Information dense feature descriptors using multiple lev- els,

Information Sciences 345 (2016) 226–242Contents lists available atScienceDirectInformation Sciencesjournal Dense Descriptor and Hierarchical FeatureMatching for Copy–Move Forgery DetectionXiuli Bi, Chi-Man Pun?, Xiao-Chen YuanDepartment of Computer and Information Science, University of Macau, Macau SAR, Chinaarticle infoArticle history:Received 17 September 2015Revised 6 January 2016Accepted 11 January 2016Available online 4 February 2016Keywords:Copy–Move Forgery Detection (CMFD)Multi-Level Dense Descriptor (MLDD)Hierarchical Feature MatchingColor Texture DescriptorInvariant Moment DescriptorabstractIn this paper, aMulti-Level Dense Descriptor(MLDD) extraction method and a Hierarchi-cal Feature Matching method are proposed to detect copy–move forgery in digital images.TheMLDDextraction method extracts the dense feature descriptors using multiple lev-els, while the extracted dense descriptor consists of two parts: theColor Texture Descriptorand theInvariant Moment Descriptor. After calculating theMLDDfor each pixel, the Hier-archical Feature Matching method subsequently detects forgery regions in the input im-age. First, the pixels that have similar color textures are grouped together into distinctiveneighbor pixel sets.

Next, each pixel is matched with pixels in its corresponding neigh-bor pixel set through its geometric invariant moments. Then, the redundant pixels frompreviously generated matched pixel pairs are ?ltered out by the proposed Adaptive Dis-tance and Orientation Based Filtering method. Finally, some morphological operations areapplied to generate the ?nal detected forgery regions. Experimental results show that theproposed scheme can achieve much better detection results compared with the existingstate-of-the-art CMFD methods, even under various challenging conditions such as geo-metric transforms, JPEG compression, noise addition and down-sampling.© 2016 Elsevier Inc.

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All rights reserved.1. IntroductionRecently, there has been much interest in Copy–Move Forgery Detection (CMFD). Copy–move forgery (CMF) is one of themost common types of image forgery. An image with CMF contains at least two regions with identical content where one ormore distinct regions are copied and pasted into one or more destination locations in the same image to conceal importantinformation.

Sometimes, the copied content is modi?ed using a pre-processing operation such as scaling, rotation, noiseaddition, or JPEG compression to make it match the surrounding regions in such a way that the tampering is not visible.Many CMFD schemes have been proposed for ?nding these tampered regions, and most of the detection schemes follow acommon pipeline that includes three main steps9: (1) feature extraction, which extracts an appropriate feature from eachof the blocks or interesting pixels; (2) feature matching, which obtains the best match of the blocks or interesting pixelsbased on corresponding extracted features; and (3) post-processing, which ?lters the offset ?eld and the linking pixels withtheir nearest neighbors to improve the detection accuracy.Generally speaking, the three-step pipeline can be applied to each pixel of the host image, in which case the ?eld isdense. Alternatively, it can be applied to selected key points, in which case the ?eld is sparse. Of the existing CMFD schemes,the keypoint-based methods1,7,13,18,26,31,35were proposed, which extract a relatively small set of pixels from the host?Corresponding author. Tel.:+853 88224369.

E-mail addresses:[email protected](X. Bi),[email protected](C.-M.

Pun),[email protected](X.-C. Yuan).http://dx.doi.

org/10.1016/j.ins.2016.01.0610020-0255/© 2016 Elsevier Inc.

All rights reserved.X. Bi et al. / Information Sciences 345 (2016) 226–242227images and then perform dense matching based on the feature descriptors of the keypoints.

This approach is usually muchfaster than methods that are based entirely on dense matching. Pan and Lyu ?rst proposed the keypoint-based algorithmin26, where a Scale Invariant Feature Transform (SIFT)21was used to extract the keypoints and which can guaranteerobustness against geometrical transformations. Similarly, SIFT was frequently used for feature extraction in CMFD19,28.Other well-known local descriptors such as Speeded Up Robust Features (SURF)2and DAISY33have also been consideredfor feature extraction and keypoint-based CMFD1,13,31,35. A benchmarking paper6evaluated the related approaches andclearly showed the performance gaps.

Although the computational complexity of the sparse-?lled methods is comparativelyless because the number of keypoints represents only a relatively small set of all the pixels in the image, most of them areintrinsically less accurate than the dense-?eld methods, especially when copy–moves involve only smooth regions, whichis typically the case with occlusive forgeries. In addition, the performance of the feature points-based forgery methods ishighly related to the resolution of the host images6. When the host image is down-sampled, the performance of thefeature points-based forgery methods drops considerably.Considering those problems, we focus on the dense-?eld approach in this paper.

Unfortunately, the complexity of thedense ?eld approach is relatively high because all the pixels undergo the three-step pipeline. The solutions to this problemare to intrinsically simplify the feature extraction and speed up the matching phase itself as much as possible. In addi-tion to considering detection accuracy and complexity, the robustness of the performance should be accounted for, whichmeans that the performance should not be affected by common distortions such as JPEG compression, noise addition, orgeometric distortions such as rotation and scaling. In the existing CMFD schemes, the dense ?eld approaches are alwaysknown as block-based approaches because the host images are usually divided into overlapping blocks, each of which isconsidered to be an individual superpixel for calculating the corresponding pixel features. In the existing block-based CMFDmethods3–5,10,14–16,20,22,24,25,27,29,32,34,38, transforms such as the Discrete Cosine Transform (DCT)5,10,14, Prin-cipal Component Analysis (PCA)24,27, Wavelet25,SVD15,38, or Histogram Of Orientated Gradients (HOG)17areapplied to extract the features, which improves the robustness.

Fridrich et al.10calculated the quantized DCT coe?cientsof the overlapping blocks as feature descriptors. Popescu and Farid27used the PCA method to reduce the feature dimen-sions. Mahdian and Saic24employed the 24 blur-invariant moments as block features. However, these features are notparticularly robust against geometric distortions such as rotation and scaling. In consequence, Ryu et al.29used Zernikemoments as block features, and Li20applied the polar cosine transform to calculate the coe?cients for the block featuresto achieve rotation invariance.

Additionally, Wu et al.34proposed applying the Fourier–Mellin Transform to calculate theblock features, thus achieving scale invariance. Lee et al.17applied HOG to each block and extracted statistical features tomeasure the similarity.

Lynch et al.23used the average gray values of blocks as dominant descriptors. Recently, Cozzolinoet al.

