Pattern Anal Applic

DOI 10.1007/s10044-016-0588-1

THEORETICAL ADVANCES

Robust copy–move forgery detection using quaternion exponent

moments
Xiang-yang Wang1 • Yu-nan Liu1 • Huan Xu1 • Pei Wang1 • Hong-ying Yang1

Received: 21 December 2015 / Accepted: 20 October 2016

Ó Springer-Verlag London 2016

Abstract The detection of forgeries in color images is a 88% across postprocessing operations, at image level and
very important topic in forensic science. Copy–move (or at pixel level, respectively.
copy–paste) forgery is the most common form of tamper-
ing associated with color images. Conventional copy–move Keywords Digital image forensics  Copy–move forgery
forgeries detection techniques usually suffer from the detection  Quaternion exponent moments  E2LSH
problems of false positives and susceptibility to many
signal processing operations. It is a challenging work to
design a robust copy–move forgery detection method. In 1 Introduction
this paper, we present a novel block-based robust copy–
move forgery detection approach using invariant quater- With the development of multimedia technology and
nion exponent moments (QEMs). Firstly, original tempered multimedia processing tools, digital image forgery has
color image is preprocessed with Gaussian low-pass filter, been increasingly easy to perform. It has become a severe
and the filtered color image is divided into overlapping threat to security that anyone may access and modify the
circular blocks. Then, the accurate and robust feature content of an image without leaving visually
descriptor, QEMs modulus, is extracted from color image detectable traces. In recent years, many researchers have
block holistically as a vector field. Finally, exact Euclidean begun to focus on the problem of digital image forgery, and
locality sensitive hashing is utilized to find rapidly the various methods have been developed to counter tampering
matching blocks, and the falsely matched block pairs are and forgery in order to ensure the authenticity of images.
removed by customizing the random sample consensus Current image forgery detection methods can be roughly
with QEMs magnitudes differences. Extensive experi- categorized as active and passive (blind). Active methods
mental results show the efficacy of the newly proposed such as watermarking or illegal image copy detection
approach in detecting copy–paste forgeries under various depend on prior information about the image. However, in
challenging conditions, such as noise addition, lossy many situations, prior information regarding an image is
compression, scaling, and rotation. We obtain the average not available and passive, or blind methods should be used
forgery detection accuracy (F-measure) in excess of 96 and to authenticate the image. The practicality and wide
applicability of passive methods have made them a popular
topic of research [1].
Copy–move (or copy–paste) forgery is one of the most
& Xiang-yang Wang common types of image forgeries, where a region from one
wxy37@126.com part of an image is copied and pasted onto another part,
& Hong-ying Yang thereby concealing the image content in the latter region.
yhy_65@126.com Such concealment can be used to hide an undesired object
1 or increase the number of objects apparently present in the
School of Computer and Information Technology,
Liaoning Normal University, Dalian 116029, Liaoning, image. Although a simple translation may be sufficient in
People’s Republic of China many cases, additional operations are often performed in

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 Pattern Anal Applic

order to better hide the tampering. These include scaling, regions (i.e., the ‘‘keypoints’’). A feature vector is then
rotation, lossy compression, noise addition, blurring, extracted per keypoint. Consequently, fewer feature vec-
among others. Because the wide availability of image tors are estimated, resulting in reduced computational
processing software has made it easy to perform copy– complexity of feature matching and postprocessing. The
move operations, passive copy–move forgery detection lower number of feature vectors dictates that postprocess-
(CMFD) is becoming one of the most important and pop- ing thresholds are also to be lower than that of block-based
ular digital image forensic techniques currently [2, 3]. In methods. Because the number of the keypoints is much
this paper, we focus passive image copy–move forgery smaller than that of the blocks divided in an overlapping
detection. In previous years, many passive forgery detec- way, the keypoint-based algorithms require less computa-
tion approaches have been proposed for copy–move for- tional resource than the block-based ones. In this regard,
gery detection. According to the existing approaches, the the keypoint-based methods are faster and more favorable
copy–move forgery detection algorithms can be catego- than the block-based ones. However, on the other hand,
rized into two main categories: block-based algorithms and keypoint-based method also has the following two prob-
keypoint-based algorithms. They both try to detect the lems. Firstly, the keypoints lying spatially close to each
copy–move forgery through describing the local patches of other should not be compared because they may be natu-
one image. rally similar. The determination of the shortest distance
The block-based forgery detection methods usually between two comparable keypoints is tricky. Most prior
divide the input images into overlapping and regular image arts empirically select this threshold but neglect its rela-
blocks, and then the tampered region can be obtained by tionship with the image size and content. Secondly, it is
matching blocks of image pixels or transform coefficients. uneasy to accurately localize and distinguish the copying
Because the descriptor of the block is important for the source region and the pasting target region, because, unlike
algorithm, various description methods, like 1D fourier the overlapping blocks, the keypoints are often not con-
transform (FT), discrete cosine transform (DCT), discrete centrated together [4–9].
wavelet transform (DWT), singular value decomposition Based on invariant quaternion exponent moments
(SVD), geometric moment, histogram, and principal com- (QEMs), we propose a novel block-based robust copy–
ponent analysis (PCA), were tested in these papers [4–9]. move forgery detection approach in this paper. The novelty
Although these block-based forgery detection methods are of the proposed approach includes: (1) Image blocks are
effective in forgery detection, they have four main draw- represented by QEMs holistically as a vector field. The
backs: (1) Nearly all of these methods are based on a large accurate and invariant property of QEMs magnitude makes
number of blocks and the feature vectors extracted from the these moments particularly promising CMFD features; (2)
blocks are large, which results in high computational circular image blocks are adopted instead of rectangular
complexity due to the fact that multiple-index sorting is blocks, which are robust to geometrical transformations
required to enable lexicographical sorting of all of the (e.g., scaling, rotation); (3) the E2LSH-based image block
blocks. In addition, higher computational load for extract- matching is introduced. It can effectively detect the image
ing feature vectors is also the weakness of some block- block pairs with similar feature vectors; (4) QEMs mag-
based forgery detection methods; (2) the host image is nitudes are incorporate into the false matching reduction
usually divided into overlapping rectangular blocks, which procedure, which can effectively remove false positives
are fragile to geometrical transformations (e.g., scaling, and enhance the detection accuracy significantly.
rotation). So, the existing methods always cannot address The rest of this paper is organized as follows. A review
significant geometrical transformations of the forgery of previous related work is presented in Sect. 2. Section 3
regions; (3) their recall rate is low under various noises and introduces the quaternion Exponent moments and analyzes
geometric transformations, the reason for this is that the the invariant property of quaternion Exponent moments.
extracted feature description usually cannot stably capture Section 4 contains the description of our copy–move for-
the image information; and (4) most of the existing copy– gery detection procedure. Simulation results in Sect. 5 will
move forgery detections are designed mainly for gray show the performance of our scheme. Finally, Sect. 6
images in which the significant information correlation concludes this presentation.
between different color channels is ignored, and they are
often not robust with respect to photometric variations such
as illumination direction, intensity, colors, and highlights. 2 Related work
As an alternative to the block-based methods, keypoint-
based forgery detection methods were proposed. Unlike Over the past decades, passive copy–move forgery detec-
block-based algorithms, keypoint-based methods rely on tion has been an active area of research in many applica-
the identification and selection of high-entropy image tions, including: criminalization, surveillance systems,

