part of the same image to hide unwanted information. The available image forgery techniques are having very high computational complexity of a digital image can be used as an evidence or as an important resource of information in image processing. Image forgery detection system is required in various fields for preventing forgery or intentional alteration of images as well as for copyright protection because very few methodologies are available to verify the authenticity and ∗
Corresponding author. Tel.: +91-1792-239229 ; fax: +91-1792-245365. E-mail address: [email protected]
1877-0509 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Organizing Committee of ICECCS 2015 doi:10.1016/j.procs.2015.10.058
Rajeev Kaushik et al. / Procedia Computer Science 70 (2015) 130 – 136
integrity of images. Image forgery detection is applied in many fields such as journalism, scientific publications, digital forensic science, multimedia security and surveillance systems etc. The digital image forgery detection techniques are classified into active 3,4,9 and passive approaches 1,2,12,13 . In active approach, the digital image requires some watermark embedding or signature generation at the time of creation, which is called pre-processing of image. However, there are a huge number of digital images on internet without watermark or digital signature. So, in that case active approach is not the best way to find the authentication of the image. The passive approaches does not need any watermark embedding or signature generation at the time of creation. Block matching techniques are employed in passive technology for detecting the forged images. There are roughly two classes of image forgeries possible: • Copy-Move: This type of image forgeries includes images tampered by means of copying one area within an image and pasting it onto another. • Splicing: This type of forged images deals with creating the forgery by using more than just the single image for copying and pasting. This is done by taking one or more images and copying and pasting from various areas within each to form a forged image. In Copy-Move image forgery, a part of a picture is duplicated and then pasted onto other regions to cover any unwanted portion within the same picture. The authenticity of the image come under doubt as duplication of objects or regions occurs in the image. Since the copied segments come from the same image, though it may probably be altered geometrically, but it shares some similar features with the original region which is duplicated. Its properties will be compatible with the rest of the image, thus it is very difficult for a human eye to detect such type of forgery. There are various methods that provide solutions for copy-move forgery detection. Each of these methods provides a solution under a set of conditions or assumptions; the method will fail if its assumptions are not realized 5,16,17 . In this paper, we propose a robust and efficient forgery detection approach based on 2D-DCT and statistical moments as compared with other methods, the main advantages of our method can be summarized as: • The feature vector is having lower dimension; • It is robust to various attacks, such as: multiple copy-move forgery, Gaussian blurring, and noise contamination forgery; • It has lower computational complexity. 2. Related Work A bibliography on blind image forgery detection methods can be found in Mahdian et al. 7,8 . Bayram et al. 1 used a scale and rotation invariant Fourier-Mellin Transform (FMT) as the notion of bloom filters to detect copy-move forgery. Their methods are computationally efficient and can detect forgery in highly compressed images. Copy move forgery detection based on blur moment invariants has been proposed in Mahdian et al. 7,8 . This method can detect duplicated regions degraded by blurring or corrupted with noise. Huang et al. 5 proposed a copy move forgery detection method based on Scale Invariant Feature Transform (SIFT) descriptors. After extracting the descriptors of different regions, they match them with each other to find possible forgery in images. A sorted neighborhood approach based on Discrete Wavelet Transform (DWT) and Singular Value Decomposition (SVD) has been proposed in Li et al. 6 . In this method, first DWT is applied to the image and then SVD is used on low-frequency components to reduce their dimension. SV vectors are then lexicographically sorted, where duplicated blocks will be close in the sorted list. Solario et al. 14 use log-polar coordinates to obtain a one dimensional descriptor invariant to reflection, rotation, and scaling for detecting duplicated regions. The Discrete Cosine Transform (2D-DCT) was used in Fridrich et al. 2 . They use lexicographic sorting after extracting 2D-DCT coefficients of each block in an image. A computationally efficient method based on Principal Component Analysis (PCA) was presented in Popescu et al. 12 . The DWT and phase correlation based method was proposed in Zhang et al. 16 . Their algorithm is based on pixel matching to locate copy move regions. Sutcu et al. 15 proposed tamper detection based on the regularity of wavelet coefficients. In their method, they used undecimated DWT. A robust blind copy move image forgery detection method using undecimated Dyadic Wavelet Transform (DyWT) proposed by Muhammad et al. 10 in which, after extracting low frequency component
