Detection of Copy-Move Forgery Using Wavelet

Decomposition

Abhishek Kashyap Department of Electronics and Communication Engineering,

Jaypee Institute of Information Technology, Noida-20 1 304, Uttar Pradesh, India.

Shiv Dutt Joshi Department of Electrical Engineering, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi- 1 100 16, India.

Email: abhishek.kashyap @jiit .ac .in

Abstract-Nowadays, it is possible to copy and paste important information from one image to other or within the same image, without leaving any clues of tampering. Hence, the authenticity of digital images can no longer be taken for granted. There is a requirement for the implementation of new powerful and efficient algorithms for forgery detection of a tampered images. In this paper, we have proposed a new computationally efficient algorithm for copy-move forgery detection of an image using wavelet decomposition method. The proposed method achieves an accuracy of 86.67 % within a small processing time.

Index Terms-Blur moment; peA; JPEG; PSF.

I. INTRODUCTION

In our society digital images has significant role in every­one's life, which are widely used in medium of cOlmnunica­tion, forensic investigations, insurance processing, surveillance systems, intelligence services, medical imaging and political campaigns . The average user today has access to sophisticated photo-editing and computer graphics software, high perfor­mance computers, and high-resolution digital cameras [ 1 ] .

Cheap and easy availability o f sophisticated and powerful image manipulation tools have caused doubts on the integrity of digital images. Its a fact that many of the images we come across in our daily life are either fake or altered. There are significant number of magazines and newspapers which are publishing doctored images . The courts all over the world accept digital photographs, but in the prevalent circumstances require reliable mechanisms to assure authenticity of images [2] . In the following, we will discuss different types of digital image forgeries and digital images forgery detection approaches .

This paper is organized as follows . The motivation of image forgery detection has been discussed in the first section. The second section describes the techniques used for image forgery detection and types of digital image forgery. The third section describes a novel method based on wavelet decomposition of an image for forgery detection. The fourth section provides the computer simulation results and the last section presents conclusions and the future work.

II . TECHNIQUES USED FOR IMAGE FORGERY DETECTION

As pointed out in [3], there are two approaches for detection of digital image forgery such as active approach and passive approach.

Email: sdjoshi @ee.iitd.ac . in

1) Active approaches: In the active approach method, we insert certain authentic information inside the image at the time of capturing or after capturing the image, it will be further processed by using watermarking technique and after that it will be disseminated to the public .

2) Passive approaches: In the passive approach method, we will never insert any information for authentication purpose, rather it works purely by analyzing binary information of digital image.

A. Types of digital image forgeries

The detailed image forgeries are discussed in this section, which can be of different types such as image retouching, image splicing and cloning etc . Among them cloning is one of the most common image manipulation technique; which is copy and paste portions of the image to conceal a person or object in the scene [3] . It will be difficult to detect cloning visually. To detect these forgeries we have different forgery detection tools, they are roughly grouped into five categories [3] : 1 ) camera based techniques that exploit artifacts introduced by camera lens, sensor, or on chip post processing ; 2) format-based techniques that leverage the statistical corre­lations introduced by a specific lossy compression scheme; 3) pixel based techniques that detect statistical anomalies intro­duced at the pixel level; 4) geometric based Techniques that make measurement of object in the world and their positions relative to the camera; 5) physically based techniques that explicitly model and detect anomalies in the three dimensional interaction between physical objects, light and the camera.

Many researchers have suggested different algorithms for forgery detection [4] - [ 12] . Therefore in this paper we have proposed a new image forgery detection algorithm for copy­move type of forgery. This algorithm has many advantages as compared with existing digital image forgery detection methods, which have been presented in this paper.

B. Drawback of existing method for forgery detection

The existing method based on blur moment invariants [4] follows the different steps for image forgery detection, such as overlapping blocks, blur moment invariant representation of each blocks, principal component analysis (PCA), duplicated region map. This method has some drawbacks : 1 ) we have to

978-1 -4799-1 607-8/1 3/$31 .00©201 3 IEEE 396

define threshold parameter; 2) it can't detect tampered region of large image and it requires longer time for analysis, hence we can't use this method for real time analysis of forged images .

III . PROPOSED METHOD FOR IMAGE FORGERY DETECTION

A novel image forgery detection method is presented in this section, which is used to detect copy-move image forgeries. The proposed algorithm for image forgery detection involves the following steps : 1 ) wavelet decomposition of the input image; 2) tiling the image with overlapping grid or block; 3) blur moment invariants representation of each overlapping blocks ; 4) principal component analysis ; 5) block similarity analysis ; 6) duplicated regions map creation.

To facilitate the description, we begin with a (M x N) di­mensional forged image. From subsection 1 -5 we will develop our proposed algorithm.

