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Information Sciences 345

Information Sciences 345 (2016) 226–242
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Information Sciences
journal homepage:www.elsevier.com/locate/ins
Multi-Level Dense Descriptor and Hierarchical Feature
Matching for Copy–Move Forgery Detection
Xiuli Bi, Chi-Man Pun?, Xiao-Chen Yuan
Department of Computer and Information Science, University of Macau, Macau SAR, China
article info
Article history:
Received 17 September 2015
Revised 6 January 2016
Accepted 11 January 2016
Available online 4 February 2016
Keywords:
Copy–Move Forgery Detection (CMFD)
Multi-Level Dense Descriptor (MLDD)
Hierarchical Feature Matching
Color Texture Descriptor
Invariant Moment Descriptor
abstract
In 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 Descriptor
and 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 distinctive
neighbor 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 from
previously generated matched pixel pairs are ?ltered out by the proposed Adaptive Dis-
tance and Orientation Based Filtering method. Finally, some morphological operations are
applied to generate the ?nal detected forgery regions. Experimental results show that the
proposed scheme can achieve much better detection results compared with the existing
state-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. All rights reserved.
1. Introduction
Recently, there has been much interest in Copy–Move Forgery Detection (CMFD). Copy–move forgery (CMF) is one of the
most common types of image forgery. An image with CMF contains at least two regions with identical content where one or
more distinct regions are copied and pasted into one or more destination locations in the same image to conceal important
information. Sometimes, the copied content is modi?ed using a pre-processing operation such as scaling, rotation, noise
addition, 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 a
common pipeline that includes three main steps9: (1) feature extraction, which extracts an appropriate feature from each
of the blocks or interesting pixels; (2) feature matching, which obtains the best match of the blocks or interesting pixels
based on corresponding extracted features; and (3) post-processing, which ?lters the offset ?eld and the linking pixels with
their 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 is
dense. 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.2016.01.061
0020-0255/© 2016 Elsevier Inc. All rights reserved.

X. Bi et al. / Information Sciences 345 (2016) 226–242227
images and then perform dense matching based on the feature descriptors of the keypoints. This approach is usually much
faster than methods that are based entirely on dense matching. Pan and Lyu ?rst proposed the keypoint-based algorithm
in26, where a Scale Invariant Feature Transform (SIFT)21was used to extract the keypoints and which can guarantee
robustness 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 considered
for feature extraction and keypoint-based CMFD1,13,31,35. A benchmarking paper6evaluated the related approaches and
clearly showed the performance gaps. Although the computational complexity of the sparse-?lled methods is comparatively
less because the number of keypoints represents only a relatively small set of all the pixels in the image, most of them are
intrinsically less accurate than the dense-?eld methods, especially when copy–moves involve only smooth regions, which
is typically the case with occlusive forgeries. In addition, the performance of the feature points-based forgery methods is
highly related to the resolution of the host images6. When the host image is down-sampled, the performance of the
feature points-based forgery methods drops considerably.
Considering those problems, we focus on the dense-?eld approach in this paper. Unfortunately, the complexity of the
dense ?eld approach is relatively high because all the pixels undergo the three-step pipeline. The solutions to this problem
are 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, which
means that the performance should not be affected by common distortions such as JPEG compression, noise addition, or
geometric distortions such as rotation and scaling. In the existing CMFD schemes, the dense ?eld approaches are always
known as block-based approaches because the host images are usually divided into overlapping blocks, each of which is
considered to be an individual superpixel for calculating the corresponding pixel features. In the existing block-based CMFD
methods3–5,10,14–16,20,22,24,25,27,29,32,34,38, 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)17are
applied to extract the features, which improves the robustness. Fridrich et al.10calculated the quantized DCT coe?cients
of 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 not
particularly robust against geometric distortions such as rotation and scaling. In consequence, Ryu et al.29used Zernike
moments as block features, and Li20applied the polar cosine transform to calculate the coe?cients for the block features
to achieve rotation invariance. Additionally, Wu et al.34proposed applying the Fourier–Mellin Transform to calculate the
block features, thus achieving scale invariance. Lee et al.17applied HOG to each block and extracted statistical features to
measure the similarity. Lynch et al.23used the average gray values of blocks as dominant descriptors. Recently, Cozzolino
et 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-based
CMFD approaches.