9proposed an e?cient dense ?eld technique for CMFD and the fast approximate nearest-neighbor search algorithm,PatchMatch, was re-sorted. The experiments show that their dense-?eld technique is more reliable than the keypoint-basedCMFD approaches.The above description compels us to focus on the dense ?eld approach. In this paper, we propose a novelMulti-LevelDense Descriptor (MLDD)extraction method, which includes theColor Texture Descriptor(MLDD_CT)andtheInvariant MomentDescriptor(MLDD_IM) to extract the dense features instead of the existing sparse features.

After obtaining theMLDDforeach pixel, the pixels must be compared to each other to ?nd the matched pairs. Then, to reduce the high computationalcomplexity of the dense-?eld approach, to enhance the robustness against various attacks, and to make the result of thematching process be as accurate as possible, we propose a novel Hierarchical Feature Matching method that includes threemain steps: 1.Color Texture Based Filtering,2.Geometrical Invariant Moments Based Matching,and3.Adaptive Distance andOrientation Based Filtering.

Using theColor Texture Based Filteringtechnique, we sort the pixels of the host image accordingto theirMLDD_CTvalues to generate the selected neighbor pixels set for each pixel. In this way, pixels with similar colortexture will be grouped together into distinctive neighbor pixel sets. With theGeometrical Invariant Moments Based Matchingtechnique, we match each pixel with its corresponding neighbor pixel set only through itsMLDD_IM, which greatly reducesthe computational complexity. Finally, theAdaptive Distance and Orientation Based Filteringtechnique can help to ?lter outredundant pixels and improve the detection accuracy.

In the following, we will provide the framework of the proposed CMFD algorithm using Multi-Level Dense Descriptors(MLDD) and Hierarchical Feature Matching inSection 2and explain the proposedMulti-Level Dense Descriptorextractionand Hierarchical Feature Matching methods in detail. InSection 3, a large number of experiments will be conducted todemonstrate the effectiveness and robustness of the proposed method. Conclusions are drawn inSection 4.2. Proposed Copy–Move Forgery Detection algorithmThe proposed CMFD method consists of two stages. The ?rst stage isMulti-Level Dense Descriptor Extraction,in which theMLDD is generated as a pixel feature.

Each MLDD contains two parts: aColor Texture Descriptor(MLDD_CT)andanInvariantMoment Descriptor(MLDD_IM). The second stage isHierarchical Feature Matching, in which the pixels of the host image are?rst sorted according to theirMLDD_CT, and a selected neighbor pixel set is generated for each pixel. In this way, pixelswith similar color texture are grouped together into distinctive neighbor pixel sets. Then, each pixel is matched with itscorresponding neighbor pixel set through the calculatedMLDD_IM, and matched pixels are indicated as matched pixel pairs.Finally, the Adaptive Distance and Orientation based Matching method is proposed to ?lter out the redundant pixels fromthe previously generated matched pixel pairs, and the ?nal Detected Forgery Regions can be generated from the remainder.228X. Bi et al. / Information Sciences 345 (2016) 226–242Fig.

1.Framework of the proposed CMFD method.Fig. 1shows the framework of the proposed CMFD method.Sections 2.

1and2.2, respectively, demonstrate the details of theMulti-Level Dense DescriptorextractionandHierarchical Feature Matching.2.1. Multi-Level Dense Descriptor extractionExisting forgery detection methods are usually divided into two categories: block-based forgery detection methods andfeature points-based forgery detection methods.

In the existing block-based methods3,4,10,15,22,24,27,29, the input imageis usually divided into overlapping blocks of a regular shape, for example, when the size of an input image isM×Nandthe block size isB, then the number of blocks is(M?B+1)×(N?B+1); therefore, each block will be matched with theother(M?B+1)×(N?B+1)?1 blocks to ?nd corresponding matched blocks. In this case, the computational complexityof the block matching operation increases as the number of pixels in the host image increases. To reduce the computa-tional complexity, one widely used solution is to downscale the host images and divide those downscaled images intonon-overlapping blocks19,28. However, the process of downscaling the image often makes it di?cult to extract features.In the existing feature points-based forgery detection methods1,7,13,26,31,35, image keypoints, which are known as sparsefeatures, are extracted and matched with one another to identify duplicated regions. In1,7,13,26,SIFT21was appliedto the host images to extract feature points; in31,35,SURF2was applied to extract features instead of SIFT. However,although these methods can locate matched keypoints, most of them cannot locate forgery regions very well. In addition,the performance of feature points-based forgery methods is closely related to the resolution of the host images6.

Whenthe host image is down-sampled, the performance of the feature points-based forgery methods drops considerably.Considering the above-mentioned problems, in this paper, we propose aMulti-Level Dense Descriptorextraction methodto extract dense features instead of sparse features. In addition, we propose a novel matching method to reduce the com-putational complexity typically caused by dense feature matching methods. First, for each pixel, we extract its color texturefeature, denoted byMLDD_CT; then, the pixels of the host image are sorted according to their color texture descriptorsMLDD_CT,and a selected neighbor pixel set is generated for each pixel. Afterward, the geometric invariant moments of eachX.

Bi et al. / Information Sciences 345 (2016) 226–242229Fig. 2.The mask sequence demonstration. (a) Demonstration of the multi-level mask of the given pixel, and (b) de?ned mask sequence.pixel are calculated and denoted asMLDD_IM.

In this way, for each pixel, theMLDD_IMis matched only with its corre-sponding neighbor pixel rather than with all the other pixels in the host image. Therefore, the computational expense canbe decreased to a great extent when using the proposed method.S e c t i o n s 2 .1.1and2.

1.2will explain the details of thecalculation of the proposed color texture descriptorMLDD_CTand invariant moment descriptorMLDD_IM, respectively.2.1.1.

Color Texture Descriptor (MLDD_CT) calculationConsidering that the human visual system is more sensitive to the luminance component than to the chrominance com-ponents, we ?rst convert the host image from the RGB color space to the YCbCr color space using (1). After the colorspace conversion, the host image in the YCbCr color space can be represented asI(x,y)={IY(x,y),ICb(x,y),ICr(x,y)},where1?x?M,1?y?N,andM×Nis the size of the host image.Y=0.299R+0.



587G?0.114B(1)To calculate the Color Texture DescriptorMLDD_CT, ?rst, the multi-level maskWmult iis de?ned in (2), and the mask inthemth level is represented asW2m+1, which has the size(2m+1)×(2m+1),asdemonstratedinFig. 2. At each level, theneighbor pixels of the corresponding pixel, as de?ned inFig. 2(b), are used to calculate the color texture value of each pixel,using (3)–(5).

Wmult i={W3,W5,W7,…,W2L+1}(2)whereW?is the mask sequence that we de?ned to calculate the corresponding color texture,Lindicates the highest levelof the de?ned masks,W2L+1indicates theLth level mask, andWmult iis the multi-level mask.