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(approximate) LL1 and high frequency component (detail) HH1 at scale one, a similarity measure is applied between the blocks in LL1 and HH1 separately. A decision is made based on the similarity between blocks in LL1 and dissimilarity between the blocks in HH1. A preliminary explanation of this method is given in Muhammad et al. 11 . Regularity in sharpness or blurriness is measured in the decay of wavelet coefficients across scales. Most of the above methods suffer from false positives. Therefore, human interpretation is necessary to obtain the correct result. 3. The Proposed Approach The primary purpose of copy-move forgery is to find large similar regions in an image, as we know that the duplicated regions are unknown both in size and shape. The method of comparing every possible pairs pixel by pixel is not simple, as well as it leads to higher computational complexity. In order to make an efficient forgery detection an image window is used. Some appropriate and robust features are extracted from the image window, therefore, a good features extraction not only represent the whole image windows, but also reduces the dimension of feature vector, and due to less dimension of feature matrix, forgery detection algorithm has lower computational complexity. In this paper, we propose copy-move forgery detection method based on the 2D-DCT and a feature matrix F containing 4 columns. Firstly, sliding a window centered around every pixel of the suspicious image, then each window is passed through 2D-DCT to obtain the 2D-DCT quantized coefficient matrix. The low dimensional statistical feature vector of each 2D-DCT matrix is obtained and arranged in a feature matrix F. The columns of F contain 4 statistical features mean Me, variance Var, third order moment skewness S k and fourth order moment kurtosis Kr obtained from 2DDCT matrix. In order to make similar windows adjacent, the feature matrix F is lexicographically sorted using radix sort. Finally, a copy-move forgery detection is performed using the adjacent pairs of feature vectors. For a suspicious gray scale image I of size (M × N), and a sliding window of size (p × p), the 4 features extracted from the window centered at pixel (x, y) are given by the following equations: Me =
Var =
1 MN
1 Sk = MN Kr =
1 MN
1 MN
(p−1)/2
(p−1)/2
I(x + i, y + j),
(1)
(I(x + i, y + j) − Me)2 ,
(2)
(I(x + i, y + j) − Me)3 ,
(3)
(I(x + i, y + j) − Me)4 .
(4)
i=−(p−1)/2 j=−(p−1)/2
(p−1)/2
(p−1)/2
i=−(p−1)/2 j=−(p−1)/2 (p−1)/2
(p−1)/2
i=−(p−1)/2 j=−(p−1)/2 (p−1)/2
(p−1)/2
i=−(p−1)/2 j=−(p−1)/2
It may be noted that p must have an odd value to obtain a centered window around each pixel and the spatial scanning order of an image is performed pixel by pixel from left to right and top to bottom. 4. The Proposed Algorithm Based on the proposed approach, the following are the steps of the proposed algorithm: 1. Select a M × N gray scale suspicious image I (if the image is colored, we can use the standard formula: I = 0.228R + 0.587G + 0.114B to convert it to gray scale).
Rajeev Kaushik et al. / Procedia Computer Science 70 (2015) 130 – 136
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Fig. 1. Image Forgery Detection Flow Chart
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2. Slide window of size (p × p) on the suspicious image pixel by pixel from left to right and top to bottom. Each Sliding window is denoted as Wi j , where i and j indicates the starting point of the window’s row and column, respectively. Wi j (x, y) = I(x + i, y + j)
(5)
where x, y ∈ {0, 1, · · · , p − 1}, i ∈ {1, 2, · · · , M − p + 1} and j ∈ {1, 2, · · · , N − p + 1}. Hence, we obtained the total number of overlapped image windows as T windows = (M − p + 1) × (N − p + 1) from suspicious image I. 3. 2D-DCT coefficients matrix is obtained by applying 2D-DCT to each sliding window Wi , i = (M − p + 1) × (N − p + 1). 4. The feature vectors extracted from each quantized matrix Wi obtained in step 3, are arranged in a matrix, denote as F with the size of (M − p + 1)(N − p + 1) × 4 and defined as ⎡ ⎢⎢⎢ ⎢⎢⎢ ⎢ F = ⎢⎢⎢⎢⎢ ⎢⎢⎢ ⎣
f1 f2 .. . f(M−p+1)×(N−p+1)
⎤ ⎥⎥⎥ ⎥⎥⎥ ⎥⎥⎥ ⎥⎥⎥ , ⎥⎥⎥ ⎦
where fi = (Mei , Vari , S ki , Kri ). 5. The feature matrix F is then lexicographically sorted meantime, record the left corner’s coordinate of each sliding window Wi . 6. The Euclidean distance d( fi , fi+1 ) between adjacent pairs of F is calculated. If the distance is smaller than a preset threshold T s , then we initialize a black map B with the size M × N and consider the inquired windows as a pair of candidate for the forgery detection. Let fi = (Mei , Vari , S ki , Kri ). and fi+1 = (Mei+1 , Vari+1 , S ki+1 , Kri+1 ) are adjacent pair of F, then Euclidean distance d( fi , fi+1 ) between adjacent pairs fi and fi+1 is defined as
d( fi , fi+1 ) =
4 k 2 ( fik − fi+1 ) .