The above description compels us to focus on the dense ?eld approach. In this paper, we propose a novelMulti-Level
Dense Descriptor (MLDD)extraction method, which includes theColor Texture Descriptor(MLDD_CT)andtheInvariant Moment
Descriptor(MLDD_IM) to extract the dense features instead of the existing sparse features. After obtaining theMLDDfor
each pixel, the pixels must be compared to each other to ?nd the matched pairs. Then, to reduce the high computational
complexity of the dense-?eld approach, to enhance the robustness against various attacks, and to make the result of the
matching process be as accurate as possible, we propose a novel Hierarchical Feature Matching method that includes three
main steps: 1.Color Texture Based Filtering,2.Geometrical Invariant Moments Based Matching,and3.Adaptive Distance and
Orientation Based Filtering. Using theColor Texture Based Filteringtechnique, we sort the pixels of the host image according
to their
MLDD_CTvalues to generate the selected neighbor pixels set for each pixel. In this way, pixels with similar color
texture will be grouped together into distinctive neighbor pixel sets. With theGeometrical Invariant Moments Based Matching
technique, we match each pixel with its corresponding neighbor pixel set only through itsMLDD_IM, which greatly reduces
the computational complexity. Finally, theAdaptive Distance and Orientation Based Filteringtechnique can help to ?lter out
redundant 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 Descriptorextraction
and Hierarchical Feature Matching methods in detail. InSection 3, a large number of experiments will be conducted to
demonstrate the effectiveness and robustness of the proposed method. Conclusions are drawn inSection 4.
2. Proposed Copy–Move Forgery Detection algorithm
The proposed CMFD method consists of two stages. The ?rst stage isMulti-Level Dense Descriptor Extraction,in which the
MLDD is generated as a pixel feature. Each MLDD contains two parts: aColor Texture Descriptor(MLDD_CT)andanInvariant
Moment 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, pixels
with similar color texture are grouped together into distinctive neighbor pixel sets. Then, each pixel is matched with its
corresponding 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 from
the previously generated matched pixel pairs, and the ?nal Detected Forgery Regions can be generated from the remainder.

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228X. Bi et al. / Information Sciences 345 (2016) 226–242
Fig. 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 the
Multi-Level Dense DescriptorextractionandHierarchical Feature Matching.
2.1. Multi-Level Dense Descriptor extraction
Existing forgery detection methods are usually divided into two categories: block-based forgery detection methods and
feature points-based forgery detection methods. In the existing block-based methods3,4,10,15,22,24,27,29, the input image
is usually divided into overlapping blocks of a regular shape, for example, when the size of an input image isM×Nand
the block size isB, then the number of blocks is
(M?B+1)×(N?B+1); therefore, each block will be matched with the
other
(M?B+1)×(N?B+1)?1 blocks to ?nd corresponding matched blocks. In this case, the computational complexity
of 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 into
non-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 sparse
features, are extracted and matched with one another to identify duplicated regions. In1,7,13,26,SIFT21was applied
to 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.When
the 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 method
to 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 texture
feature, denoted byMLDD_CT; then, the pixels of the host image are sorted according to their color texture descriptors
MLDD_CT,and a selected neighbor pixel set is generated for each pixel. Afterward, the geometric invariant moments of each

X. Bi et al. / Information Sciences 345 (2016) 226–242229
Fig. 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 can
be 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 the
calculation of the proposed color texture descriptorMLDD_CTand invariant moment descriptorMLDD_IM, respectively.
2.1.1. Color Texture Descriptor (MLDD_CT) calculation
Considering 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 color
space conversion, the host image in the YCbCr color space can be represented asI
(x,y)={IY(x,y),ICb(x,y),ICr(x,y)},where
1?x?M,1?y?N,andM×Nis the size of the host image.