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Pattern Anal Applic

Table 1 Survey of the state-of-the-art passive copy–move forgery detection (CMFD) algorithms
Category Methods Authors

Block-based CMFD algorithms Using color-dependent feature vectors and 1-D descriptors Bravo-Solorio et al. [10]
Using Zernike moments of rectangular image blocks Ryu et al. [11]
Using multiresolution local binary patterns Davarzani et al. [12]
Using fast approximate nearest neighbor search Cozzolino et al. [13]
Using approximate 2D-DWT coefficients Fattah et al. [14]
Using Krawtchouk moments Imamoglu et al. [15]
Using histogram of orientated gradients Lee et al. [16]
Using dual tree complex wavelet transform Wu et al. [17]
Using DCT and SVD Jie et al. [18]
Using 1D-Fourier transform Ketenci et al. [19]
Using the histogram of orientated Gabor magnitude Lee et al. [20]
Using undecimated dyadic wavelet transform Muhammad et al. [21]
Using Zernike moments Al-Qershi et al. [22]
Keypoint-based CMFD algorithms Using SIFT features Amerini et al. [23]
Using multi-scale analysis and voting process Silva et al. [24]
Using multiscale Harris operator and MPEG-7 descriptor Kakar et al. [25]
Using local warping algorithms Caldelli et al. [26]
By matching triangles of keypoints Ardizzone et al. [27]
Using distribution of SIFT keypoints Costanzo et al. [28]
Using segmentation and keypoints extraction Li et al. [29]
Using Harris corner detector Chen et al. [30]
Using mirror reflection invariant feature transform (MIFT) features Jaberi et al. [31]
Using MROGH and HH Yu et al. [32]

medical imaging, and news media. Many approaches have duplicated regions after arbitrary rotations, and a novel
been proposed to solve this problem. They can be roughly block matching procedure was devised based on locality
divided into two major categories: block-based algorithms sensitive hashing. Davarzani et al. [12] presented an effi-
and keypoint-based algorithms. Table 1 summarizes some cient method for copy–move forgery detection using mul-
inspiring and pioneering copy–move forgery detection tiresolution local binary patterns (MLBP). The proposed
algorithms. method is robust to geometric distortions and illumination
variations of duplicated regions. Furthermore, the proposed
2.1 Block-based algorithms block-based method recovers parameters of the geometric
transformations. Cozzolino et al. [13] proposed a new
These algorithms seek dependence between the image algorithm for the accurate detection and localization of
original area and the pasted one, by dividing the image into copy–move forgeries, based on rotation-invariant features
overlapping blocks and then applying a feature extraction computed densely on the image. Here, the PatchMatch
process in order to represent the image blocks through a algorithm was used to compute efficiently a high-quality
low-dimensional representation. Different block-based approximate nearest neighbor field for the whole image.
representations have been previously proposed in the lit- Fattah et al. [14] developed a copy–move image forgery
erature such as FT, DCT, DWT, SVD, geometric moment, detection scheme based on a block matching algorithm.
histogram, and PCA. Bravo-Solorio et al. [10] proposed a Instead of considering spatial blocks, 2D-DWT is per-
new method to detect duplicated regions, which uses color- formed on the forged image and then DWT domain blocks
dependent feature vectors to reduce the number of com- are considered, where only approximate DWT coefficients
parisons in the search stage, and one-dimensional (1-D) are utilized. Imamoglu et al. [15] used Krawtchouk
descriptors to perform an efficient search in terms of moments to extract features of non overlapping image
memory usage. Ryu et al. [11] proposed a forensic tech- blocks. For each block, the Krawtchouk moments of order
nique to localize duplicated image regions based on Zer- (n ? m) are calculated to form the feature vector. Then,
nike moments of small image blocks. The rotation blocks’ similarities are tested by inspecting the lexico-
invariance properties were exploited to reliably unveil graphically sorted array of features. Lee et al. [16]

