Copy-Move Forgery Detection and Localization

 Understanding if a digital image is authentic or not, is a key purpose of image forensics.
There are several diff erenttampering attacks but, surely, one of the most common and immediate one is copy-move. A recent and eff ectiveapproach for detecting copy-move forgeries is to use local visual features such as SIFT. In this kind of methods, SIFTmatching is often followed by a clustering procedure to group keypoints that are spatially close. Often, this procedurecould be unsatisfactory, in particular in those cases in which the copied patch contains pixels that are spatially verydistant among them, and when the pasted area is near to the original source. In such cases, a better estimationof the cloned area is necessary in order to obtain an accurate forgery localization. In this paper a novel approach ispresented for copy-move forgery detection and localization based on the J-Linkage algorithm, which performs a robustclustering in the space of the geometric transformation. Experimental results, carried out on diff erent datasets, showthat the proposed method outperforms other similar state-of-the-art techniques both in terms of copy-move forgerydetection reliability and of precision in the manipulated patch localization.

Nowadays, digital crime is growing at a rate that farsurpasses defensive measures. Sometimes a digital me-dia content, such as an image or a video, may be foundto be incontrovertible evidence of a crime or of a malev-olent action. By looking at a digital data as a digitalclue, multimedia forensics technologies are introduc-ing a novel methodology for supporting clue analysisand providing an aid for making a decision on a crime. Multimedia forensics deals with developing tech-nological instruments which generally allow to deter-mine, without any additional information inside the im-age (e.g. a watermark), if that asset has been tamperedwith or which has been the adopted acquisition device.In particular, tampering detection refers to the problemof assessing the authenticity of digital images , andthis is the topic of this paper.

and features matching, and improves our previous work by introducing a new robust clustering phasebased on the J-Linkage algorithm, and an accurateforgery localization procedure. The localization of theduplicated region has been set up on the basis of theclusters obtained in the previous phase. This is done us-ing ZNCC (Zero mean Normalized Cross-Correlation)between the original image and the warped image ob-tained from the estimated geometric transformation oc-curred in the tampering attack. In order to obtain anaccurate localization, it is necessary to have an effec-tive clustering procedure (like the one presented in thispaper) that is able to guarantee a good estimate of thegeometric transformation.The rest of this paper is organized as follows. In Sec-tion 2, we discuss the existing works concerning the de-tection of copy-move forgeries. Section 3 presents theproposed copy-move forgery detection and localizationmethod, while Section 4 contains experimental results.Conclusions are finally drawn in Section 5.

As discussed earlier, copy-move manipulations in-volve concealing or duplicating one region in an imageby overlaying portions of the same image on it. In orderto address the problem, researchers have developed var-ious techniques which can be classified into two maincategories: block-based and visual feature-based

These methods seek a dependence between the im-age original area and the pasted one, by dividing theimage into overlapping blocks and then applying a fea-ture extraction process in order to represent the im-age blocks through a low dimensional representation.

Different block-based representations have been pre-viously proposed in the literature, such as PrincipalComponent Analysis, Discrete CosineTransform  and Discrete Wavelet Transform, for both tasks of copy-move detection and image splicing . Recently, inthe study of Basharetal., the authors proposed aduplication detection approach that can adopt two ro-bust features based on DWT and kernel principal com-ponent analysis (kPCA). A different kind of featuresare used in, in fact the authors choose the aver-ages of red, green and blue components with other fourfeatures, computed on overlapping blocks, obtained bycalculating the energy distribution of luminance alongfour different directions. To improve the computationalcomplexity of these methods, in  the authors pro-posed to use the radix sort for sorting the feature vectorsof the divided sub-blocks, as an alternative to lexico-graphic sorting, which is commonly adopted. However,all these methods assume that the copied region has notundergone any post-processing such as scaling, rotationand JPEG compression.To deal with this issue, a preliminary work by Mah-dian
et al.has been presented in  where the authorsproposed a block-based representation calculated usingblur invariants. They used PCA to reduce the number of features and a k-tree to identify the interested regions.Authors in proposed a different kind of feature thatis based on the Fourier-Mellin Transform that is invari-ant to small rotation and resizing of the copied regions.However, the technique fails when the rotation and theresizing is significant. This method was improved in which better rotation invariance was achievedby taking projections along angular directions insteadof radius direction. However, also in this case the scaleinvariance seems to be valid only over a small range,and the number of false positives yielded is quite high.Recently, methods more robust to reflection, rotationand scaling have been proposed in the literature. In overlapping blocks of pixels are mapped into log-polarcoordinates, and then summed along the angle axis, toobtain a one-dimensional descriptor invariant to reflec-tion and rotation. Wangetal.  proposed the useof circle region instead of square block and adopt asfeature the mean of the intensities of the circle regionwith different radii to overcome the effect of rotation.Ryuetal. exploited the Zernike moments as fea-tures since their magnitude is algebraically invariant torotation transformation. To this end, a more generalapproach is presented in which is reported atechnique to better detect variations in rotation and scal-ing in the copied part by introducing a post-processing.