Below are the de?nitions of(3)–(5):CTYm(x,y)=ms=?mmt=?mw2m+1(s,t)IY(x+s,y+t)ms=?mmt=?mw2m+1(s,t)(3)CTCbm(x,y)=ms=?mmt=?mw2m+1(s,t)ICb(x+s,y+t)ms=?mmt=?mw2m+1(s,t)(4)CTCrm(x,y)=ms=?mmt=?mw2m+1(s,t)ICr(x+s,y+t)ms=?mmt=?mw2m+1(s,t)(5)wheremindicates themth level,m=1,2,…,L,whereLindicates the highest level,IY,ICbandICrare the luminance com-ponent and chrominance components of the corresponding pixel in the YCbCr color space; andCTYm(x,y),CTCbm(x,y)andCTCrm(x,y)are themth level luminance and chrominance color texture values, respectively, of the corresponding pixel(x,y),1?x?M,1?y?N.

Therefore, the color texture descriptor in themth level can be represented using (6), and theMLDD_CTof the corre-sponding pixel can be de?ned accordingly in (7):CTm(x,y)={CTYm(x,y),CTCbm(x,y),CTCrm(x,y)}(6)MLDD_CT(x,y)={CT3(x,y),CT5(x,y),…,CTL(x,y)}(7)In (6)and(7), it should be noted that the orders of the components and levels gain signi?cance. In the case of thecomponents, the human visual system is more sensitive to the luminance component (Y) compared with the chrominancecomponents (Cb)and(Cr).

In the case of the levels, whenmis smaller, the neighbor pixels will be closer to the right pixel;therefore, the corresponding color texture value will be more meaningful.230X. Bi et al. / Information Sciences 345 (2016) 226–2422.1.2. Invariant Moment Descriptor (MLDD_IM) calculationConsidering that some of the common image processing operations, especially geometrical distortions such as rotationand scaling, are usually applied to the host images or forged regions to enhance the visual effect of the forgery image,the geometric invariant feature is necessary.

PCET36is a new type of orthogonal moment that is de?ned on the circulardomain. The magnitudes of PCET are invariant to image rotation and scale. At the same time, the computational cost ofPCET is extremely low. Furthermore, PCET is free of numerical instability issues; thus, high order moments can be obtainedaccurately.

Due to the above-mentioned features of PCET, in this paper, we choose PCET moments as geometric invariantfeature descriptors; therefore, the Invariant Moment DescriptorMLDD_IMcanbecalculatedfromthePCETmomentsofeachpixel.The PCET with ordernand repetitionl,|n|,|l|=0,1,…,?,isde?nedin(8):Mn,l=1?2?010Hn,l(r,?)?f(r,?)rdrd?(8)where ·?denotes the complex conjugate.Hn,l(r,?)is the kernel of PCET, and it is composed of a radial componentRn(r)=ei2?nr2and a circular componenteil?, as de?ned in (9):Hn,l(r,?)=Rn(r)·eil?=ei2?nr2·eil?=ei(2?nr2+l?)(9)To calculate the PCET moments of the image pixels, a distinct region should ?rst be assigned to each pixel. In the pro-posed method, we use the highest level mask–theLth level, as de?ned inSection 2.1.

1–to de?ne the local neighbor pixelmatrix. Thus, the size of the local neighbor matrix should beLmax×Lmax,Lmax=2L+1. Given the local neighbor matrixg(x,y)of the corresponding pixel(x,y), we ?rst transform (8) into Cartesian coordinates, as in (10):Mn,l=1?x2+y2?1Hn,l(x,y)?f(x,y)dxdy(10)whereHn,l(x,y)=Hn,l(rcos?,rsin?)=Hn,l(r,?)andf(x,y)=f(rcos?,rsin?)?f(r,?).Then, we map the local neighbor matrixg(x,y)to a domain of(px,qy)??1,1×?1,1 with (11). Now, the PCETmoments ofg(x,y)can be calculated using (12):px=x?Lmax/2Lmax/2,qx=y?Lmax/2Lmax/2(11)wherex, yindicate the coordinates on the discrete domain,x=0,1,2,.


.,Lmax?1, andpx,qyindi-cate the mapped domain,p2x+q2y?1:Mn,l(x,y)=1?Lmax?1x=0Lmax?1y=0Hn.l(px,qy)?g(px,qy)xy=4?Lmax·LmaxLmax?1x=0Lmax?1y=0Hn.l(px,qy)?g(px,qy)(12)whereg(px,qy)=g(x,y),x=2/M,andy=2/M.As mentioned earlier, in the YCbCr color space, the luminance component (Y) is more important than the chrominancecomponents (CbandCr); therefore, we choose the luminance componentIY(x,y)of each pixel, to calculate the InvariantMoment DescriptorIM, using (13). TheMLDD_IMof the corresponding pixel can be de?ned accordingly in (14):Mn,l(x,y)=4?Lmax2Lmax?1x=0Lmax?1y=0Hn.l(px,qy)?IY(x,y)(13)whereLmax=2L+1, L indicates the maximum mask size, which we de?ned for calculating theColor Texture Descriptor(MLDD_CT),pxandqyindicate the mapped domain, as de?ned in (11),nindicates the order, andlindicates the repetition,|n|,|l|=0,1,..

.,Omax,whereOmaxis the maximum order andIY(x,y)indicates the luminance component of the corre-sponding pixel located in(x,y).Note that with ordern, the number of PCET Moments for each pixel region is(n+1)(n+2)/2. In factHn,l(x,y)=Hn,?l(x,y);thus,onlyIMn,l(x,y)withl?0 is considered in our method.MLDD_IM(x,y)={IM0,0(x,y),…,IM0,Omax(x,y),IM1,0(x,y),.

..,IM1,Omax(x,y),…,IMOmax,Omax(x,y)}(14)With the calculatedMLDD_CTandMLDD_IM, as de?ned in (7)and(14), respectively, for each pixel, the Multi-Level DenseDescriptorMLDDcan be generated as in (15):MLDD(x,y)={MLDD_CT(x,y),MLDD_IM(x,y)}(15)X.

Bi et al. / Information Sciences 345 (2016) 226–242231Fig. 3.Demonstration of lexicographically sorted pixels and the corresponding index vector.2.2. Hierarchical Feature MatchingWith theMLDDscalculated for each pixel inSection 2.1, in this stage, we must obtain the matched pixels.

A desirablematching process should have low computational complexity and, at the same time, should be robust against various attacks,especially the geometrical transformation attacks. Furthermore, the result of the matching process should be as accurate aspossible. To achieve better matching results, in this paper, we propose the Hierarchical Feature Matching method, which is athree-step process: 1.Color Texture Based Filtering,2.Geometrical Invariant Moments Based Matching,and3.