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proposed a blind forensics approach to the detection of 2.2 Keypoint-based algorithms

copy–move forgery. The input image is segmented into
overlapping blocks, whereupon a histogram of orientated As an alternative to the block-based approaches, keypoint-
gradients is applied to each block. Statistical features are based forgery detection algorithms were proposed, where
extracted and reduced to facilitate the measurement of image keypoints are extracted and matched over the whole
similarity. Finally, feature vectors are lexicographically image to resist some image transformations while identi-
sorted, and duplicated image blocks are detected by iden- fying duplicated regions. Some works have recently
tifying similar block pairs after post-processing. Wu et al. appeared on copy–move forgery detection based on scale-
[17] presented a new forensic method to detect the repli- invariant features transform (SIFT) or Speed up Robust
cated areas rotated by arbitrary angles, even by JPEG Feature (SURF) features. Amerini et al. [23] proposed a
compression. To achieve this, overlapping blocks of pixels novel methodology to support image forensics investiga-
are decomposed using dual tree complex wavelet transform tion based on SIFT features, which are used to robustly
(DTCWT), and then channel energies are extracted from detect and describe clusters of points belonging to cloned
each sub-band at each decomposition level using the L1 areas. After detection, these points are exploited to recon-
norm. Finally, the anisotropic rotationally invariant fea- struct the parameters of the geometric transformation. By
tures are extracted using magnitudes of discrete Fourier using multi-scale analysis and voting processes of a digital
transform for these channel energies. Jie et al. [18] pro- image, Silva et al. [24] proposed a new approach to detect
posed a robust copy–move forgery detection method based copy–move forgeries in digital images that is focused
on DCT and SVD. Firstly, the suspicious image is divided mainly on investigating and spotting out traces of copy–
into fixed-size overlapping blocks and 2D-DCT is applied move forgeries aided by complex operation. Kakar et al.
to each block, and then the DCT coefficients are quantized [25] proposed a copy–move forgery detection technique
by a quantization matrix to obtain a more robust repre- using multiscale Harris operator and MPEG-7 image sig-
sentation of each block. Secondly, each quantized block is nature tools. They also used a feature matching process that
divided nonoverlapping sub-blocks and SVD is applied to utilizes the inherent constraints in matched feature pairs to
each sub-block, and then features are extracted to reduce improve the detection of cloned regions. Caldelli et al. [26]
the dimension of each block using its largest singular investigated the effectiveness of some methodologies
value. Finally, the feature vectors are lexicographically which introduce a local warping onto the copy–pasted
sorted, and duplicated image blocks will be matched by patches in order to reduce the detection capability of SIFT-
predefined shift frequency threshold. Ketenci et al. [19] based approaches. They compared four different local
presented a copy–move forgery detection technique that warping algorithms in terms of removed matches after the
uses 1D-Fourier Transform (FT) for feature extraction. attack and visual quality of the attacked patches. Ardizzone
Each block is transformed into frequency domain using et al. [27] presented a very novel hybrid approach, which
1D-FT over the rows. Average values of FT coefficients compares triangles rather than blocks, or single points.
along the columns are calculated to extract the feature Interest points are extracted from the image and objects are
vectors from the blocks. Lee et al. [20] proposed a modeled as a set of connected triangles built onto these
scheme for detecting instances of copy–move forgery and points. Triangles are matched according to their shapes
authenticating images based on the Gabor transform. The (inner angles), their content (color information), and the
image is first divided into overlapping fixed-size blocks. local feature vectors extracted onto the vertices of the tri-
The histogram of orientated Gabor magnitude (HOGM) angles. Costanzo et al. [28] proposed three novel forensic
descriptor is then applied to each block for the extraction of detectors for the identification of images whose SIFT
local features. Finally, each feature vector is lexicograph- keypoints have been artificially removed and possibly
ically sorted, and regions of image forgery are detected reinserted. The proposed algorithms scan image regions
through the identification of similar block pairs. Muham- with sufficiently high variance in search of suspect incon-
mad et al. [21] proposed a blind method for copy–move sistencies in the number and in the distribution of SIFT
image forgery detection using undecimated dyadic wave- keypoints. By relying on such algorithms, the forensic
lets, in which both the LL1 and HH1 sub-bands are utilized analyst can decide on the authenticity of the image as a
to find similarities and dissimilarities between the blocks of whole or localize tampered regions within the image by
an image. Al-Qershi et al. [22] proposed an enhanced means of a sliding window approach. Li et al. [29] pro-
matching method that can be used to detect copy–move posed a scheme to detect the copy–move forgery in an
forgery based on Zernike moments. By dividing the blocks image, mainly by extracting the keypoints for comparison.
into buckets and adopting relative error instead of Eucli- The main difference to the traditional methods is that the
dean distance, the proposed method enhanced the detection proposed scheme first segments the test image into
accuracy significantly. semantically independent patches prior to keypoint

