1. INTRODUCTION

Digital cameras and smart phones, and digital image procesing software such as Photoshop, Paintshop Pro, you can duplicate digital counterfeit images relatively easily [1-14].

A variety of algorithms for detecting duplicated forgery images or tampering images have ben proposed in many papers [1-14]. A technique of digital image forgery is copy-move image forgery. Copy-move image forgery is a method of forging an image by copying a specific image area of the image itself and then ataching it to another area of the same image [1-14]. The purpose of copymove image forgery detection is to detect the same or very similar region image within the original image.

An example of copy-move forged image is showed by Fig. 1 (a) and (b), and each of Fig. 1(a)and Fig. 1(b) shows an original image and a copymoved forged image respectively.

(a) Original image (b) Copy-move forgery image  

Fig. 1. Conception of copy-move forged image.

J. Fridrich [1] proposed an exacting match method for the forged image detection of a copymove forged image. J. Fridrich [1] studied detecting copy-move forgery image and explaining an eficient and reliable detection method. This method can sucesfuly detect the forged image part even if the copied area is enhanced/modified [1]. Popescu [2] proposed Principal Component Analysis (PCA) to reduce the representation of dimensions in image blocks [9]-[12]. We presented an eficient and robust technology that automaticaly detects duplicate areas of an image. This technique works by aplying PCA first on a smal fixed-size image block to produce a reduced dimension representation. Detection of copy-forgery has become one of the areas studied in blind image forensics. Christlein etc. [3] proposed that copymove forgery detection methods and procesing steps are in various post-procesing methods. The point of [3] is to evaluate the performance of previously proposed feature sets [3].

Most of the copy-move forgery image detection methods are divided by overlaping blocks in the matching search area [1-14]. The N×N image size data is divided into (N-B+1)2 overlaping blocks having a block size of B×B in order to match of copy-move forgery image detection [6], [9-14].

The exhaustive search method require huge computational complexity to match forged block in the copy-move forgery image detection [1-4], [9- 14]. However, Shin [1]-[14] proposed low complexity algorithms to match forged block. Shin [1-14] proposed a fast detection method of the copy-move forgery image using DCT and spatial domain. The proposed algorithm reduced computational complexity, when compared to the conventional various copy-move forgery detection methods. In this paper, we proposed a four step search fast detection of forgery image using discrete cosine transform. We proposed a new four step search using discrete cosine transform (FSSDCT). The computational complexity of our algorithm reduced 34.23% than conventional thre step search algorithm using DCT (TSSDCT).

2. THE PROPOSED METHOD

Copy-move forgery image is shown in Fig. 2.From the Fig. 2, C block image is copy image of the original image \(I(i, j)\) , \(I(P)\) is copy-move forgery image block. We have an original image \(I(i, j)\) by shifting motion vector (\(x, y\)), we can get the forgery image \(I(P)\), such that[9]

\(I(P)=I(i-x, j-y)\)       (1)

The C block and P block of the Fig. 2 show copy block and pasted block respectively. The Fig. 2 is copy-move forgery image by shifting motion vector x and motion vector y.

Fig. 2. Motion vector x and y of copy-move forgery image.

We proposed a fast detection method of forgery image using four step search algorithm using discrete cosine transform (DCT) (FSSDCT) to reduce computational complexity. The Koga et al [15] proposed the thre step search algorithm (TSS) for motion estimation in the spatial domain [9-12]. The TSS algorithm of video has ben widely used for motion estimation due to its simplicity and excelent performance

We proposed four step search algorithm using DCT (FSSDCT). Our FSSDCT algorithm works as folows. Our algorithm obtained DCT coeficients of 8×8 pixel block for FSSDCT in the frequency domain. The DCT algorithm [16] converts the image/video signal in the spatial domain 6into the image/video signal in the frequency domain [9-12], Most of image/video signal energy lies in the DC and low frequency region [1]; These represent the DCT DC (0) and thre (1, 2, 3) coeficients of Fig. 3 [14]. The high frequency of the DCT domain is often a smal energy value, and the energy of the high frequency region can be neglected with litle visible distortion [16]. The DCT transform algorithm is equation (1), also the Inverse DCT algorithm is shown in Equation (2) [16].