(6)
k=1
5. Experimental Results and Discussion We consider two standard set of images for the implementation of the proposed algorithm. In order to make these images forged, we have used adobe photoshop 7.0 and then these images along with their corresponding forged images are stored in png format of size 128 × 128. The sliding window is placed on each pixel of size 3 × 3 taken in the proposed forgery detection algorithm. Threshold value in the proposed method is set to be zero. the proposed method is applied on the both forged images to find the image forgery result. Finally, we find the forgery detection in the forged images and the obtained results are shown in figure 2 and figure 3.
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Rajeev Kaushik et al. / Procedia Computer Science 70 (2015) 130 – 136
Original Gray Scale Image
Forge Gray Scale Image
Image Forgery Detection Result
Fig. 2. Forgery Detection Results I
Original Gray Scale Image
Forge Gray Scale Image
Image Forgery Detection Result
Fig. 3. Forgery Detection Results II
6. Conclusions The proposed copy-move forgery detection method is based on the 2D-DCT and the feature matrix F containing 4 columns. The main advantage of the proposed method is the lower dimension feature vector, consequently the lowest computational complexity. It is robust to various attacks such as multiple copy-move forgery, Gaussian blurring, and noise contamination forgery. Using proposed method some experimental results of image forgery detection are obtained. In order to sort the feature matrix, we applied the radix sort which has high computational cost. This computational cost of sorting method can be reduced by the most famous c-mean algorithm of data clustering.
References 1. Bayram S, Sencar HT, Memon N. An efficient and robust method for detecting copy-move forgery. ICASSP 2009; 1053–1056. 2. Fridrich J, Soukal D, Luk´a sˇ J. Detection of copy-move forgery in digital images. In: Proceedings of Digital Forensic Research Workshop 2003. 3. Hartung F, Kutter M. Multimedia watermarking techniques. In Proceedings of the IEEE 1999; 87(7):1079–1107. 4. Hsieh CT, Wu YK. Geometric invariant semi-fragile image watermarking using real symmetric matrix. WSEAS Transaction on Signal Processing 2006; 2(5); 612–618. 5. Huang H, Guo W, Zhang Y. Detection of copy-move forgery in digital images using SIFT algorithm. In: Proc. IEEE Pacific-Asia workshop on Computational Intelligence and Industrial Application 2008; 272–276. 6. Li G, Wu Q, Tu D, Sun S. A sorted neighborhood approach detecting duplicated forgeries based on DWT and SVD. IEEE International Conference on Multimedia and Expo 2007; 1750–1753. 7. Mahdian B, Saic S. A bibliography on blind methods for identifying image forgery. Signal Processing: Image Communication 2010; 25(6):389–399.