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Pattern Anal Applic

extraction. As a result, the copy–move regions can be where a, b, c, and d are real numbers, and i; j and k are
detected by matching between these patches. Chen et al. three imaginary units.
[30] proposed an effective method to detect region dupli- Using this representation, a color image f ðx; yÞ, sized by
cation based on the image interest points detected through M  N, can be considered as an array of pure quaternion
the Harris corner detector. After the interest points are numbers (e.g., with no real parts)
obtained, a rotation-robust image region description f ðx; yÞ ¼ fR ðx; yÞi þ fG ðx; yÞj þ fB ðx; yÞk
method based on step sector statistics is proposed to give a
unique representation for each small circle region around where fR ðx; yÞ, fG ðx; yÞ, and fB ðx; yÞ represent, respectively,
the interest points. Then the matching of the representa- the classical red, green, and blue components. Obviously,
tions of the interest points will reveal the duplicate regions by using the quaternion-type representation, a color image
in the forged digital images. Jaberi et al. [31] adopted can be treated as a vector field and be processed directly,
keypoint-based features for copy–move image forgery without losing color information.
detection, which employing a new set of keypoint-based Let f ðr; hÞ be a RGB color image defined in polar
features, called MIFT, for finding similar regions in an coordinates, the quaternion Exponent moments (QEMs)
image. To estimate the affine transformation between [34] of order n with repetition m (n and m in (1) are gen-
similar regions more accurately, an iterative scheme was erally called order and repetition, respectively),
proposed which refines the affine transformation parameter jnj ¼ jmj ¼ 0; 1. . .; 1, is defined as
by finding more keypoint matches incrementally. Yu et al. Z Z
1 2p 1
[32] proposed two-stage feature detection to obtain better En;m ¼ f ðr; hÞAn ðr Þ expðlmhÞrdrdh ð1Þ
4p 0 0
feature coverage and enhance the matching performance by
combining the multi-support region order-based gradient where l is a unit pure quaternion chosen as
pffiffiffi
histogram (MROGH) and hue histogram (HH) descriptor. l ¼ ði þ j þ kÞ= 3, and An ðrÞ is the conjugate of radial
basis function An ðrÞ given by
qffiffiffiffiffiffi
3 Introduction to quaternion exponent moments An ðrÞ ¼ 2=r expðj2nprÞ; m ¼ 1; . . .; 0; . . .; þ1

In 2011, Jiang et al. [33] extended radial harmonic Fourier Since the radial Exponent basis functions are orthogo-
moments and introduced a new moment named Exponent nal, the color image f ðr; hÞ can be reconstructed approxi-
moments (EMs) according to the relation between the mately from a limited orders of QEMs (n  nmax ,
exponential function and triangular function. Compared m  mmax ). The more orders used, the more accurate the
with other orthogonal moment, EMs has a better image color image description
reconstruction, lower noise sensitivity, and lower compu- þ1 X
X þ1
0
tational complexity, especially for small images. Besides, f ðr; hÞ ¼ En;m An ðrÞ expðlmhÞ
EMs is free of numerical instability issues so that high- n¼1 m¼1
order moments can be obtained accurately. Generally, by X
þn max X
þm max

 En;m An ðr Þ expðlmhÞ ð2Þ

using the quaternion-type representation, a color image can n¼nmax m¼mmax
be treated as a vector field and be processed directly, 0
without losing color information. In 2014, Wang et al. [34] where f ðr; hÞ is the reconstructed color image. The basis
extended the excellent EMs defined in gray-scale image to functions An ðrÞ expðlmhÞ of the QEMs are orthogonal over
color image using the algebra of quaternion and proposed the interior of the unit circle, and each order of the QEMs
the quaternion Exponent moments (QEMs) for describing makes an independent contribution to the reconstruction of
color images. Experimental results show that the QEMs the color image.
modulus has good robustness against various noises, geo- Below, we will derive and analyze the geometric
metric transformations, and color variations. So, the EQMs invariant property of QEMs. Let f r ðr; hÞ ¼ f ðr; h þ aÞ
modulus is suitable for descripting color image content, denote the rotation change of a color image f ðr; hÞ by the
especially for small image blocks. angle a, then QEMs of f ðr; h þ aÞ and f ðr; hÞ have the
A quaternion is regarded as a four-parameter represen- following relations
tation of a coordinate transformation matrix, where the four
En;m ðf r Þ ¼ En;m ð f Þ expðlmaÞ ð3Þ
components of the quaternion are treated on an equal basis.
A quaternion consists of one real part and three imaginary where En;m ðf r Þ and En;m ðf Þ are the QEMs of f r ðr; hÞ and
parts as follows f ðr; hÞ, respectively. According to Eq. (3), we know that a
q ¼ a þ bi þ cj þ dk rotation of the color image by an angle a induces a phase