Y=0.299R+0.587G+0.114B
Cb=?0.299R?0.587G+0.886B
Cr=0.701R?0.587G?0.114B
(1)
To calculate the Color Texture DescriptorMLDD_CT, ?rst, the multi-level maskW
mult iis de?ned in (2), and the mask in
themth level is represented asW
2m+1, which has the size(2m+1)×(2m+1),asdemonstratedinFig. 2. At each level, the
neighbor 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 level
of the de?ned masks,W
2L+1indicates theLth level mask, andWmult iis the multi-level mask. Below are the de?nitions of
(3)–(5):
CTY
m(x,y)=
m
s=?mm
t=?mw2m+1(s,t)IY(x+s,y+t)m
s=?mm
t=?mw2m+1(s,t)(3)
CTCb
m(x,y)=
m
s=?mm
t=?mw2m+1(s,t)ICb(x+s,y+t)m
s=?mm
t=?mw2m+1(s,t)(4)
CTCr
m(x,y)=
m
s=?mm
t=?mw2m+1(s,t)ICr(x+s,y+t)m
s=?mm
t=?mw2m+1(s,t)(5)
wheremindicates themth level,m=1,2,…,L,whereLindicates the highest level,I
Y,ICbandICrare the luminance com-
ponent and chrominance components of the corresponding pixel in the YCbCr color space; andCTY
m(x,y),CTCb
m(x,y)and
CTCr
m(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)={CTY
m(x,y),CTCb
m(x,y),CTCr
m(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 the
components, the human visual system is more sensitive to the luminance component (Y) compared with the chrominance
components (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) 226–242
2.1.2. Invariant Moment Descriptor (MLDD_IM) calculation
Considering that some of the common image processing operations, especially geometrical distortions such as rotation
and 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 circular
domain. The magnitudes of PCET are invariant to image rotation and scale. At the same time, the computational cost of
PCET is extremely low. Furthermore, PCET is free of numerical instability issues; thus, high order moments can be obtained
accurately. Due to the above-mentioned features of PCET, in this paper, we choose PCET moments as geometric invariant
feature descriptors; therefore, the Invariant Moment DescriptorMLDD_IMcanbecalculatedfromthePCETmomentsofeach
pixel.
The PCET with ordernand repetitionl,
|n|,|l|=0,1,…,?,isde?nedin(8):
Mn,l=1?
2?
0
1
0Hn,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 pixel
matrix. Thus, the size of the local neighbor matrix should beL
max×Lmax,Lmax=2L+1. Given the local neighbor matrix
g
(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)
whereH
n,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 PCET
moments ofg
(x,y)can be calculated using (12):
px=x?Lmax/2
Lmax/2,qx=y?Lmax/2
Lmax/2(11)
wherex, yindicate the coordinates on the discrete domain,x=0,1,2,…,L
max?1,y=0,1,2,…,Lmax?1, andpx,qyindi-
cate the mapped domain,p2
x+q2
y?1:
Mn,l(x,y)=1?
Lmax?1
x=0L
max?1
y=0
Hn.l(px,qy)?g(px,qy)xy
=4
?Lmax·LmaxL
max?1
x=0L
max?1
y=0
Hn.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 chrominance
components (CbandCr); therefore, we choose the luminance componentI
Y(x,y)of each pixel, to calculate the Invariant
Moment DescriptorIM, using (13). TheMLDD_IMof the corresponding pixel can be de?ned accordingly in (14):
Mn,l(x,y)=4?Lmax2L
max?1
x=0L
max?1
y=0
Hn.l(px,qy)?IY(x,y)(13)
whereL
max=2L+1, L indicates the maximum mask size, which we de?ned for calculating theColor Texture Descriptor
(MLDD_CT),p
xandqyindicate 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)=
H
n,?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 Dense
DescriptorMLDDcan 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) 226–242231
Fig. 3.Demonstration of lexicographically sorted pixels and the corresponding index vector.