Adaptive Distanceand Orientation Based Filtering.IntheColor Texture Based Filteringstep, we sort the pixels of the host image according totheirMLDD_CTvalues, thus generating the selected neighbor pixels set for each pixel. In this way, pixels with similar colortexture will be grouped together into distinctive neighbor pixel sets. Afterward, in theGeometrical Invariant Moments BasedMatchingstep, we match each pixel with its corresponding neighbor pixel set through itsMLDD_IM, and the matched pixelswill be indicated as matched pixel pairs. Finally, theAdaptive Distance and Orientation Based Filteringmethod is proposed to?lter out the redundant pixels from the previously generated matched pixel pairs, thus generating the ?nal Detected ForgeryRegions.

The followingSections, 2.2.1, 2.2.2and2.2.

3will explain these three steps in detail.2.2.1. Color Texture Based FilteringThe existing forgery detection methods usually consist of either block-based forgery detection methods or feature pointsbased forgery detection methods. For the block-based forgery detection methods, after dividing the host image into blocks,each block is matched to the other blocks, and then the matched blocks will be indicated as the suspected forgery regions.In this situation, the computational cost stems from the requirement to compare each block to all the other blocks to ?ndthe matched blocks. For the feature points based forgery detection methods, after extracting the feature points, each featurewill be matched to the other feature points, and the matched feature points will be indicated as points of the suspectedforgery regions.

In this case, the computational expense is strongly related to the number of feature points and the matchingmethod. In the proposed method, we propose theMulti-Level Dense Descriptor(MLDD) extraction method to extract thefeatures for each pixel. To e?ciently reduce the computational complexity, theColor Texture Based Filteringis proposed togenerate the neighbor pixels set for each pixel. In this manner, pixels with similar color texture are grouped together intodistinctive neighbor pixel sets, and each pixel will be matched only to its corresponding neighbor pixels that have a similarcolor texture, instead of to all the other pixels in the host image. The detailed steps of the proposedColor Texture BasedFilteringare explained inAlgorithm 1, as follows.InSTEP 2ofAlgorithm 1, the lexicographical sorting method is applied to sort the pixels. Given two partially orderedsetsAandB, the lexicographical order on the Cartesian product0is de?ned as(a,b)?(a,b)if and only ifa?aor (a=aandb?b).

The lexicographical order of two totally ordered sets is thus a linear extension of their product order. Moregenerally, one can de?ne the lexicographic order on the Cartesian product ofn_lexiordered sets, on the Cartesian productof a countable in?nite family of ordered sets, and on the union of such sets12.Fig. 3demonstrates the lexicographical-sorted pixels and the corresponding index vectorLabel_Vec.

InFig. 3(a), the attributes in the rows indicate the pixels, andthe attributes in the columns indicate theMLDD-CTvalues of the corresponding pixels. InFig.

3(b),NPSidx_iindicates theneighbor pixels of theith pixel inLabel_Vec,andRindicates the neighbor pixels size. Thus, the size ofNPSshould be 2R+1,except wheni?Rori?M×N?R.232X. Bi et al. / Information Sciences 345 (2016) 226–242Algorithm 1Color Texture Based Filtering.Input:Multi-Level Dense Descriptors – Color Texture (MLDD_CT)Output:Selected Neighbor Pixels Sets (NPS)STEP 1:Load the host image with the sizeM×Nand resize it into an(M×N)×1vector,andthenloaditsMLDD_CTfeature values and initializethe pixel index asLabel_Vec=?.

STEP 2:Apply the lexicographical sorting method12to sort the pixels according to theirMLDD_CTfeature values.Fig. 3(a) shows thelexicographical-sorted pixels demonstration.

At the same time, save the index of the corresponding pixel inLabel_Vec, as shown inFig. 3(b).STEP 3:Initialize the neighbor pixel size asR.Then, the index of theith pixel in the sorted sequenceLabel_VecisLabel_Vec(idx_i); therefore, theindexes of its neighbor pixels are{Label_Vec(idx_i?R),…,Label_Vec(idx_i?1)}and{Label_Vec(idx_i+1),.

..,Label_Vec(idx_i+R)},asdemonstrated inFig. 3(b).

STEP 4:Using the neighbor pixels, the Neighbor Pixels Set (NPS)oftheith pixel inLabel_Veccan be generated asNPSidx_i={Label_Vec(idx_i?R),…,Label_Vec(idx_i),..

.,Label_Vec(idx_i+R)}. Similarly, theNPSvalues of all the pixels can be generated.InSTEP 3ofAlgorithm 1, an appropriateRis expected to achieve a low computational complexity and, at thesame time, gain high detection performance. When the value ofRdecreases, the computational complexity of the sub-sequent matching process will decrease accordingly; however, the detection performance will become worse. In con-trast, a higherRvalue will bring higher computational complexity of the subsequent matching process and better de-tection performance. To gain balance between the computational complexity and detection performance, we setR=4000 by trial and error in this paper.

InSTEP 4ofAlgorithm 1,theNPSof all the pixels can be generated usingNPSidx_i={Label_Vec(idx_i?R),…,Label_Vec(idx_i),.



,Label_Vec(M×N)}. Because the pixels are sorted according to their color texture, the pixels in the sameNPSshould have similar color tex-ture features.2.

2.2. Geometrically Invariant Moment Based MatchingAfter achieving theNPS, in the proposed method, using the Geometrical Invariant Moments,MLDD_IM,weneedtomatcheach pixel only to its neighbor pixels in the correspondingNPSinstead of to all the other pixels. In this section, the MatchedPixel Pairs (MPP) will be indicated by the proposed novelGeometrical Invariant Moment Based Matchingmethod. The pixelsin the sameNPSare matched to one another through theirMLDD_IMusing thebest-bin-?rstalgorithm with their Euclid-ian distance, which means that pixelMLDD_IMidx_iwill be matched to pixelMLDD_IMidx_jonly if they meet the followingcondition:DIMM(MLDD_IMidx_i,MLDD_IMidx_j)·TIMM?DIMM(MLDD_IMidx_i,MLDD_IMidx_k)(16)whereDIMM(MLDD_IMidx_i,MLDD_IMidx_j)means the Euclidian distance betweenMLDD_IMidx_iandMLDD_IMidx_j, whichis de?ned in (17). Here,DIMM(MLDD_IMidx_i,MLDD_IMidx_k)means the Euclidian distances between theMLDD_IMidx_iandMLDD_IMof all the other pixels in the sameNPS, which is de?ned in (18).