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Rajeev Kaushik et al. / Procedia Computer Science 70 (2015) 130 – 136 8. Mahdian B, Saic S. Detection of copy-move forgery using a method based on blur moment invariants. Forensic Science International 2007; 171(2-3):180–189. 9. Meerwald P, Uhl A. A Survey of Wavelet-Domain Watermarking Algorithms. In Proceedings of SPIE, Electronic Imaging, Security and Watermarking of Multimedia Contents 2001; 4314:505–516. 10. Muhammad G, Hussain M, Khawaji K, Bebis G. Passive copy move image forgery detection using undecimated dyadic wavelet transform. Digital Investigation 2012; 9:49–57. 11. Muhammad G, Hussain M, Khawaji K, Bebis G. Blind copy move image forgery detection using dyadic undecimatedwavelet transform. In: 17th International Conference on Digital Signal Processing, Corfu, Greece 2011; 1–6. 12. Popescu AC, Farid H. Exposing Digital Forgeries by Detecting Duplicated Image Regions. TR 2004-515, Department of Computer Science, Dartmouth College 2004. 13. Shinfeng D, Lin SD. An Integrated Technique for Splicing and Copy-move Forgery Image Detection. 4th International Congress on Image and Signal Processing (CISP) 2011; 2: 1086–1090. 14. Solario SB, Nandi AK. Passive forensic method for detecting duplicated regions affected by reflection, rotation, and scaling. 17th European Signal Processing Conference (EUSIPCO 2009), Glasgow, Scotland, August 24–28, 15. Sutcu Y, Coskun B, Sencar HT, Memon N. Tamper detection based on regularity of wavelet transform coefficients. IEEE International Conference on Image Processing 2007; 397–400. 16. Zhang J, Feng Z, Su Y. A New Approach for Detecting Copy-Move Forgery in Digital Images. 11th IEEE Singapore International Conference on Communication Systems 2008; 362–366. 17. Michael Z, Sun X. DWT-PCA (EVD) Based Copy-move Image Forgery Detection. International Journal of Digital Content Technology and its Applications 2011; 5(1):251–258.
ScienceDirect Procedia Computer Science 70 (2015) 130 – 136
4th International Conference on Eco-friendly Computing and Communication Systems, ICECCS 2015
On Image Forgery Detection Using Two Dimensional Discrete Cosine Transform and Statistical Moments Rajeev Kaushika , Rakesh Kumar Bajajb,∗, Jimson Mathewc b Jaypee
a Gyan Bharti Institute of Technology, Meerut, Uttar Pradesh, PIN- 250 103, INDIA University of Information Technology, Waknaghat, Solan, Himachal Pradesh, PIN-173234, INDIA c University of Bristol, Bristol, UK
Abstract In the present communication, we propose a new approach for detecting copy-move forgery in digital images using statistical moments and two dimensional discrete cosine transform. We first slide a window centered around every pixel of the suspicious image, then each window is passed through two dimensional discrete cosine transform (2D − DCT ) to obtain the quantized coefficient matrix. The low dimensional statistical feature vector of each quantized coefficient matrix is obtained and arranged in a feature matrix F. The columns of F contain 4 - statistical features, i.e., mean Me, variance Var, third order moment skewness S k and fourth order moment kurtosis Kr obtained from the quantized coefficient matrix. In order to make similar windows adjacent, the feature matrix F is lexicographically sorted using radix sort. Finally, a copy-move forgery detection is performed using the adjacent pairs of feature vectors. It has also been observed that the proposed method has the lower dimension feature vector with lower computational complexity. c 2015 2015The TheAuthors. Authors. Published by Elsevier © Published by Elsevier B.V. B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Organizing Committee of ICECCS 2015. Peer-review under responsibility of the Organizing Committee of ICECCS 2015 Keywords: Copy-Move Image Forgery; Discrete Cosine Transform; Statistical Moments; Feature Matrix; Euclidean Distance.