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shift elma of the En;m ðf Þ. Taking the norm on both sides of 4.1 Gaussian low-pass filter preprocessing
Eq. (3), we have
      Gaussian filtering is a common denoising technique often
En;m ðf r Þ ¼ En;m ð f Þ expðlmaÞ ¼ En;m ð f ÞjexpðlmaÞj
  used in image processing, and it can help to improve the
¼ En;m ð f Þ
detection result when there are some post-processing
So, the rotation invariance can be achieved by taking the operation such as JPEG compression and noise contami-
norm of the color images’ QEMs. In other words, the nation [35]. The reason is that the features extracted from
QEMs modulus jEn;m ðf Þj is invariant with respect to rota- the Gaussian filtered image are more robust against those
tion transform. Besides, the QEMs modulus is invariant to operations. Thus, we first preprocess the tempered color
scaling if the computation area can be made to cover the image I by a 2-D Gaussian low-pass filter
same content. In practice, this condition is met because the 1 x2 þy2 2
QEMs are defined on the unit disk. Fðx; y; rÞ ¼ e 2r ð4Þ
2pr2
Some examples of the reconstructed image Lena are
where ðx; yÞ denotes the position of the pixel and r is the
shown in Fig. 1. As more moments are added to the
standard deviation of the distribution, which is usually
reconstruction process, the reconstructed images get closer
chosen as r = 1. The Gaussian filtered image Ilow can be
to the original images. As can be observed from the
expressed as
reconstructed images, QEMs capture the color image
information, especially the edges. Ilow ðx; yÞ ¼ Fðx; y; rÞ  Iðx; yÞ ð5Þ
Figure 2 shows the QEMs modulus distribution for color
where * denotes the convolution operator. If Ihigh stands for
image Lena under various attacks. It can be seen that the
the high-frequency component removed by the Gaussian
QEMs modulus has good robustness against various noises,
filtering from the tempered color image I, it follows
geometric transformations, and color variations.
Ihigh ðx; yÞ ¼ Iðx; yÞ  Ilow ðx; yÞ ð6Þ
In practice, the size of the Gaussian mask F is often
4 The proposed robust copy–move forgery
chosen using expression ð2kr þ 1Þð2kr þ 1Þ, where k is a
detection
positive integer. In this paper, we set k to be 3, thus the size
of the Gaussian mask F is 7 9 7.
The proposed framework for robust copy–move forgery
detection shown in Fig. 3 is carried out in five steps
4.2 Dividing the filtered color image
here. First, Gaussian low-pass filter preprocessing is
into overlapping circular blocks
applied to the original tempered color image to reduce
noise impact. Second, the filtered color image is divided
To identify forged regions, the Gaussian filtered image
into overlapping circular blocks, which are robust to
should be firstly divided into numbers of overlapped
geometrical transformations (e.g., scaling, rotation).
blocks, and then the similarity between every two image
Third, the accurate feature descriptor, QEMs modulus, is
blocks is computed. But for the existing CMFD approa-
extracted from color image block holistically as a vector
ches, the image is usually divided into overlapping rect-
field, which can achieve good robustness against various
angular blocks, which are fragile to some geometrical
noises, geometric transformations, and color variations.
transformations such as rotation. So, these methods always
Fourth, the exact Euclidean LSH (E2LSH), a scheme of
cannot address significant geometrical transformations of
locality sensitive hashing (LSH) realized in Euclidean
the forgery regions.
space, is adopted to find rapidly the matching image
In this paper, we divide the Gaussian filtered image into
blocks. Finally, the random sample consensus (RAN-
overlapping circular blocks. The circular image blocks
SAC) algorithm is utilized to remove the false positives
slide along the Gaussian filtered image for feature extrac-
from the set of potential copy–move image blocks. The
tion, from upper left to bottom right, with a displacement of
following sections provide detailed steps in this proposed
one pixel in horizontal or vertical directions at each time.
framework.

Fig. 1 Reconstructed images for color image Lena of size 128 9 128 (moment orders K = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50)

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Pattern Anal Applic

Fig. 2 QEMs modulus for color image Lena under various noises, geometric transformations, and color variations: a original image, b Gaussian
filtering, c salt and pepper noise, d JPEG 50, e blurring, f contrast changing, g rotation (45°), h scaling (0.8), i affine translation

Tempered Detection
color results
image

Gaussian filter Color image Block feature Block pairs Detection results
preprocessing blocking extraction matching post-processing

Fig. 3 Proposed framework for robust copy–move forgery detection

Given an M 9 N color image under analysis, we denote image, even under some severe conditions. However, most
overlapping circular blocks with radius R as Bi;j , where of the existing CMFD algorithms are designed mainly for
subscript ði; jÞ 2 fR; R þ 1; . . .; M  Rg  fR; R þ 1; . . .; gray images in which the significant information correla-
N  Rg refers to row and column index of a circular tion between different color channels is ignored, and they
block’s center in the intensity plane, respectively. So, the are often not robust with respect to photometric variations
number of the overlapping circular image blocks is such as illumination direction, intensity, colors, and
ðM  2R þ 1Þ  ðN  2R þ 1Þ. highlights.
From the foregoing, we know that QEMs can effec-
4.3 Image block feature extraction tively capture the color image contents holistically as a
vector field, and QEMs modulus has good robustness
Feature extraction is a prerequisite step for CMFD and against various noises, geometric transformations, and
crucial to detection accuracy. It is desired that the blocks in color variations, especially for small image blocks. So,
a copy–move pair can be mapped to similar features even the QEMs modulus is employed to extract features from
in the presence of post-processing. At the same time, the the circular image blocks in this paper, and the feature
features should correctly distinguish distinct blocks in the vector Eði;jÞ of each circular block Bi;j is composed of the

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Table 2 List of the selected QEMs features for different max orders
Order Moments No. of moments Accumulative no.

1 jE1;1 j 1 1
2 jE2;2 j; jE2;1 j; jE2;0 j 3 4
3 jE3;3 j; jE3;2 j; jE3;1 j; jE3;0 j 4 8
4 jE4;4 j; jE4;3 j; jE4;2 j; jE4;1 j; jE4;0 j 5 13
8 jE8;8 j; jE8;7 j; jE8;6 j; jE8;5 j; jE8;4 j; jE8;3 j; jE8;2 j; jE8;1 j; jE8;0 j 9 43
9 jE9;9 j; jE9;8 j; jE9;7 j; jE9;6 j; jE9;5 j; jE9;4 j; jE9;3 j; jE9;2 j; jE9;1 j; jE9;0 j 10 53