TIMMindicates the matching threshold; a largervalue forTIMMwill bring a higher matching accuracy, but at the same time, it will cause a greater missing probability.Therefore, in the following experiments, we setTIMM=2 by trial and error to provide a good trade-off between the match-ing accuracy and missing probability.DIMM(MLDD_IMidx_i,MLDD_IMidx_j)=(MLDD_IM(xidx_i,yidx_i)?MLDD_IM(xidx_j,yidx_j))(17)DIMM(MLDD_IMidx_i,MLDD_IMidx_k)=(MLDD_IM(xidx_i,yidx_i)?MLDD_IM(xidx_k,yidx_k))(18)whereidx_i,idx_jandidx_kindicate pixels of a givenNPS,k=i,k=j;(xidx_?,yidx_?)means the spatial coordinates ofthe?thpixel inLabel_Vec;andMLDD_IM(xidx_?,yidx_?)means the geometrical invariant moments of the pixel located at(xidx_?,yidx_?), which is de?ned in (14).In eachNPS, the pixels are matched to their neighbor pixels by theirMLDD_IM, and the pixels that meet the condition(16) will be indicated as theMPP.2.2.3.

Adaptive Distance and Orientation Based FilteringUsing theGeometrical Invariant Moment Based Matchingprocess, theMPPwere generated. However, inMPP,someoftheredundant pixels were detected in addition to the forged pixels; therefore, this paper proposes theAdaptive Distance andOrientation Based Filtering (ADOF)method to ?lter out the redundant pixels and generate the forged pixels, on which somemorphological operations are applied; thus, the forgery regions can be detected.Fig. 4shows the ?owchart of the proposedADOFmethod. First, theMPPis classi?ed into Symmetrical Pixel Pairs (SPP) and Unsymmetrical Pixel Pairs (UPP). Then, thedistribution of the distance and orientation of theSPPandUPPis calculated, respectively; on this basis, the threshold forSPPandUPPis adaptively calculated asTSPPandTUPP.

Thus, the irrelevant pixels ofSPPandUPPare ?ltered out, and theremaining pixels are indicated as forged pixels. Finally, some morphological operations are applied to the forged pixels; thus,the detected forgery regions are generated.X. Bi et al. / Information Sciences 345 (2016) 226–242233Fig. 4.

Flowchart of Adaptive Distance and Orientation Based Filtering (ADOF)method.InMPP, the pixel pairs can be divided into Symmetrical Pixel Pairs (SPP), which means two-way matched pixel pairs, andUnsymmetrical Pixel Pairs (UPP), which means one-way matched pixel pairs, using (19). Because the pixel pairs ofSPPoccurtwo times inMPP, they have a higher probability of indicating the forgery regions. At the same time, inUPP,although thepixel pairs occur only once, some of them are also helpful in locating the forgery regions. Hence, different threshold valuesare required forSPPandUPP.

ifpidx_i,pidx_j?MMP&pidx_j,pidx_i?MMP,then(pidx_i,pidx_j)?SPPifpidx_i,pidx_j?MMP&pidx_j,pidx_i?MMP,then(pidx_i,pidx_j)?UPP(19)Most of the existing block-based forgery detection methods employ only the distance attribute in the matching process.Given the same shift vector, when it exceeds a user-speci?ed threshold, the matched blocks that contributed to that spe-ci?c shift vector are identi?ed as regions that might have been copied and moved. In the proposedADOF, the orientationattributes of the pixels are employed in addition to the distance attribute. Given a pixel pair(xidx_i,yidx_i),(xidx_j,yidx_j),the distance and orientation can be calculated using (20)and(21), respectively. Similarly, the distance and orientation ofallthepixelpairsinMPPcan be calculated.

Fig. 5shows a comparison of the matching results with different features. InFig. 5, the results in blue indicate the detection results of the proposed method, which employs both the distance and ori-entation for matching.

At the same time, the results in rose-red indicate the detection results of the traditional methods,which employ only distance for matching. The triangle, star, and circle symbols indicate theprecisionrate,recallrate, andFscore, respectively.d=(xidx_i?xidx_j)2+(yidx_i?yidx_j)2(20)?=arctan 2yidx_i?yidx_jxidx_i?xidx_j+?,??0,2?(21)After calculating the?for all the pixel pairs inMPP,?is quantized intoTorientation bins, and the quantization functionis de?ned in (22). In our method, we setT=36. Afterward, the distribution of the number of pixel pairs inSPPandUPP234X. Bi et al. / Information Sciences 345 (2016) 226–242Fig. 5.

Comparison of matching results with different features: (a) detection performances under rotation, and (b) detection performances under scaling.(For interpretation of the references to color in this ?gure legend, the reader is referred to the web version of this article.)Fig.

6.Demonstration of Distance and Orientation Bin Distribution of SPP: (a) distribution ofNumSPP(t,d), (b) matched pixel pairs in SPP, and (c) diagram-matic drawing for calculation of distance and orientation. (For interpretation of the references to color in this ?gure legend, the reader is referredtotheweb version of this article.)can be generated, as shown inFigs. 6and7,whereNumSPP(t,d)andNumUPP(t,d)mean the number of pixel pairs with thedistancedthat are located in thetth orientation bin inSPPandUPP, respectively.

?t=2?T·t,where t=mod ?2?/T+12,T(22)wheretindicates thetth orientation bin,t=0,1,2,…,35,?tmeans the quantized angle of thetth orientation bin, and thecorresponding orientation interval should be ?t??/T,?t+?/T.By analyzing the distribution ofNumSPP(t,d)andNumUPP(t,d), we propose a data-driven based threshold calculationmethod to ?lter out the irrelevant pixels and thus generate the forged pixels. The core of data-driven based techniques is totake full advantage of the huge amounts of available process data, aiming to acquire the useful information within30,37,while the model-based schemes require a priori physical and mathematical knowledge of the process.

Currently, the data-driven based approach can be employed in many applications11. To calculate the threshold, we ?rst sort the values ofNumSPPin ascending order and remove the repeated values as inNumSPP_S={numSPP1,numSPP2,numSPP3,…,numSPPk}. Then,we calculate the ?rst derivative ofNumSPP_Sand its mean value, which are represented as?(NumSPP_S)and?(NumSPP_S),respectively, and the second derivative ofNumSPP_S, which is represented as?2(NumSPP_S). Finally, the valuesnumSPPiforX.

Bi et al. / Information Sciences 345 (2016) 226–242235Fig. 7.Demonstration of Distance and Orientation Bin Distribution ofUPP: (a) distribution ofNumUPP(t,d), and (b) matched pixel pairs inUPP.which the second derivative is larger than the mean value of the corresponding ?rst derivative vector, as de?ned in (23),are selected, and their minimum value is extracted as the ?ltering threshold forSPP, which is represented asTSPP.