1. Introduction The authenticity of a digital image can be used as an evidence or as an important resource of information in image processing. Due to availability of various powerful editing software as well as sophisticated digital cameras, digital image forgery has become more and more popular in image manipulation, where a part of the image is copied and pasted on another part of the same image to hide unwanted information. The available image forgery techniques are having very high computational complexity of a digital image can be used as an evidence or as an important resource of information in image processing. Image forgery detection system is required in various fields for preventing forgery or intentional alteration of images as well as for copyright protection because very few methodologies are available to verify the authenticity and ∗
Corresponding author. Tel.: +91-1792-239229 ; fax: +91-1792-245365. E-mail address: [email protected]
1877-0509 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Organizing Committee of ICECCS 2015 doi:10.1016/j.procs.2015.10.058
Rajeev Kaushik et al. / Procedia Computer Science 70 (2015) 130 – 136
integrity of images. Image forgery detection is applied in many fields such as journalism, scientific publications, digital forensic science, multimedia security and surveillance systems etc. The digital image forgery detection techniques are classified into active 3,4,9 and passive approaches 1,2,12,13 . In active approach, the digital image requires some watermark embedding or signature generation at the time of creation, which is called pre-processing of image. However, there are a huge number of digital images on internet without watermark or digital signature. So, in that case active approach is not the best way to find the authentication of the image. The passive approaches does not need any watermark embedding or signature generation at the time of creation. Block matching techniques are employed in passive technology for detecting the forged images. There are roughly two classes of image forgeries possible: • Copy-Move: This type of image forgeries includes images tampered by means of copying one area within an image and pasting it onto another. • Splicing: This type of forged images deals with creating the forgery by using more than just the single image for copying and pasting. This is done by taking one or more images and copying and pasting from various areas within each to form a forged image. In Copy-Move image forgery, a part of a picture is duplicated and then pasted onto other regions to cover any unwanted portion within the same picture. The authenticity of the image come under doubt as duplication of objects or regions occurs in the image. Since the copied segments come from the same image, though it may probably be altered geometrically, but it shares some similar features with the original region which is duplicated. Its properties will be compatible with the rest of the image, thus it is very difficult for a human eye to detect such type of forgery. There are various methods that provide solutions for copy-move forgery detection. Each of these methods provides a solution under a set of conditions or assumptions; the method will fail if its assumptions are not realized 5,16,17 . In this paper, we propose a robust and efficient forgery detection approach based on 2D-DCT and statistical moments as compared with other methods, the main advantages of our method can be summarized as: • The feature vector is having lower dimension; • It is robust to various attacks, such as: multiple copy-move forgery, Gaussian blurring, and noise contamination forgery; • It has lower computational complexity. 