2.2. Hierarchical Feature Matching
With theMLDDscalculated for each pixel inSection 2.1, in this stage, we must obtain the matched pixels. A desirable
matching 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 as
possible. To achieve better matching results, in this paper, we propose the Hierarchical Feature Matching method, which is a
three-step process: 1.Color Texture Based Filtering,2.Geometrical Invariant Moments Based Matching,and3.Adaptive Distance
and Orientation Based Filtering.IntheColor Texture Based Filteringstep, we sort the pixels of the host image according to
theirMLDD_CTvalues, thus generating the selected neighbor pixels set for each pixel. In this way, pixels with similar color
texture will be grouped together into distinctive neighbor pixel sets. Afterward, in theGeometrical Invariant Moments Based
Matchingstep, we match each pixel with its corresponding neighbor pixel set through itsMLDD_IM, and the matched pixels
will 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 Forgery
Regions. The followingSections, 2.2.1, 2.2.2and2.2.3will explain these three steps in detail.
2.2.1. Color Texture Based Filtering
The existing forgery detection methods usually consist of either block-based forgery detection methods or feature points
based 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 ?nd
the matched blocks. For the feature points based forgery detection methods, after extracting the feature points, each feature
will be matched to the other feature points, and the matched feature points will be indicated as points of the suspected
forgery regions. In this case, the computational expense is strongly related to the number of feature points and the matching
method. In the proposed method, we propose theMulti-Level Dense Descriptor(MLDD) extraction method to extract the
features for each pixel. To e?ciently reduce the computational complexity, theColor Texture Based Filteringis proposed to
generate the neighbor pixels set for each pixel. In this manner, pixels with similar color texture are grouped together into
distinctive neighbor pixel sets, and each pixel will be matched only to its corresponding neighbor pixels that have a similar
color texture, instead of to all the other pixels in the host image. The detailed steps of the proposedColor Texture Based
Filteringare explained inAlgorithm 1, as follows.
InSTEP 2ofAlgorithm 1, the lexicographical sorting method is applied to sort the pixels. Given two partially ordered
setsAandB, the lexicographical order on the Cartesian product0is de?ned as
(a,b)?(a,b)if and only ifa?aor (a=a
andb?b). The lexicographical order of two totally ordered sets is thus a linear extension of their product order. More
generally, one can de?ne the lexicographic order on the Cartesian product ofn_lexiordered sets, on the Cartesian product
of 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, and
the attributes in the columns indicate theMLDD-CTvalues of the corresponding pixels. InFig. 3(b),NPS
idx_iindicates the
neighbor 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) 226–242
Algorithm 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 initialize
the pixel index asLabel_Vec=?.
STEP 2:Apply the lexicographical sorting method12to sort the pixels according to theirMLDD_CTfeature values.Fig. 3(a) shows the
lexicographical-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, the
indexes 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)},as
demonstrated inFig. 3(b).
STEP 4:Using the neighbor pixels, the Neighbor Pixels Set (NPS)oftheith pixel inLabel_Veccan be generated as
NPS
idx_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 the
same 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 using
NPS
idx_i={Label_Vec(idx_i?R),…,Label_Vec(idx_i),…,Label_Vec(idx_i+R)},exceptwheni?Rori?M×N?R.Wheni?
R,NPS
idx_i={Label_Vec(1),…,Label_Vec(idx_i+R)};wheni?M×N?R,NPSidx_i={Label_Vec(idx_i?R),…,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 Matching
After achieving theNPS, in the proposed method, using the Geometrical Invariant Moments,MLDD_IM,weneedtomatch
each pixel only to its neighbor pixels in the correspondingNPSinstead of to all the other pixels. In this section, the Matched
Pixel Pairs (MPP) will be indicated by the proposed novelGeometrical Invariant Moment Based Matchingmethod. The pixels
in the sameNPSare matched to one another through theirMLDD_IMusing thebest-bin-?rstalgorithm with their Euclid-
ian distance, which means that pixelMLDD_IM
idx_iwill be matched to pixelMLDD_IMidx_jonly if they meet the following
condition:
DIMM(MLDD_IMidx_i,MLDD_IMidx_j)·TIMM?DIMM(MLDD_IMidx_i,MLDD_IMidx_k)(16)
whereD
IMM(MLDD_IMidx_i,MLDD_IMidx_j)means the Euclidian distance betweenMLDD_IMidx_iandMLDD_IMidx_j, which
is de?ned in (17). Here,D
IMM(MLDD_IMidx_i,MLDD_IMidx_k)means the Euclidian distances between theMLDD_IMidx_iand
MLDD_IMof all the other pixels in the sameNPS, which is de?ned in (18).T
IMMindicates the matching threshold; a larger
value forT
IMMwill bring a higher matching accuracy, but at the same time, it will cause a greater missing probability.