WhenNumSPP(t,d)?TSPP, the pixel pairs that have the distancedandthatarelocatedinthetthorientation bin inSPPwill beconsidered to be the forged pixels, as demonstrated inFig. 6, where (a) shows the distribution ofNumSPP(t,d); (b) showsthematchedpixelpairsinSPP; and (c) shows the diagrammatic drawing calculating the distancedand orientation?.InFig. 6(a), the distribution represented with different colors means different numbers of pixels, and the red, sky-blue, andorange colors indicate that the corresponding pixel pairs can ful?ll the conditionNumSPP(t,d)?TSPP; consequently, they areconsidered to be the forged pixels. At the same time, the distribution results labeled with ‘1’ in sky-blue, ‘2’ in rose-red,and ‘3’ in yellow inFig.

6(a) correspond to the detection results that are indicated with sky-blue, rose-red, and yellow inFig. 6(b), respectively.?2numSPPi>?(NumSPP_S)(23)Similarly, the ?ltering threshold forUPPcan be calculated with the proposed data-driven based threshold calculationmethod, and whenNumUPP(t,d)?TUPP, the corresponding pixel pairs are detected as forged pixels, as demonstrated inFig.

7.Fig. 8shows the ?ltering results based on the proposed data-driven based threshold calculation method, where (a)shows theMPP,which is composed of (b)SPPand (c)UPP, and (e) and (f) show the ?ltering results of (b)SPPand (c)UPP,respectively, with the adaptively calculatedTSPPandTUPP. Finally, (d) shows the integrated results of (e) and (f).In the last step ofADOF, we simply apply the close morphological operation to the detected forged pixels to generate theforged regions.

The structural element is de?ned as a circle whose radius is related to the size of the input image. The closeoperation can ?ll the gaps in the detected pixels while keeping the shape of the regions unchanged.3. Experimental results and discussionsWe have proposed a novel CMFD method in this paper. The novel feature extraction method is proposed to extract theMulti-Level Dense Descriptor, and the Hierarchical Feature Matching method is proposed to detect the forgery regions basedon theMLDDfeatures. In this section, a series of experiments are conducted to evaluate the effectiveness and robustnessof the proposed CMFD method. In the following experiments, the image dataset CMFDA6is used to test the proposedmethod.

This CMFDA dataset, which has 1728 images in total, as shown inTable 1, was created based on 48 high-resolutionuncompressed PNG true-color images. The average size of the images is 3000×2300. In the dataset, the copied regionscome from various categories of living, natural, man-made and even mixed images, and they range from overly smoothto highly textured.

The copy–move forgeries were created by copying, scaling and rotating semantically meaningful imageregions. Furthermore, JPEG compression and noise addition can be added to the forgery images. In summary, the datasetcontains realistic copy–move forgery images. Note that in the following experiments, to improve the computational e?-ciency, the images in the dataset CMFDA are ?rst rescaled down to half their original size before being used to evaluatethe methods.Fig. 9shows the Copy–Move Forgery Detection results of the proposed scheme. InFig.

9(a1), (b1), (c1), (d1)and (e1) display the host images, which are forged images selected from the dataset, while (a2), (b2), (c2), (d2) and (e2)show the corresponding ground truth forgery regions, and (a3), (b3), (c3), (d3) and (e3) show the forgery regions that weredetected using the proposed scheme.236X. Bi et al. / Information Sciences 345 (2016) 226–242Fig.

8.Data-driven based threshold based ?ltering results ofSPPandUPP: (a) matched pixel pairs (MPP); (b) Symmetrical Pixel Pairs (SPP); (c) Unsymmet-rical Pixel Pairs (UPP); (d) ?ltered forged pixels ofMPP; (e) ?ltered pixels fromSPP; (f) ?ltered pixels fromUPP.Ta b l e 1Parameter settings of the dataset CMFDA.

Parameters Range Step Number of forgery imagesJPEG compressionQuality factor 20–100 10 432Noise additionStandard deviation 20–100 20 240ScaleScaling factor 91%–109% 2% 480RotationAngle 2°–10°2°240Down sampling90% –10% 20% 240Plain copy–move 48Fig. 9.The copy–move forgery detection results of the proposed scheme.

Row 1: ?ve host images from the dataset; Row 2: the ground-truth forgeryregions of the corresponding host images; Row 3: the detected forgery regions of the corresponding images, using the proposed forgery detection scheme.X. Bi et al.

/ Information Sciences 345 (2016) 226–242237Ta b l e 2Detection results under plain copy–move at image level.Image level SIFT6SURF6Bravo4SBFD19ASBFD28Proposed method on CMFDA Proposed method on CMFDPMPrecision(%) 88.37 91.4 9 87.

27 70.169688.89 89.53Recall(%) 79.

17 89.5810 083.33100 100.096.25F(%) 83.

52 90.52 93.20 76.1897.9694.12 92.77Ta b l e 3Detection results under plain copy–move at pixel level.

Image level SIFT6SURF6Bravo4SBFD19ASBFD28Proposed method on CMFDA Proposed method on CMFDPMPrecision(%) 62.26 69.43 83.23 81.

90 82.4587.20 91.37Recall(%) 69.

56 74.85 41.80 54.095 70.7989.68 84.

64F(%) 65.71 72.04 55.65 65.16 76.1888.42 87.88To evaluate the performance of the proposed scheme,precisionandrecallrates6,19,28are used.

Precisionis the proba-bility that the detected regions are relevant, and it is de?ned as the ratio of the number of correctly detected forged pixelsto the total number of detected forged pixels.Recallis the probability that the relevant regions are detected, which is de-?ned as the ratio of the number of correctly detected forged pixels to the number of forged pixels in the ground-truthforged image. In addition, theFscore is used as a measure that combinesprecisionandrecallinto a single value, which isde?ned in (24):F=21/precision+1/recall=2·precision·recallprecision+recall(24)Because Christlein et al.6recommended all the benchmark methods and we use the same dataset that they provided,we can compare our experimental results with the copy–move detection evaluation results in their paper. In6, their featurepoint based algorithm combined the methods of1and26; they built the clusters described by1and then computed thea?ne transformation between the clusters using RANSAC. In the following, the results of the proposed method are comparedwith those of the state-of-the-art CMFD algorithms, the SIFT and SURF feature points based forgery detection methods6,the block-based method4, and the segmentation based forgery detection methods (9and28). The followingSections3.1, 3.

2,and3.3, respectively, demonstrate the forgery detection results when under plain copy–move, various attacks, anddown-sampling. Finally,Section 3.4demonstrates the summary of the comparison.3.1.