QEMs modulus computed with different values of n and range of multimedia applications, such as content-based
m, as image retrieval, image classification, and scene recogni-
         T tion. To identify duplicated block pairs with the same or
 ði;jÞ   ði;jÞ   ði;jÞ   ði;jÞ   
Eði;jÞ ¼ E0;0 ; E1;0 ; E1;1 ; . . .; Enmax ;mmax 1 ; Enði;jÞ
max ;mmax
 similar block features is a key step in copy–move forgery
ð7Þ detection, and exhaustive searching and lexicographic
sorting strategies have been utilized in most of the existing
Here, the selected QEMs modulus conveys different block-based CMFD methods in recent years. The exhaus-
visual information of the circular block. Those with small tive searching and lexicographic sorting for the neighbors
values of n and m capture the coarse skeleton of the circular according to their similarities entails exhaustively com-
block, and the others characterize its visual details. In this paring the queries with the blocks over the entire image.
manner, the feature vector can provide a rich representation These strategies have linear complexity with respect to the
of the circular block, which can effectively reduce the rate scale of the image blocks, which is infeasible on ever larger
of false detections. image. Besides, to achieve satisfying performance on such
However, we do not need all the QEMs modulus in images, most of the related CMFD methods have to rely on
color image block pairs matching. The choice of the max the high-dimensional or structured image block represen-
order value nmax will depend on the size of the given color tations, as well as the computationally considerable dis-
image and also on the resolution needed. The number of tance functions. Therefore, the exhaustive searching and
QEMs modulus required, however, does not need to be lexicographic sorting strategies are prohibitively expensive
large, since color image features can normally be captured in practical situations.
by just a few low-frequency modulus. Further, the QEMs In order to match image blocks and accurately identify
modulus jEn;m j ¼ jEn;m j and the values of jE0;0 j and jE1;0 j regions that are likely to have been forged, the corre-
are nearly constant for all normalized images, so only sponding image blocks should be identified by estimating
jEn;m j (n  1; m  0) is selected as the color image block the Euclidean distances of the feature vectors
feature in this paper. Table 2 lists the selected QEMs
features for different max orders. From the reconstruction  ði;jÞ 
E  Eðk;lÞ   D1
process presented in Sect. 3 (see Fig. 1), we can see that
QEMs, with the max order up to twenty, could have a where D1 is feature Euclidean distance threshold. In this
sufficiently good color image representation power. paper, we improve the structure of image block pairs
matching algorithm and propose an enhanced model based
4.4 Image block pairs matching on the exact Euclidean locality sensitive hashing (E2LSH)
[36], which has been widely used in large scale video/
After image block feature extraction, the CMFD algorithm image similarity search and rapid retrieval applications.
will identify a number of potential copy–move pairs by E2LSH is a scheme of LSH realized in Euclidean space.
searching the image blocks with similar feature vectors, The key idea of LSH is to hash the points using several
and these potential image block pairs will consequently hash functions so as to ensure that for each function, the
undergo further verifications. We know, with the explosive probability of collision is much higher for objects which
data growth, fast similarity indexing and search are always are close to each other than for those which are far apart.
considered to be one of the most fundamental problems for Here, collision refers to locating the same hash
the multimedia communities. This problem is also known h(x) = h(x0 ) with two different inputs x and x0 .
as nearest neighbor (NN) search, which is defined as According to the choice of hash function h, LSH has
accurately finding the close samples for a given query many different formats, among which E2LSH is a repre-
within a large data set. It is of great importance to a wide sentative scheme. The LSH function family that E2LSH

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Pattern Anal Applic

employed is based on p-stable distributions, and the fol- 4.5 Postprocessing to reduce false matching
lowing LSH functions was employed in this paper,
  Although the aforementioned E2LSH-based image block
aEþb
ha;b ðEÞ ¼ ð8Þ pairs matching can effectively detect the pairs with similar
x
feature vectors, false matching occurs when pairs of orig-
where bc is the floor operation, a is a d-dimensional vector inal image blocks have similar QEMs magnitudes despite
with components that are selected at random from a p- not being duplicated. To remove such false positives from
stable distribution, b is a random variable uniformly dis- the set of potential copy–move image blocks, we can
tributed in [0, x], E is the feature vectors, and x is a estimate the affine transformation parameters by cus-
constant. The hash function ha;b ðEÞ maps a d-dimensional tomizing the Random Sample Consensus (RANSAC)
vector E into the integer set. algorithm with QEMs magnitudes differences. These affine
In practical application, E2LSH usually combines k transformation parameters always have a high degree of
LSH functions, and a function set is defined as accuracy even when a significant number of errors are
present and can be used to verify whether two regions
n ¼ fg : S ! U k g
correspond by mapping one region to the other.
where gðEÞ ¼ ðh1 ðEÞ; . . .; hk ðEÞÞ, for each E 2 Rd , k RANSAC algorithm was first introduced by Fischler and
dimensional vector E ¼ ða1 ; a2 ; . . .; ak Þ is obtained after Bolles [37], which is a simple, yet powerful parameter
the mapping of gðEÞ 2 n. Then a primary hash function estimation approach designed to cope with a large pro-
hash1 and secondary hash function hash2 are utilized to portion of outliers in the input data. In essence, RANSAC
hash the vector a ¼ ða1 ; a2 ; . . .; ak Þ, constructing the hash is a resampling technique that generates candidate solu-
tables and saving the data points. hash1 and hash2 are tions using the minimum number data points required to
defined as follows estimate the underlying model parameters. This algorithm
! ! estimates a global relation that fits the data, while simul-
Xk
0
hash1 ðaÞ ¼ ri ai mod m mod s taneously classifying the data into inliers and outliers. Due
i¼1 to its ability to tolerate a large fraction of outliers, RAN-
! ð9Þ
X
k SAC is a popular choice for a variety of robust estimation
00
hash2 ðaÞ ¼ r i ai mod m problems.
i¼1 Denoting the set of all E2LSH-matched image block
0 00
where ri and ri are random integers, s is the size of hash pairs as P, a reduced set P is constructed from P by
tables, and m is a prime number. E2LSH puts data points keeping only those pairings for which at least one spatially
having the same hash1 and hash2 value into the same adjacent image block pair is also included in P. Assuming
bucket in a hash table, thus realizing data points’ partition. that the block size is smaller than the duplicated region, the
After the above E2LSH hash table building procedure rationale is that spatial neighbors of a duplicated block are
are repeated Q times with the QEMs feature vector Eði;jÞ to with high probability part of the same duplicated region.
further increase the clustering accuracy for near-duplicate Then, the RANSAC algorithm is applied to the reduced set
vectors, we can construct the overall Q hash tables, P . Denoting a pair of matched image blocks as
whereas each feature vector is stored in corresponding ðEði;jÞ ; Eðk;lÞ Þ, we select three spatially adjacent collinear
buckets g0 ðEði;jÞ Þ; g1 ðEði;jÞ Þ; . . .; gQ1 ðEði;jÞ Þ. Once the hash pairs from P to infer their 2  2 affine transformation R in
the spatial domain,
tables are generated, finding a near-duplicate image block
for a query EðqueryÞ Eði;jÞ means inspecting all buckets ði; jÞT ¼ R  ðk; lÞT þ t
g0 ðEðqueryÞ Þ; g1 ðEðqueryÞ Þ; . . .; gQ1 ðEðqueryÞ Þ for a feature