1) Wavelet decomposition: This method begins with the computation of wavelet transform of the image, after comput­ing wavelet transform we have the low-high bands, the high­low bands and the high-high bands of the image at different scales. We have further processed the coarse part of the image for image forgery detection. We have used Harr wavelet, 1/J(x) , which is orthogonal to the scaling function and it is defined [ 1 3] - [ 15] by the eq. ( 1 ) 00

1/J (x) = L (- 1 ) kaN_ 1_kV20 (2x - k) . ( 1 ) k=-oo

The two dimensional wavelet decomposition of the function g (x , y) is defined [ 15] by the eq. (2) 00 00

f (x , y) = L L L dj,k , l1/Jj,dx)1/Jj, l (y) . (2) j=-oo k=-oo l=-oo

2) Tiling the image with overlapping grid or block : The wavelet decomposed image is being tiled [4] by the block of R x R pixels . This block is horizontally slid by one pixel rightwards starting with the upper left corner and ending with the bottom right corner as shown in Fig. 1 . Here the size of the duplicated regions are assumed to be larger than block size and the total number of overlapping blocks are (M - R + 1 ) x (N - R + 1 ) for an image size of (M x N) pixels .

I - - � - - - - - - - - - - - - - -

�--1 Image

- - - - - - - - - - - - - - -I->f--t--f--t--f--t--t-+t-H 2

(N, - II)(N, - II ) 2 3 . . .

Fig. 1 . Pixel block scan and array dimensions for the matching algorithm [ 1 6]

� Object 0 -/ Image

PSF

Fig. 2. Description of PSF [ 1 7]

3) Blur moment invariants representation of each overlap­ping blocks: Variation in duplicated region is introduced by the 2-D convolution of duplicated region and point spread function (PSF) [4]

g (x , y) = (J * h) (x , y) + n(x , y) ,

where, f (x , y) is the function of duplicated region and g(x , y) is the acquired region created by falsifier via

convolution of f (x , y) and PSF.

(3)

The PSF is assumed to be axial symmetric and energy­preserving that is defined by

h (x , y) = h (-x , y) = h(y , x) , (4)

1:00 1:00 h (x , y) dxdy = 1 . (5)

PSF describe the response of an imaging system to a point source or point object. The more general term for PSF is a system's impulse response, which is shown in Fig . 2.

Each block is represented by blur invariants, which are functions of central moments. The two-dimensional (p + q)th order moment mpq of image function f(x , y) is defined by the integral

j+OO j+oo mpq = -00 -00 xPyq f (x , y)dxdy . (6)

The two-dimensional (p + q) th order central moment J.Lpq of f(x , y) is defined as [4]

(7)

Xt = mlO /mOO Yt = mol /moo , (8)

where Xt and Yt denote the centroid or the center of gravity of f (x , y) .

By supposing that

g (x , y) = (J * h) (x , y) + n(x , y) . (9)

We can simply derive that central moments of g(x , y) [4] are defined as

p q ( ) ( ) (9) _ P q (f) (h) J.Lpq - L L k j J.Lkj J.Lp-k ,q-j '

k=O J=O ( 10)

397

We are looking for features invariant to blur. Feature B is called blur invariant [4] , which is shown by the eq. ( 1 1 )

B (!) = B(f*h) = B(g) . ( 1 1 )

We can construct blur invariants based o n central moments [ 1 8] of any order by using the following recursive relation, which is shown by the eq. ( 12 )

1 k m2 ( p B (p, q) = /-lpq - a/-lpq - L L t - 2i /-loo n=O i=ml B (p - t + 2i , q - 2i ) /-It=2i , 2i , ( 1 2)

where,

k = [P + � - 4 ] , t = 2 (k - n + 1 ) , ( 1 3)

ml = max (0 , [ t -�+ 1 ] ) , m2 = min (� , [�J ) , ( 1 4)

a = 1 {==} P 1\ q is even, a = 0 {==} P V q is odd. ( 1 5)

Our algorithm uses 24 blur invariants [ 1 9 ] , [20] up to the seventh order to create the feature vector

Normalized invariants are also invariant to contrast change, which improve the duplication detection ability of the algo­rithm [4] , which are defined by the eq. ( 1 7)

, B · Bi = (R/2)� /-loo ' ( 1 7)

where R is defined as the block size and r the order of B i . In case of gray-scale image, each block i s represented by a

feature vector of length 24. Moment invariants of each block in each channel are computed separately for RGB images, resulting in feature vector Brgb = {Bblue , Bred , Bgreen } of length 72.

4) Principal component transformation: In this step, we have reduced the dimensionality of the Blur moment invariants of each overlapping blocks and these blocks are carrying the information related to the coarse part of wavelet decomposed image.

We have reduced the dimensionality using principal com­

ponent analysis (PCA). Let us consider X vector

X = (X l , X2 , X3 , X4 , · . . XmO , · . . Xm ) , ( 1 8)

consider only mo in m neglect (m-mo) .