We present a novel approach for detecting copy-moveforgeries based on SIFT features and J-Linkage cluster-ing. A schema of the whole system is shown in Fig-ure 2. The first step consists of SIFT feature extractionand keypoint matching, the second step is devoted tothe clustering and forgery detection, while the third onelocalizes the copied region, if a tampering has been de-tected. We summarize the whole procedure for tamper-ing detection and localization in Algorithm 1.
3.1. Feature extraction and keypoint matching The first step in our approach is based on SIFT fea-tures since they are robust to scaling, rotation and a ffi netransformations that are well-suited for the detection of copy-move forgeries as has been recently demonstratedin. We detect keypoints that are stable local ex-trema in the scale space and, for each of them, a featurevector is computed from a local pixel area around thedetected point. Given a test image I ,
let S : = { s 1 ,..., s n } be the list of n interest points taken from this image,where s i = { x i ,
f i } is a vector containing the keypointcoordinates x i = ( x , y ) and f i is the feature descriptor of the local patch around the keypoint (i.e. an histogram of gradient orientations of 128 elements).In presence of a copy-move manipulation the ex-tracted SIFT keypoints from the copied and the orig-inal regions have similar descriptor vectors. There-fore, matching among SIFT features is adopted to de-tect if an image has been tampered with and, subse-quently, localize such forgery. The simplest approachto match keypoints is to fix a global threshold on theEuclidean distance between descriptors but, due to thehigh-dimensionality of the feature space, this approachobtains a low accuracy because some descriptors aremuch more discriminative than others. For this reasonLowe considers, given a keypoint, not only the dis-tance with the first most similar keypoint, but also withthe second one; in particular, he uses the ratio betweenthe distance to the candidate match and the distance tothe second similar feature point (i.e. the so-called 2NNtest). To declare a match, this ratio must be lower thana fixed threshold
τ (often equal to 0 .6). This techniqueworks well when a region is copied one time, but not if it is copied several times. To deal with this case, we usea generalization of Lowe’s matching technique
 ( g 2NNtest) recently proposed by Amerini et al. The g2NN starts from the observation that in a high-dimensional feature space such as that of SIFT features,keypoints that are different from the one considered.

share very high and very similar values (in terms of Eu-clideandistances)amongthem. Instead, similarfeaturesshow low Euclidean distances respect to the others. Theideaofthe2NNtestisthattheratiobetweenthedistanceof the candidate match and the distance of the 2
nd near-est neighbor is low in the case of a match (e.g. lowerthan 0.6) and very high in case of two “random fea-tures” (e.g. greater than 06). Our generalization con-sists in iterating the 2NN test between
i /d i + 1 until thisratio is greater than τ (in our experiments we set thisvalue to 0.5). If k is the value in which the procedurestops, each keypoint in correspondence to a distance in { d 1 ,..., d k } ( where 1  k <
n ) is considered as a matchfor the inspected keypoint. Using this g 2NN strategy onall the keypoints S
, we obtain a set of q matched pairs P : = { p 1 ,..., p q } , where p i = ( s , s  ). It allows, in thefollowing steps, to identify the duplicated regions andtherefore detect if the image has been tampered with.

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