Therefore, in the following experiments, we setT
IMM=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 of
the?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 Filtering
Using theGeometrical Invariant Moment Based Matchingprocess, theMPPwere generated. However, inMPP,someofthe
redundant pixels were detected in addition to the forged pixels; therefore, this paper proposes theAdaptive Distance and
Orientation Based Filtering (ADOF)method to ?lter out the redundant pixels and generate the forged pixels, on which some
morphological operations are applied; thus, the forgery regions can be detected.Fig. 4shows the ?owchart of the proposed
ADOFmethod. First, theMPPis classi?ed into Symmetrical Pixel Pairs (SPP) and Unsymmetrical Pixel Pairs (UPP). Then, the
distribution of the distance and orientation of theSPPandUPPis calculated, respectively; on this basis, the threshold for
SPPandUPPis adaptively calculated asT
SPPandTUPP. Thus, the irrelevant pixels ofSPPandUPPare ?ltered out, and the
remaining 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) 226–242233
Fig. 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, and
Unsymmetrical Pixel Pairs (UPP), which means one-way matched pixel pairs, using (19). Because the pixel pairs ofSPPoccur
two times inMPP, they have a higher probability of indicating the forgery regions. At the same time, inUPP,although the
pixel pairs occur only once, some of them are also helpful in locating the forgery regions. Hence, different threshold values
are required forSPPandUPP.
ifpidx_i,pidx_j?MMP&pidx_j,pidx_i?MMP,then(pidx_i,pidx_j)?SPP
if
pidx_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 orientation
attributes 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 of
allthepixelpairsinMPPcan be calculated.Fig. 5shows a comparison of the matching results with different features. In
Fig. 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, andF
score, respectively.
d=

(xidx_i?xidx_j)2+(yidx_i?yidx_j)2(20)
?=arctan 2
yidx_i?yidx_j
xidx_i?xidx_j

+?,??0,2?(21)
After calculating the
?for all the pixel pairs inMPP,?is quantized intoTorientation bins, and the quantization function
is de?ned in (22). In our method, we setT=36. Afterward, the distribution of the number of pixel pairs inSPPandUPP

234X. Bi et al. / Information Sciences 345 (2016) 226–242
Fig. 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 referredtothe
web version of this article.)
can be generated, as shown inFigs. 6and7,whereNumSPP(t,d)andNumUPP(t,d)mean the number of pixel pairs with the
distancedthat 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 the
corresponding 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 calculation
method to ?lter out the irrelevant pixels and thus generate the forged pixels. The core of data-driven based techniques is to
take 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 of
Num
SPPin ascending order and remove the repeated values as inNumSPP_S={numSPP
1,numSPP
2,numSPP
3,…,numSPP
k}. Then,
we calculate the ?rst derivative ofNum
SPP_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 valuesnumSPP
ifor

X. Bi et al. / Information Sciences 345 (2016) 226–242235
Fig. 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 asT
SPP.When
NumSPP(t,d)?TSPP, the pixel pairs that have the distancedandthatarelocatedinthetthorientation bin inSPPwill be
considered to be the forged pixels, as demonstrated inFig. 6, where (a) shows the distribution ofNumSPP(t,d); (b) shows
thematchedpixelpairsinSPP; and (c) shows the diagrammatic drawing calculating the distancedand orientation
?.In
Fig. 6(a), the distribution represented with different colors means different numbers of pixels, and the red, sky-blue, and
orange colors indicate that the corresponding pixel pairs can ful?ll the conditionNum
SPP(t,d)?TSPP; consequently, they are
considered 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 in
Fig. 6(b), respectively.