sx 0 cos u  sin u t
vector EðmatchÞ Eðk;lÞ . As image blocks in close spatial R¼  ; t¼ x
0 sy sin u cos u ty
proximity are likely to yield relatively similar QEMs

tx sx 0 cos u  sin u
modulus, we further evaluate the spatial distance between where , ; and are shift
ty 0 sy sin u cos u
image blocks in the intensity plane and require
vector, scaling matrix and rotation matrix, respectively.
kði; jÞ  ðk; lÞk  D2 ð10Þ All image pairs in P are classified into inliers or outliers
pffiffiffi
where the spatial distance threshold D2 ¼ 2 2R, R is the by checking the condition
image blocks radius. jjði; jÞT ¼ R  ðk; lÞT þ tjj\T
Among candidate image blocks satisfying (10), the pair
with minimum distance in the feature space is selected and for classification threshold T. This procedure is repeated
considered as potentially being part of a duplicated region. Niter times, each time initialized with a triple of block pairs

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 Pattern Anal Applic

Table 3 Categorization of Christlein’s dataset by texture properties

Category Assigned images
Small copied area Large copied area

Smooth Ship, motorcycle, sailing, disconnected shift, noise pattern, berries, Four babies, Scotland, hedge, tapestry, Malawi
sails, mask, cattle, swan, Japan tower, wading
Rough Supermarket, no beach, fisherman, barrier, three hundred, writing Lone cat, kore, white, clean walls, tree, christmash edge,
history, central park stone ghost, beach wood, red tower
Structured Bricks, statue, giraffe, dark and bright, sweets, Mykene, jellyfish chaos, Fountain, horses, port, wood carvings, extension
Egyptian, window, knight moves

randomly drawn from set P . The algorithm outputs the set smooth; the copy–move forgeries are created by copying,
of pairings with the largest number of inliers as duplicated rotating, and scaling semantically meaningful image
region. In this paper, the RANSAC parameters are set to regions. Table 3 shows the assignment of images to cate-
classification threshold T = 2 and iteration times gories. In summary, the dataset has 1826 color images in
Niter = 100, which resemble literature settings [37]. total, which are realistic copy–move forgeries.
After postprocessing to reduce false matching, we can In this work, we evaluate the CMFD performance at
construct a duplication map to visualize the forgery two levels: at pixel level, where we focus on how
detection result. We firstly create an all-zeros matrix M that accurately can the tampered image regions be identified;
has the same size as the tempered image and set the entry at image level, where we evaluate whether the fact that
Mi,j to one if the coordinate (i, j) in the image is covered by an image has been tampered or not can be detected. At
a copy–move pair. Then, we use a forged area threshold A, image level, we computed the error measures Precision
a value denoting the minimum area of the duplicated and Recall as
region, to remove small isolated regions. Finally, we use TP TP
mathematical morphological operations to smooth and Precision ¼ ; and Recall ¼
TP þ FP TP þ FN
connect the boundaries of the detected duplicated regions,
and the duplication map can be obtained by multiplying the where Precision denotes the probability that a detected
binary matrix with the tempered image. forgery is truly a forgery, while Recall shows the proba-
bility that a forged image is detected. TP denotes the
number of correctly detected forged images, FP denotes the
5 Simulation results number of images that have been erroneously detected as
forged, and FN denotes the falsely missed forged images.
In this section, we present the experimental results of the We also compute another criterion F as a measure which
proposed copy–move forgery detection approach. We combines Precision and Recall in a single value.
firstly discuss the various parameter values used in our
CFMD approach. We then present the quantitative results Precision  Recall
F ¼2
and examples for the detection of copy–move forgeries Precision þ Recall
subjected to many image processing operations. Also, We also used these measures at pixel level. In that case,
experimental results are compared with methods in TP denotes the number of correctly detected forged pixels.
[9, 11, 13]. All measurements are performed on a desktop FP is the number of falsely detected forged pixels, and FN
computer with Dual Core 3.4-GHz Pentium CPU and 4 GB denotes the falsely missed pixels. The previous definition
RAM memory, running MATLAB R2010b. of Precision, Recall and F measures also hold on the pixel
level.
5.1 Test image dataset and error measures In this paper, we evaluate the proposed CMFD approach
at the image level and pixel level simultaneously. This is
In this paper, the public available image dataset is utilized because that the pixel-level decisions are useful for
to evaluate the performance of different CMFD schemes, assessing the general localization performance of the
which was constructed by Christlein et al. [2]. The image approach when the ground-truth data are available and the
dataset is composed of 48 high-resolution uncompressed image-level metrics are especially interesting with respect
color images. In this dataset, the copied image regions are to the automated detection of manipulated color images. In
from the categories of nature, living, man-made, and general, a higher recall, a higher precision, and a higher F-
mixed, and they range from overly highly textured to measure indicate superior performance.