Forgery detection results under plain copy–moveIn this section, we evaluate the proposed method under ideal conditions, those of one-to-one plain CMF. In this case, inaddition to the CMFDA6, which consists of 48 original images and 48 forgery images, we also test the proposed scheme inthe dataset CMFDPM8, which is made up of 80 images with a 768×1024-pixel resolution ( The task isto distinguish the original images from the forgery images. We evaluate the scheme at both the pixel level and image level.While pixel-level metrics are useful to assess the general localization performance of the algorithm when the ground-truthdata are available, image level decisions are of particular interest for automated detection of manipulated images.

At thepixel level, theprecisionandrecallrates are calculated by counting the number of pixels in the corresponding regions. Atthe image level, theprecisionis the probability that a detected forgery is truly a forgery, whilerecallis the probability thata forgery image is detected. In general, higherprecisionas well as higherrecallindicates superior performance. To reducethe effect of random samples, the averageprecision/recallis computed for all the images in the dataset. Implemented on aPC running the Windows 7 operating system and a 2.4 GHz CPU, the new proposed method takes approximately 2263.

15 son average for each image in the CMFDA dataset, and 2098.67 s on average for each image in the CMFDPM dataset.To show the performance of the proposed method,Tables 2and3list the detection results of plain copy–move operationsat the image level and pixel level, respectively. Considering the time complexity, we ?rst down-sampled the images tohalf their size; therefore, the following experiments are conducted on images of moderate resolution, with a typical sizeof 1500×1150. To ensure a fair comparison, the existing state-of-the-art methods are evaluated using images of mediumresolution as well.

InTables 2and3, text in bold indicate the best results, while text in italics indicate the results of theproposed method. As shown inTable 2, at the image level, our method achieves aprecisionof 88.89% on the CMFDA datasetand aprecisionof 89.53% on the CMFDPM dataset. Simultaneously, it achieves a 100%recallon the CMFDA dataset and a96.25%recallon the CMFDPM dataset.

In contrast, while the SIFT based method6achieves aprecisionof 88.37% and a79.17%recall, the SURF based method6achieves aprecisionof 91.49% and an 89.58%recall.

The method proposed by Bravo4achieves aprecisionof 87.27% and a 100%recall, and the SBFD method19achieves aprecisionof 70.16% and an 83.33%recall. It can be easily observed that the method proposed in this paper outperforms most of the existing state-of-the-artforgery detection methods except for the ASBFD method28, which we proposed earlier, which achieves aprecisionof 96%and a 100%recall.238X. Bi et al. / Information Sciences 345 (2016) 226–242According toTable 3, at the pixel level, the advantage of the proposed detection method is especially important; ourmethod can achieve aprecisionof 87.

20% on the CMFDA dataset and aprecisionof 91.37% on the CMFDPM dataset, andsimultaneously, an 89.68%recallon the CMFDA dataset and an 84.64%recallon the CMFDPM dataset, which is much betterthan the other state-of-the-art forgery detection methods: the SIFT based method6can achieve aprecisionof only 62.26%and a 69.56%recall; the SURF based method6can achieve aprecisionof only 69.43% and a 74.85%recall;themethodproposed by Bravo4and the SBFD method19can achieve aprecisionabove 80%, but theirrecallis only approximately50%; and the ASBFD method28, which we proposed earlier, can achieve aprecisionof 82.