?2numSPP
i>?(NumSPP_S)(23)
Similarly, the ?ltering threshold forUPPcan be calculated with the proposed data-driven based threshold calculation
method, and whenNum
UPP(t,d)?TUPP, the corresponding pixel pairs are detected as forged pixels, as demonstrated in
Fig. 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 calculatedT
SPPandTUPP. 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 the
forged regions. The structural element is de?ned as a circle whose radius is related to the size of the input image. The close
operation can ?ll the gaps in the detected pixels while keeping the shape of the regions unchanged.
3. Experimental results and discussions
We have proposed a novel CMFD method in this paper. The novel feature extraction method is proposed to extract the
Multi-Level Dense Descriptor, and the Hierarchical Feature Matching method is proposed to detect the forgery regions based
on theMLDDfeatures. In this section, a series of experiments are conducted to evaluate the effectiveness and robustness
of the proposed CMFD method. In the following experiments, the image dataset CMFDA6is used to test the proposed
method. This CMFDA dataset, which has 1728 images in total, as shown inTable 1, was created based on 48 high-resolution
uncompressed PNG true-color images. The average size of the images is 3000×2300. In the dataset, the copied regions
come from various categories of living, natural, man-made and even mixed images, and they range from overly smooth
to highly textured. The copy–move forgeries were created by copying, scaling and rotating semantically meaningful image
regions. Furthermore, JPEG compression and noise addition can be added to the forgery images. In summary, the dataset
contains 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 evaluate
the 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 were
detected using the proposed scheme.

236X. Bi et al. / Information Sciences 345 (2016) 226–242
Fig. 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 1
Parameter settings of the dataset CMFDA.
Parameters Range Step Number of forgery images
JPEG compressionQuality factor 20–100 10 432
Noise additionStandard deviation 20–100 20 240
ScaleScaling factor 91%–109% 2% 480
RotationAngle 2°–10°2°240
Down sampling90% –10% 20% 240
Plain copy–move 48
Fig. 9.The copy–move forgery detection results of the proposed scheme. Row 1: ?ve host images from the dataset; Row 2: the ground-truth forgery
regions 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) 226–242237
Ta b l e 2
Detection results under plain copy–move at image level.
Image level SIFT6SURF6Bravo4SBFD19ASBFD28Proposed method on CMFDA Proposed method on CMFDPM
Precision(%) 88.37 91.4 9 87.27 70.169688.89 89.53
Recall(%) 79.17 89.5810 083.33100 100.096.25
F(%) 83.52 90.52 93.20 76.1897.9694.12 92.77
Ta b l e 3
Detection results under plain copy–move at pixel level.
Image level SIFT6SURF6Bravo4SBFD19ASBFD28Proposed method on CMFDA Proposed method on CMFDPM
Precision(%) 62.26 69.43 83.23 81.90 82.4587.20 91.37
Recall(%) 69.56 74.85 41.80 54.095 70.7989.68 84.64
F(%) 65.71 72.04 55.65 65.16 76.1888.42 87.88
To 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 pixels
to 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-truth
forged image. In addition, theFscore is used as a measure that combinesprecisionandrecallinto a single value, which is
de?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 feature
point based algorithm combined the methods of1and26; they built the clusters described by1and then computed the
a?ne transformation between the clusters using RANSAC. In the following, the results of the proposed method are compared
with 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 followingSections
3.1, 3.2,and3.3, respectively, demonstrate the forgery detection results when under plain copy–move, various attacks, and
down-sampling. Finally,Section 3.4demonstrates the summary of the comparison.