2. Related Work A bibliography on blind image forgery detection methods can be found in Mahdian et al. 7,8 . Bayram et al. 1 used a scale and rotation invariant Fourier-Mellin Transform (FMT) as the notion of bloom filters to detect copy-move forgery. Their methods are computationally efficient and can detect forgery in highly compressed images. Copy move forgery detection based on blur moment invariants has been proposed in Mahdian et al. 7,8 . This method can detect duplicated regions degraded by blurring or corrupted with noise. Huang et al. 5 proposed a copy move forgery detection method based on Scale Invariant Feature Transform (SIFT) descriptors. After extracting the descriptors of different regions, they match them with each other to find possible forgery in images. A sorted neighborhood approach based on Discrete Wavelet Transform (DWT) and Singular Value Decomposition (SVD) has been proposed in Li et al. 6 . In this method, first DWT is applied to the image and then SVD is used on low-frequency components to reduce their dimension. SV vectors are then lexicographically sorted, where duplicated blocks will be close in the sorted list. Solario et al. 14 use log-polar coordinates to obtain a one dimensional descriptor invariant to reflection, rotation, and scaling for detecting duplicated regions. The Discrete Cosine Transform (2D-DCT) was used in Fridrich et al. 2 . They use lexicographic sorting after extracting 2D-DCT coefficients of each block in an image. A computationally efficient method based on Principal Component Analysis (PCA) was presented in Popescu et al. 12 . The DWT and phase correlation based method was proposed in Zhang et al. 16 . Their algorithm is based on pixel matching to locate copy move regions. Sutcu et al. 15 proposed tamper detection based on the regularity of wavelet coefficients. In their method, they used undecimated DWT. A robust blind copy move image forgery detection method using undecimated Dyadic Wavelet Transform (DyWT) proposed by Muhammad et al. 10 in which, after extracting low frequency component
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(approximate) LL1 and high frequency component (detail) HH1 at scale one, a similarity measure is applied between the blocks in LL1 and HH1 separately. A decision is made based on the similarity between blocks in LL1 and dissimilarity between the blocks in HH1. A preliminary explanation of this method is given in Muhammad et al. 11 . Regularity in sharpness or blurriness is measured in the decay of wavelet coefficients across scales. Most of the above methods suffer from false positives. Therefore, human interpretation is necessary to obtain the correct result. 3. The Proposed Approach The primary purpose of copy-move forgery is to find large similar regions in an image, as we know that the duplicated regions are unknown both in size and shape. The method of comparing every possible pairs pixel by pixel is not simple, as well as it leads to higher computational complexity. In order to make an efficient forgery detection an image window is used. Some appropriate and robust features are extracted from the image window, therefore, a good features extraction not only represent the whole image windows, but also reduces the dimension of feature vector, and due to less dimension of feature matrix, forgery detection algorithm has lower computational complexity. In this paper, we propose copy-move forgery detection method based on the 2D-DCT and a feature matrix F containing 4 columns. Firstly, sliding a window centered around every pixel of the suspicious image, then each window is passed through 2D-DCT to obtain the 2D-DCT quantized coefficient matrix. The low dimensional statistical feature vector of each 2D-DCT matrix is obtained and arranged in a feature matrix F. The columns of F contain 4 statistical features mean Me, variance Var, third order moment skewness S k and fourth order moment kurtosis Kr obtained from 2DDCT matrix. In order to make similar windows adjacent, the feature matrix F is lexicographically sorted using radix sort. Finally, a copy-move forgery detection is performed using the adjacent pairs of feature vectors. For a suspicious gray scale image I of size (M × N), and a sliding window of size (p × p), the 4 features extracted from the window centered at pixel (x, y) are given by the following equations: Me =
Var =
1 MN
1 Sk = MN Kr =
1 MN
1 MN
(p−1)/2
(p−1)/2
I(x + i, y + j),
(1)
(I(x + i, y + j) − Me)2 ,
(2)
(I(x + i, y + j) − Me)3 ,
(3)
(I(x + i, y + j) − Me)4 .
(4)
i=−(p−1)/2 j=−(p−1)/2
(p−1)/2
(p−1)/2
i=−(p−1)/2 j=−(p−1)/2 (p−1)/2
(p−1)/2
i=−(p−1)/2 j=−(p−1)/2 (p−1)/2
(p−1)/2
i=−(p−1)/2 j=−(p−1)/2