\(X(u, v)=\frac{2}{B} C(u) Q(v) \sum_{i=0}^{B-1 B-1} x(i, j) \cos \left[\frac{(2 i+1) u \pi}{2 B}\right] \cos \left[\frac{(2 j+1) v \pi}{2 B}\right]\)       (2)

Inverse DCT (IDCT) is

\(\begin{aligned} &x(i, j)=\frac{2}{B} C(u) C(v) \sum_{n=0}^{B-1} \sum_{v=0}^{B-1} X(u, v) \cos \left[\frac{(2 i+1) u \pi}{2 B}\right] \cos \left[\frac{(2 j+1) v \pi}{2 B}\right]\\ &C(0)=1 /(\sqrt{2}), C(u)=C(v)=1(u \neq 0, v \neq 0), \text { Where, } B i s a b l o c k s i z e \end{aligned}\)       (3)

The DCT transform coeficient DC value for u=0, v=0, is the average value of the DCT transform domain for the spatial domain B × B pixel block, where B is the 8 × 8 pixel block [10]. AC co￾eficients of the DCT transform domain are al oth￾er coeficients except the DC value.

Fig. 3. Algorithm of the DCTFSS.

The proposed algorithm try to find copy-moved motion vectors in the forged image using FSSDCT. The copy-moved motion vectors of forged image can be obtained by using FSSDCT, which reduces computational complexity. It wil be described in detail the proposed method in the folowing. Step 1: We use the DCT transform of Eq. (1) to compute the DCT coeficients from the forged input image by 8x8 pixel blocks [10]. The FSSDCT algorithm starts with a check point with the center of the DCT coeficient (0,0) in Fig. 3 and measures the horizontal and vertical lines for nine check points with a step size(SS) of SS=4, (4 pixels / 4 lines) in order to find copy-moved forged block image, and four-step search algorithm is performed around black check point. Find the minimum check point by calculating equation (4) from the nine check points. From Fig. 3, the minimum check point is (-4,-4).

Step 2 : From Fig. 3, Eight check points are set based on the DCT coeficient position of the check points (-4, -4) found in step 1, and the step size is set to 3, 3 pixel / 3 line in step 2. After performing FSSDCT on the eight check points, find check points satisfying minimum of equation (4). From step 2, the minimum check point is (-7, -7) in Fig.3.

Step 3 : From Fig. 3, Eight check points are set based on the DCT coeficient position of the check points (-7, -7) found in step 2, and the step size is set to 2, 2 pixel / 2 line in step 3. After performing FSSDCT on the eight check points, find check points satisfying minimum of equation (4). From step 3, the minimum check point is (-9,-9).

Step 4 : From Fig. 3, Eight check pointers are set based on the DCT coeficient position of the check points (-9, -9) found in step 3, and the step size is set to 1, 1 pixel / 1 line in step 4. After performing FSSDCT on the eight check points, find check points satisfying minimum of equation (4). From step 4, the minimum check point is (-10,-10). The best-match block (-10,-10) in the step 4 is found. The best-match check point of DCT coeficients location is the copy-moved motion vector value (-10,-10).

The computational complexity of FSSDCT algorithm neds 3 DCT coeficients check points. In the case of a maximum displacement window of 10 i.e. w= -10∼+10, the total number of checking points required is [9(Step 1) + 8(Step 2) + 8(Step 3) +8(Step4)] or 3 for search window 21×21 DCT coeficients. On the other hand, check points of the exhaustive search method ned 41 check points to search motion vector of copy-move forgery image.

We used block diference (BD) for matching of copy-moved forgery image detection based on FSSDCT. In order to search motion vectors x and y of copy-moved image forgery, we found minimum of block diference (BD) of eq. (4) based on FSSDCT.

\(\mathrm{BD}=\min \sum|D I(i+\ddot{n}, j+j j)-D I(i+i+x, j+j j+y)|\)       (4)

DI(i+i, j+j) is DCT coeficients of block at the position (i, j) of reference image, where, i=0,1,2, 3….N-B+1, j=0,1,2,3….N-B+1, i, j=0,1,2,3. DI(i+i+ x,j+j+y) are DCT coeficients of block at position (i+i, j+j) of the matching search image, and the motion vectors x and y of copy-move forgery image obtained by FSSDCT. We used 10 pixels for maximum displacement window of FSSDCT. The test image is 8 bits/pixel and 256×256 pixels, and block size is 8×8 pixel block. The FSSDCT is divided into non-overlaping 21×21 pixel blocks to search motion vector x and y of copy-move forgery image block in the matching search block image. Thus, the computational complexity is reduced to 4 instead of 64 in an 8×8 pixel block to obtain the motion vector x, y in the FSSDCT. The i and j in Equation (4) require the 4-computational complexity indicated by 0,1,2,3 in Fig. 4. Hence, the BD of FSSDCT reduces computational complexity.