3.1. Forgery detection results under plain copy–move
In this section, we evaluate the proposed method under ideal conditions, those of one-to-one plain CMF. In this case, in
addition to the CMFDA6, which consists of 48 original images and 48 forgery images, we also test the proposed scheme in
the dataset CMFDPM8, which is made up of 80 images with a 768×1024-pixel resolution (www.grip.unina.it). The task is
to 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-truth
data are available, image level decisions are of particular interest for automated detection of manipulated images. At the
pixel level, theprecisionandrecallrates are calculated by counting the number of pixels in the corresponding regions. At
the image level, theprecisionis the probability that a detected forgery is truly a forgery, whilerecallis the probability that
a forgery image is detected. In general, higherprecisionas well as higherrecallindicates superior performance. To reduce
the effect of random samples, the averageprecision/recallis computed for all the images in the dataset. Implemented on a
PC running the Windows 7 operating system and a 2.4 GHz CPU, the new proposed method takes approximately 2263.15 s
on 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 operations
at the image level and pixel level, respectively. Considering the time complexity, we ?rst down-sampled the images to
half their size; therefore, the following experiments are conducted on images of moderate resolution, with a typical size
of 1500×1150. To ensure a fair comparison, the existing state-of-the-art methods are evaluated using images of medium
resolution as well. InTables 2and3, text in bold indicate the best results, while text in italics indicate the results of the
proposed method. As shown inTable 2, at the image level, our method achieves aprecisionof 88.89% on the CMFDA dataset
and aprecisionof 89.53% on the CMFDPM dataset. Simultaneously, it achieves a 100%recallon the CMFDA dataset and a
96.25%recallon the CMFDPM dataset. In contrast, while the SIFT based method6achieves aprecisionof 88.37% and a
79.17%recall, the SURF based method6achieves aprecisionof 91.49% and an 89.58%recall. The method proposed by Bravo
4achieves 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-art
forgery 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) 226–242
According toTable 3, at the pixel level, the advantage of the proposed detection method is especially important; our
method can achieve aprecisionof 87.20% on the CMFDA dataset and aprecisionof 91.37% on the CMFDPM dataset, and
simultaneously, an 89.68%recallon the CMFDA dataset and an 84.64%recallon the CMFDPM dataset, which is much better
than 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;themethod
proposed by Bravo4and the SBFD method19can achieve aprecisionabove 80%, but theirrecallis only approximately
50%; 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 attacks
In addition to the one-to-one plain CMF, we also tested our proposed method when the copied regions are attacked
by 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 forgery
images 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 of
theprecision,recallandFscore, denoted by the symbols ”, ‘?’, and ‘
‘, respectively.Fig. 10shows the performance of the
proposed 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 several
state-of-the-art forgery detection methods: the SIFT based method6, for which the results are shown in green, the SURF
based method6, for which the results are shown in red, the method proposed by Bravo4, for which the results are
shown in rose-red, the SBFD method19, for which the results are shown in yellow, and the ASBFD method28, which we
proposed earlier, for which the results are shown in blue. The results of the method proposed in this paper are shown in
sky-blue.
It can be easily observed that with common signal processing such as noise addition and JPEG compression, as shown
inFig. 10(a)–(f), the proposed method outperforms all the other state-of-the-art methods in terms ofprecision,recall,andF
score. When under geometric attacks such as scaling and rotation, the proposed method outperforms the others in terms of
Fscore, as demonstrated inFig. 10(i) and (l). Furthermore, the performance of the proposed method is similar to the ASBFD
method28that we proposed earlier and to the method proposed by Bravo4, and its performance is much better than
the other state-of-the-art methods in terms of theprecision,asdemonstratedinFig. 10(g) and (j). In terms of therecall,the
proposed method performs similarly to the SBFD method19, and it outperforms the other methods, as demonstrated in
Fig. 10(h) and (k).