45% and a 70.79%recall.3.2. Forgery detection results under various attacksIn addition to the one-to-one plain CMF, we also tested our proposed method when the copied regions are attackedby various attacks that include both geometric distortions and common image degradation. In this case, the forgery im-ages are generated by applying various attacks into the copied regions of each of the 48 original images in the dataset.Table 1displays the attacks used to generate the dataset and their corresponding parameter settings. According toTable 1,the common attacks of JPEG compression, Noise Addition, Scale, and Rotation are applied, generating a total of 1392 forgeryimages for robustness testing.To evaluate the robustness of the proposed forgery detection method, we calculate theprecision,recall,andFscore un-der various attacks at the pixel level.Fig. 10shows the experimental results, where the three columns show the results oftheprecision,recallandFscore, denoted by the symbols ”, ‘?’, and ”, respectively.Fig. 10shows the performance of theproposed method as evaluated under various attacks, where the four rows show the results for noise addition, JPEG com-pression, scaling, and rotation, respectively. Moreover, the performance of the proposed method is compared with severalstate-of-the-art forgery detection methods: the SIFT based method6, for which the results are shown in green, the SURFbased method6, for which the results are shown in red, the method proposed by Bravo4, for which the results areshown in rose-red, the SBFD method19, for which the results are shown in yellow, and the ASBFD method28, which weproposed earlier, for which the results are shown in blue. The results of the method proposed in this paper are shown insky-blue.It can be easily observed that with common signal processing such as noise addition and JPEG compression, as showninFig. 10(a)–(f), the proposed method outperforms all the other state-of-the-art methods in terms ofprecision,recall,andFscore. When under geometric attacks such as scaling and rotation, the proposed method outperforms the others in terms ofFscore, as demonstrated inFig. 10(i) and (l). Furthermore, the performance of the proposed method is similar to the ASBFDmethod28that we proposed earlier and to the method proposed by Bravo4, and its performance is much better thanthe other state-of-the-art methods in terms of theprecision,asdemonstratedinFig. 10(g) and (j). In terms of therecall,theproposed method performs similarly to the SBFD method19, and it outperforms the other methods, as demonstrated inFig. 10(h) and (k).3.3. Forgery detection results under down-samplingBecause it has been proven that the performance of the forgery detection method depends on the quality of the hostimages, in this section, we will analyze the effect of down-sampling on the performance of the forgery detection methods.To conduct this experiment, we ?rst scale down the images in the dataset from 90% to 10%, using a step of 20%. Note thatthe detection parameters are globally ?xed to avoid over ?tting.Fig. 11displays the detection results when down-sampling,where thex-axis means the down-sampling factor, and (a), (b), and (c) display the detection results in terms of theprecision,recallandFscore, respectively. Furthermore, the results of the proposed method are compared with the existing state-of-the-art methods: the SIFT based method6, indicated in green; the SURF based method6, indicated in red; the methodproposed by Bravo4, indicated in rose-red; and the ASBFD method28, which we proposed earlier and is indicated inblue. It can be easily observed that when the down-sampling factor drops from 90% to 30%, the performances of most ofthe existing methods decline noticeably, while the performance of the proposed method remains perfectly stable, whichindicates better performance for the proposed method compared with the existing methods. In particular, when the down-sampling factor reaches 10%, all the existing compared methods fail to detect the forgery, while our proposed method stillachieves aprecisionof 58% and a 50%recall.In addition to the comparison with some of the existing state-of-the-art methods as shown inFig. 11, in this section wealso show the detected regions when under different down-sampling factors. InFig. 12, two typical examples (“Four_babies”,with a size of 3008×2000, and “Jelly?sh_choas”, with a size of 3888×2592) are selected from the dataset to demonstratethe forgery detection results of the proposed method. In addition, the traditional sparse SIFT feature and the proposed densedescriptorMLDDare used to demonstrate the superiority ofMLDD. The corresponding results are compared to reveal thebetter performance of the proposed method. InFig. 12, the 1st column shows the “Four_babies” and “Jelly?sh_choas” imagesand their ground truths. The 2nd–6th columns show the detected results when the host images are down-sampled at factorsof 90%, 70%, 50%, 30%, and 10%, respectively. In each of the two examples, the 1st row shows the detection results based onthe traditional sparse SIFT feature, while the 2nd row shows the detection results based onMLDD. It can be easily observedthat when the down-sampling factor decreases, the performance of the traditional forgery detection method using sparseSIFT declines noticeably, as shown inFig. 12(a1)–(a3), (c1)–(c3), and when the down-sampling factor drops to 30%, it is closeX. Bi et al. / Information Sciences 345 (2016) 226–242239Fig. 10.Comparison results of the CMFD methods under various attacks. The three columns show the results of precision, recall andFscore, respectively;while the four rows show the comparison results under various attacks: (a)–(c) Noise addition, (d)–(f) JPEG compression, (g)–(i) Scale, and (j)–(l)Rotation.(For interpretation of the references to color in this ?gure legend, the reader is referred to the web version of this article.)to failure at forgery detection, as shown inFig. 12(a4)–(a5), (c4)–(c5). In contrast, the proposed forgery detection methodusingMLDDperforms much better and continues to perform steadily even when the down-sampling factor drops to 10%, asshown inFig. 12(b1)–(b5),(d1)–(d5).3.4. Comprehensive comparisonsAs a summary, in this section, we provide a comprehensive comparison inTable 4,wheretheFscore de?ned in (24)isemployed to evaluate the comprehensive robustness of the schemes. InTable 4,theFscore is de?ned asF?0.5tomakethe240X. Bi et al. / Information Sciences 345 (2016) 226–242Fig. 11. Detection results under down-sampling at the pixel level. (a) Precision, (b) Recall, and (c)F. (For interpretation of the references to color in this?gure legend, the reader is referred to the web version of this article.)Fig. 12.Demonstrations of detection results under down-sampling, based on traditional sparse SIFT features and the proposed dense descriptorMLDD.Column 1:”Four_babies” (3008×2000), ground truth of “Four_babies”, “Jelly?sh_choas” (3888×2592), and ground truth of “Jelly?sh_choas”;Column 2:detected forged regions when down-sampling factors were 90%;Column 3:detected forged regions when down-sampling factors were 70%;Column 4:detected forged regions when down-sampling factors were 50%;Column 5:detected forged regions when down-sampling factors were 30%;Column 6:detected forged regions when down-sampling factors were 10%. (a1)–(a5) and (c1)–(c5) show the corresponding detection results based on the traditionalsparse SIFT feature, while (b1)–(b5) and (d1)–(d5) show the corresponding detection results based on the proposed dense descriptorMLDD.detection succeed; otherwise, the detection will fail. Under this condition, the proposed method outperforms the comparedschemes under various attacks; it is robust against: JPEG compression, with the quality factor up to 20, noise addition, withthe standard derivation up to 0.1, the scale, with the scaling factor varied between 0.91 and 1.09, and rotation, with therotation angle up to 10?. In addition to the robustness, the proposed scheme performs very well on images of differentresolutions, especially low resolution. The schemes are tested on images at high, medium and low resolutions, and theX. Bi et al. / Information Sciences 345 (2016) 226–242241Ta b l e 4Comprehensive comparisons.Robustness ResolutionJPEG compression Noise addition Scale Rotation High 100%?70% Medium 70%?40% Low40%?10 %Quality factor Standard derivation Scaling factor AngleFscoresSIFT13Fail?0.06 0.99–1.01 Fail 0.66–0.60 0.60–0.41 0.41–0.08SURF13?50?0.06 0.97–1.09?10°0.72–0.61 0.61–0.42 0.42–0.02Bravo20Fail Fail Fail Fail 0.90–0.44 0.44–0.43 0.43–0.11SBFD9?20?0.10 0.91–1.09?10°– -ASBFD10?30?0.020.91–1.09?10°0.93–0.830.83–0.61 0.61–0.04Proposed method?20?0.10 0.91–1.09?10°0.91–0.880.88–0.87 0.87–0.54?In this table, theFscore is de?ned as:F?0.5, to make detection succeed; otherwise, detection will fail.?’-‘ means that the paper did not mention the results in that condition.corresponding detection accuracy evaluated by theFscore shows the superiority of the proposed method compared withexisting methods.4. ConclusionsIn this paper, we proposed a novel CMFD method using a Multi-Level Dense Descriptor and Hierarchical Feature Match-ing. TheMulti-Level Dense Descriptorextraction method was proposed to extract the dense feature descriptors instead of theexisting sparse features. For each pixel, the color texture feature and the geometric invariant moments are calculated asMLDD_CTandMLDD_IM, respectively. Pixels with similar color textures are selected and grouped together into distinctiveneighbor pixel sets. Using this method, each pixel is matched with pixels only in its neighbor pixel set instead of all theother pixels in the host image. By taking this approach, the computational expense can be much decreased. After calcu-lating theMLDDfor each pixel, the Hierarchical Feature Matching method was proposed, in which each pixel is matchedwith its corresponding neighbor pixel set through its geometric invariant momentsMLDD_IM,thus generating the matchedpixel pairs. Afterward, an Adaptive Distance and Orientation Based Filtering method was proposed to ?lter out redundantpixels. Symmetrical Pixel Pairs (SPP) and Unsymmetrical Pixel Pairs (UPP) are extracted from the matched pixel pairs, re-spectively, and the distributions of the distance and orientation ofSPPandUPPare calculated; then, the thresholds forSPPandUPPare adaptively calculated from the distribution, and the irrelevant pixels ofSPPandUPPare ?ltered out. Finally,some morphological operations are applied to generate the detected forgery regions.A series of experiments were conducted to evaluate the effectiveness and robustness of the proposed method. The forgerydetection results were demonstrated when the host images/regions are under plain copy–move, attacked by various chal-lenge conditions, and under down-sampling. Experimental results indicate that the proposed method performs well, notonly in detection accuracy and effectiveness, but also in robustness against various attacks. 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