It may be noted that p must have an odd value to obtain a centered window around each pixel and the spatial scanning order of an image is performed pixel by pixel from left to right and top to bottom. 4. The Proposed Algorithm Based on the proposed approach, the following are the steps of the proposed algorithm: 1. Select a M × N gray scale suspicious image I (if the image is colored, we can use the standard formula: I = 0.228R + 0.587G + 0.114B to convert it to gray scale).
Rajeev Kaushik et al. / Procedia Computer Science 70 (2015) 130 – 136
dĂŬĞĂŶ/ŵĂŐĞŽĨƐŝnjĞDdžE
ŽŶǀĞƌƚŝƚŝŶƚŽŐƌĂLJƐĐĂůĞŝŵĂŐĞ͖ĨŽƌŐĞ ƚŚĞŝŵĂŐĞŽĨƐŝnjĞDdžE
&ŽƌŵĂǁŝŶĚŽǁŽĨƐŝnjĞƉdžƉ͕ƐĞƚ ƉƌĞĚĞĨŝŶĞĚƚŚƌĞƐŚŽůĚǀĂůƵĞ͘
WůĂĐĞĐĞŶƚĞƌŽĨƚŚĞǁŝŶĚŽǁĂƚĞĂĐŚ ƉŝdžĞůƉŽƐŝƚŝŽŶŽĨƚŚĞĨŽƌŐĞĚŝŵĂŐĞ͘
ĂůĐƵůĂƚĞϮͲdĐŽĞĨĨŝĐŝĞŶƚƐŵĂƚƌŝdž ĨŽƌĞĂĐŚǁŝŶĚŽǁ͘
&ĞĂƚƵƌĞǀĞĐƚŽƌƐĞdžƚƌĂĐƚĞĚŵĂƚƌŝdžŝƐ ĨŽƌŵĞĚƵƐŝŶŐƐƚĂƚŝƐƚŝĐĂůŽƌĚĞƌ ŵŽŵĞŶƚƐĨƌŽŵϮͲdĐŽĞĨĨŝĐŝĞŶƚƐ ŵĂƚƌŝdž
&ĞĂƚƵƌĞŵĂƚƌŝdž&;DͲƉнϭͿ;EͲƉнϭͿdžϰ ŝƐƚŚĞŶůĞdžŝĐŽŐƌĂƉŚŝĐĂůůLJƐŽƌƚĞĚ͘
ĂůĐƵůĂƚĞ ƵĐůŝĚĞĂŶĚŝƐƚĂŶĐĞ;ĚͿĨŽƌ ĞĂĐŚƉĂŝƌŽĨĂĚũĂĐĞŶƚƌŽǁ͘
&ŽƌŵĂďůĂĐŬŵĂƉŽĨƐĂŵĞƐŝnjĞĂƐ ƚŚĂƚŽĨŽƌŝŐŝŶĂůŝŵĂŐĞ͘
/ŵĂŐĞĨŽƌŐĞƌLJĚĞƚĞĐƚŝŽŶƌĞƐƵůƚƐ͘
Fig. 1. Image Forgery Detection Flow Chart
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2. Slide window of size (p × p) on the suspicious image pixel by pixel from left to right and top to bottom. Each Sliding window is denoted as Wi j , where i and j indicates the starting point of the window’s row and column, respectively. Wi j (x, y) = I(x + i, y + j)
(5)
where x, y ∈ {0, 1, · · · , p − 1}, i ∈ {1, 2, · · · , M − p + 1} and j ∈ {1, 2, · · · , N − p + 1}. Hence, we obtained the total number of overlapped image windows as T windows = (M − p + 1) × (N − p + 1) from suspicious image I. 3. 2D-DCT coefficients matrix is obtained by applying 2D-DCT to each sliding window Wi , i = (M − p + 1) × (N − p + 1). 4. The feature vectors extracted from each quantized matrix Wi obtained in step 3, are arranged in a matrix, denote as F with the size of (M − p + 1)(N − p + 1) × 4 and defined as ⎡ ⎢⎢⎢ ⎢⎢⎢ ⎢ F = ⎢⎢⎢⎢⎢ ⎢⎢⎢ ⎣
f1 f2 .. . f(M−p+1)×(N−p+1)
⎤ ⎥⎥⎥ ⎥⎥⎥ ⎥⎥⎥ ⎥⎥⎥ , ⎥⎥⎥ ⎦
where fi = (Mei , Vari , S ki , Kri ). 5. The feature matrix F is then lexicographically sorted meantime, record the left corner’s coordinate of each sliding window Wi . 6. The Euclidean distance d( fi , fi+1 ) between adjacent pairs of F is calculated. If the distance is smaller than a preset threshold T s , then we initialize a black map B with the size M × N and consider the inquired windows as a pair of candidate for the forgery detection. Let fi = (Mei , Vari , S ki , Kri ). and fi+1 = (Mei+1 , Vari+1 , S ki+1 , Kri+1 ) are adjacent pair of F, then Euclidean distance d( fi , fi+1 ) between adjacent pairs fi and fi+1 is defined as
d( fi , fi+1 ) =
4 k 2 ( fik − fi+1 ) .
(6)
k=1
5. Experimental Results and Discussion We consider two standard set of images for the implementation of the proposed algorithm. In order to make these images forged, we have used adobe photoshop 7.0 and then these images along with their corresponding forged images are stored in png format of size 128 × 128. The sliding window is placed on each pixel of size 3 × 3 taken in the proposed forgery detection algorithm. Threshold value in the proposed method is set to be zero. the proposed method is applied on the both forged images to find the image forgery result. Finally, we find the forgery detection in the forged images and the obtained results are shown in figure 2 and figure 3.
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Original Gray Scale Image
Forge Gray Scale Image
Image Forgery Detection Result
Fig. 2. Forgery Detection Results I
Original Gray Scale Image
Forge Gray Scale Image
Image Forgery Detection Result
Fig. 3. Forgery Detection Results II
6. Conclusions The proposed copy-move forgery detection method is based on the 2D-DCT and the feature matrix F containing 4 columns. The main advantage of the proposed method is the lower dimension feature vector, consequently the lowest computational complexity. It is robust to various attacks such as multiple copy-move forgery, Gaussian blurring, and noise contamination forgery. Using proposed method some experimental results of image forgery detection are obtained. In order to sort the feature matrix, we applied the radix sort which has high computational cost. This computational cost of sorting method can be reduced by the most famous c-mean algorithm of data clustering.
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