3.3. Forgery detection results under down-sampling
Because it has been proven that the performance of the forgery detection method depends on the quality of the host
images, 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 that
the 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 method
proposed by Bravo4, indicated in rose-red; and the ASBFD method28, which we proposed earlier and is indicated in
blue. It can be easily observed that when the down-sampling factor drops from 90% to 30%, the performances of most of
the existing methods decline noticeably, while the performance of the proposed method remains perfectly stable, which
indicates 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 still
achieves 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 we
also 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 demonstrate
the forgery detection results of the proposed method. In addition, the traditional sparse SIFT feature and the proposed dense
descriptorMLDDare used to demonstrate the superiority ofMLDD. The corresponding results are compared to reveal the
better performance of the proposed method. InFig. 12, the 1st column shows the “Four_babies” and “Jelly?sh_choas” images
and their ground truths. The 2nd–6th columns show the detected results when the host images are down-sampled at factors
of 90%, 70%, 50%, 30%, and 10%, respectively. In each of the two examples, the 1st row shows the detection results based on
the traditional sparse SIFT feature, while the 2nd row shows the detection results based onMLDD. It can be easily observed
that when the down-sampling factor decreases, the performance of the traditional forgery detection method using sparse
SIFT declines noticeably, as shown inFig. 12(a1)–(a3), (c1)–(c3), and when the down-sampling factor drops to 30%, it is close

X. Bi et al. / Information Sciences 345 (2016) 226–242239
Fig. 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 method
usingMLDDperforms much better and continues to perform steadily even when the down-sampling factor drops to 10%, as
shown inFig. 12(b1)–(b5),(d1)–(d5).
3.4. Comprehensive comparisons
As a summary, in this section, we provide a comprehensive comparison inTable 4,wheretheFscore de?ned in (24)is
employed to evaluate the comprehensive robustness of the schemes. InTable 4,theFscore is de?ned asF?0.5tomakethe

240X. Bi et al. / Information Sciences 345 (2016) 226–242
Fig. 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 traditional
sparse 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 compared
schemes under various attacks; it is robust against: JPEG compression, with the quality factor up to 20, noise addition, with
the standard derivation up to 0.1, the scale, with the scaling factor varied between 0.91 and 1.09, and rotation, with the
rotation angle up to 10
?. In addition to the robustness, the proposed scheme performs very well on images of different
resolutions, especially low resolution. The schemes are tested on images at high, medium and low resolutions, and the

X. Bi et al. / Information Sciences 345 (2016) 226–242241
Ta b l e 4
Comprehensive comparisons.
Robustness Resolution
JPEG compression Noise addition Scale Rotation High 100%?70% Medium 70%?40% Low40%?10 %
Quality factor Standard derivation Scaling factor AngleFscores
SIFT13Fail?0.06 0.99–1.01 Fail 0.66–0.60 0.60–0.41 0.41–0.08
SURF13?50?0.06 0.97–1.09?10°0.72–0.61 0.61–0.42 0.42–0.02
Bravo20Fail Fail Fail Fail 0.90–0.44 0.44–0.43 0.43–0.11
SBFD9?20?0.10 0.91–1.09?10°– –
ASBFD10?30?0.020.91–1.09?10°0.93–0.830.83–0.61 0.61–0.04
Proposed 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 with
existing methods.
4. Conclusions
In 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 the
existing sparse features. For each pixel, the color texture feature and the geometric invariant moments are calculated as
MLDD_CTandMLDD_IM, respectively. Pixels with similar color textures are selected and grouped together into distinctive
neighbor pixel sets. Using this method, each pixel is matched with pixels only in its neighbor pixel set instead of all the
other 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 matched
with its corresponding neighbor pixel set through its geometric invariant momentsMLDD_IM,thus generating the matched
pixel pairs. Afterward, an Adaptive Distance and Orientation Based Filtering method was proposed to ?lter out redundant
pixels. 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 forSPP
andUPPare 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 forgery
detection 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, not
only in detection accuracy and effectiveness, but also in robustness against various attacks. In addition, the performance of
the proposed method is compared with a number of existing state-of-the-art CMFD methods, and the comparison results
show the superiority of the proposed method even when under various challenge conditions such as geometric transforms,
JPEG compression, noise addition and down-sampling.
Acknowledgment
This research was supported in part by the Research Committee of the University of Macau (MYRG2015-00011-FST,
MYRG2015-00012-FST) and the Science and Technology Development Fund of Macau SAR (008/2013/A1,093-2014-A2).
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