We did not k,now where maximum information occurs . So we transform X of m dimensional to another space,

( 1 9)

We have designed T matrix, by which we got X new ' This vector allows us to chop off the values which are having very low variance, then we can easily chop off. The above

mentioned step is known as principal component transform (PCT) [2 1 ] .

Projection of random vector X onto unit vector 7/[, which is defined by the eq. (20 )

ai = XT .7/[ = ;;f.x, (20)

where ai is projection and qi is orthogonal basis. Summa­tion of these two is defined by the eq. ( 2 1 )

m X = L ai .7/[ .

i= l

E[aiaj ] = AiDij , if =? i = j E l ; i � j E 0 , ���T -:-+ E[qi X X qj ] = AiDij ,

� ��T -:-+ qi E [X X ] qj = AiDij , ;;fR qj = AiDij , R7/[ = Ai7/[ ,

(2 1 )

(22)

(23)

(24)

(25)

(26)

If equation (25) is satisfy then equation (26) is also sat­isfied, then we have taken eigen values in decreasing order. After dimensionality reduction, we can also reconstruct the coarse part of the wavelet decomposed image using reduced dimensionality vector.

5) Blocks similarity analyses : As pointed out in [4] , in this step similarity of blocks will be checked. This process carried out by calculating euclidean distance between the blocks, if any blocks has lesser Euclidean distance then they are similar. This is a necessary condition but not sufficient, after finding similar blocks we have to check their neighborhood if their neighborhood is also similar then there is a high probability that they are duplicated and they must be labeled.

The similarity measure S is defined as

1 S (Bi , Bj ) = l + p (Bi , Bj ) ' where p is a distance measure in the euclidean space

(27)

(28)

if S(Bi ' Bj ) � T, where T is the minimum required similarity. Then analyzes the neighborhood of Bi and Bj . Threshold T plays a very important role to take a decision for image forgery and it expresses the degree of reliability with which blocks i and j correspond with each other. We have modeled the threshold as per image characteristics .

For analyzing the blocks neighborhood, we have chosen 16 neighboring blocks with a maximum distance of 4 pixels from the analyzed block.

S (block (i + xr , j + Yr ) , block (k + Xr , 1 + Yr ) ) � T, (29)

398

where x c (-4,-3 . . . 4) and y c (-4,-3 . . . 3 , 4) and r= 1 . . . 16 . If S(block (i , j ) , block(k , l ) ) ?: T, and

V((i - k) 2 + (j - l ) 2) < D , (30)

Then we have determined the minimum size of the copied area using (29) and (30) . If similarity between the blocks is greater than the threshold T and distance between them is less than the threshold D, then these blocks will not be analysed further and will not be assigned to as duplicated. Threshold D is a user-defined parameter for determining the minimum image distance between duplicated regions and it is used to obtain more precise results for image forgery detection. We have designed a matrix Q, which will be same size of the input image. Elements of this matrix are either zero or one. An element of this matrix is set to one if the block at this position is duplicated.

6) Duplicated regions map creation : As pointed out in [4] , the output of this method is showing a duplicated regions map, which are define as the duplicated image regions . It is created by the multiplication of each element of J(x , y) by its respective element in Q(x, y) .

IV. RESULTS

In this section, we discuss the results of the method de­scribed in section III. We have analyzed different images for detection of copy-move forgery, these images have been processed using our proposed algorithm for detection of copy­move forgery, after processing the images, we have obtained the possible sign of the tampering as shown in Fig. 3-7 . Our proposed method has the detection accuracy 86.67 %, this was obtained when we have performed a blind experiment containing an unknown mixture of 15 authentic and forged JPEG images . Comparison between proposed method and an earlier method [4] on the basis of execution time is shown in Fig . 8 .

V . CONCLUSION AND S COPE F O R FUTURE WORK

In this paper, we have analyzed the area of image forensics related to the detection of digital image tampering and the detection accuracy was found to be heavily dependent on the amount of time spent for analyzing the results as well as any pre-existing tampering knowledge of the image.

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Fig. 3. Result of Image [4] l. l

I Fig. 4. Result of Image [4] l.2

. . . II Fig. 5. Result of Image [ I I ] I .3

Fig. 6 . Result of Image [4] l .4

Fig. 7 . Result of Image [4] 1 .5

The experimental results show the high ability of the proposed copy-move forgery method to detect copy move forgery in an image, even in the presence of noise, blur or contrast changes in the copied areas. The proposed method for copy­move forgery detection is better than the method presented in reference [4] . It can process large size of an image and also reduce the time complexity. In this paper we considered harr basis, but the system performance can be compared with other basis like DCT or deubechey' s basis . Here we restrict

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the analysis to linear but one can verify with scaled or rotated forgery region of the images .

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