If ( BD = 0) Copy-moved image forgery block (5) Else Not copy-moved image forgery block

The proposed method is four step search algorithm using DCT. The flowchart of the proposed method FSSDCT is shown Fig. 5. From equation (5), if BD is 0, the copied block is the same as the moved block, so that is the copy moving counterfeit block image [1-14]. If BD is not 0, the copied block image is diferent from the atached block image, so the block image is not a duplicate move counterfeit block [1-14].

Fig. 4. One DC (0) and thre (1,2,3) low frequency coeficients.

Fig. 5. The flowchart of proposed DCTFSS

3. EXPERIMENTAL RESULTS

We proposed a fast detection algorithm for copy-moved forgery image using four step search algorithm by discrete cosine transform (FSSDCT). The proposed FSSDCT method reduces computational complexity much more than the conventional forgery detection algorithms. The test image for the simulation, Bridge, Car3, and Airplane images are 8 bits and the resolution is 256×256 pixels [17]. The matching search area of the test image is divided into 21×21 which does not overlap from the first position (0,0) of the im￾age to the last image position (25,25). BD of copy-moved image forgery detection is Equation (4) based on FSSDCT method. In this paper, the computational complexity of the FSSDCT algorithm requires four DCT co￾eficients for the 21×21 pixel block matching search per checking point. In order to reduce computa￾tional complexity of the proposed FSSDCT algo￾rithm, one DC and thre low-frequency DCT co￾eficients per checkpoint are suficient instead of 64 checkpoints in an 8×8 pixel block.

Table 1 shows the computational complexity and compares the proposed FSSDCT algorithm with the existing methods. The proposed fast FSSDCT algorithm detected 9% of copy-move forgery images.

Table 1. Computational complexity of the proposed FSSDCT and conventional methods

From Table 1, IR, BS, MSACPN, FD, CC are image representation, block size of reference region, matching search area checking points number, feature dimension, computation complexity (based on reference[1])method, respectively.

The proposed FSSDCT algorithm reduced 9.52 % of computational complexity than exhaustive search [1]. As shown in Table 1, the proposed FSSDCT method reduces the computational complexity compared to the conventional method [1],[2],[7], because the FSSDCT method used DC and thre low frequency DCT coeficients which characteristic of DCT compresion in the frequency domain, and it is a matching search area -10∼+ 10, non-overlaping 21 × 21 pixel block.

The Fig. 6, 7, and 8 showed performance of proposed method. Figures showed original images, copy-moved image forgery, detection of copymoved image forgery in the Fig. 6, 7, and 8. From the Fig. 6(c), left black box is copied, right black box is moved to image forgery block. From Fig. 7(c) and 8(c), right black box is copied, left black box is moved to image forgery block. From Fig. 6, 7, and 8, our algorithm detected above 9% copymoved image forgery. Copy-moved forgery image detection rates of Bridge, Car3, and Airplane are 9.70%, 9.17%, and 9.01%, respectively. Detection rate of copy-move forgery image (DR) is expresed by equation (6).

\(\mathrm{DR}=\frac{D P N}{T P N}\)       (6)

where, detected pixel number of copy move image (DPN), total pixel number of copy move image (TPN).

(a) Original Bridge image

(b) Copy-Moved forgery Bridge image

(c) Detection block of Copy-Moved forgery Bridge image (Black box)

Fig. 6. Result of proposed FSSDCT

(a) Original Car3 image

(b) Copy-Moved forgery Car3 image

(c) Detection block of Copy-Moved forgery Car3 image (Black box)

Fig. 7. Result of proposed FSSDCT.

(a) Original Airplane image

(b) Copy-Moved forgery Airplane image

(c) Detection block of Copy-Moved forgery Airplane image (Black box)

Fig. 8. Result of the proposed FSSDCT.

4. CONCLUSION

we proposed fast detection algorithm of forgery image using four step search based on discrete cosine transform. We proposed a new four step search using discrete cosine transform (FSSDCT). The computational complexity of our algorithm reduced 34.23% than conventional thre step search algorithm using DCT (TSSDCT).