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Pattern Anal Applic

Fig. 4 Average error measures

at pixel level for different image
blocks radius

5.2 Selection of parameter values Table 4 Average CMFD performance for different values of feature
Euclidean distance at pixel level in percent
The selection of parameter values is a key component of D1 Precision Recall F
the CMFD approaches. The parameter values that we use in
50 95.21 68.37 79.58
our approach are presented in this section. These values are
100 93.89 75.58 83.74
mostly determined empirically, and the reasons for their
150 92.84 79.23 85.50
usage are explained as follows.
200 92.10 86.34 89.12
There are three parameters to be investigated: image
250 91.64 91.08 91.35
blocks radius R, feature Euclidean distance D1, and forged
300 91.08 93.25 92.15
area A. We empirically determine appropriate parameter
400 90.32 93.95 92.06
values, and several values of each parameter will be tested
500 87.62 94.14 90.76
to see their effect on the identification of the non-forged
and forged images. From the above public available image 600 84.06 94.55 88.96
dataset, we selected randomly 20 color images and created 700 79.43 94.60 86.35
100 CMFD benchmark images with common image pro- 800 70.98 95.25 81.34
cessing (additive Gaussian noise, JPEG compression, and 900 65.02 95.72 77.43
blur degradation, etc.). Thus, we evaluated on the 100 1000 60.51 95.81 74.17
tampered images. Bold and underlined values indicate the optimal feature Euclidean
distance and optimal Forged area
5.2.1 Image blocks radius R
forgery detection performance is measured by average
Precision, average Recall, and average F. Obviously, the
Since we use the overlapping circular image blocks and
comparison results indicate that the proposed CMFD
QEMs modulus method for extracting the matching fea-
algorithm can achieve much better forgery detection results
tures, selecting the radius of the circular image block is
when the feature Euclidean distance D1 is set to 300.
usually a tricky thing. Here, we use different image blocks
radius ranging from 6 to 26 with 2 increment and compute
5.2.3 Forged area A
the corresponding average error measures Precision and
Recall. As can be seen from Fig. 4, with the increase of the
We estimated forged area A by optimizing the F-measure
image block radius, the Precision is prone to decrease on
at image level. Table 5 shows the average CMFD perfor-
the whole, but the Recall is prone to increase on the whole.
mance of 100 tampered images for the different values of
Therefore, in order to make the balance between Precision
forged area. It can be seen that our method performs sig-
and Recall performance, we set the image block radius
nificantly better when the forged area A is set to 700.
R = 9.
5.3 Detection results at pixel level
5.2.2 Feature Euclidean distance D1
In this experiment, we evaluate how precisely the copy–
Table 4 shows the comparison results for our forgery moved regions can be marked. So, we focused mainly on
detection with different feature Euclidean distance. Here, the number of detected (or missed) copied-moved matches.

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 Pattern Anal Applic

Table 5 Average CMFD performance for different values of forged parametrized via the noise’s standard deviation and the
area at image level in percent filter’s radius. Here, we considered zero-mean AWGN
A Precision Recall F with standard deviation 2, 4, 6, and 8, as well as
average filters of radius 0.5, 1, 1.5, 2, and 2.5,
50 95.86 60.34 74.06 respectively.
100 95.27 63.85 76.45 4. Rotation One important question that recently gained
200 94.67 67.79 79.01 much attention was the resilience of CMFD
300 94.23 75.32 83.72 approaches to affine transformations, like rotation
400 93.97 80.12 84.50 and scaling. We rotated the copied regions with the
500 93.31 85.78 89.38 rotation angle varying from 2° to 10°, in increments of
600 92.90 92.08 92.48 2°, and with the rotation angles of 20°, 60°, and 180°
700 92.45 93.67 93.06 as well. In this case, we tested a total of 48 9 8 = 384
800 90.65 93.87 91.14 forgeries images.
900 86.55 94.03 90.13 5. Scaling We also conducted an experiment where the
1000 82.91 94.68 88.40 copied match was slightly rescaled, as is often the case
1100 73.34 95.12 82.82 in real-world image manipulations. Specifically, we
1200 65.13 95.77 77.53 rescaled the copied region between 91 and 109% of its
Bold and underlined values indicate the optimal feature Euclidean original size, in steps of 2%. We also evaluated
distance and optimal Forged area rescaling by 50, 70, 110, and 200% to test the
degradation of approaches under larger amounts of
For each detected image match, we check the centers of
copied region resizing.
two matched image blocks against the corresponding
(pixelwise) ground-truth image. All boundary pixels are Figures 5 and 6 show the detection results on some test
excluded from the evaluation. Please note that all the color images from Christlein’s dataset [2] with copy–move
measures, e.g., false positives and false negatives, are regions fused in the background. It can easily be observed
computed using all the pixels in the tampered images only. that the proposed approach detects most copy–move
In the practical test, we first evaluate the proposed regions. Figure 7 shows the average CMFD performance at
approach under ideal conditions (no postprocessing) of the pixel level under various attacks on the copied region,
pixels. Subsequent experiments examine the cases of: including common signal processing and geometric
JPEG compression on the copied region, noise on the distortions.
copied region, rotation and scaling of the copied region. Table 6 shows the average F-measure and average AUC
under ideal conditions (no postprocessing) for the proposed
1. Plain copy–move We firstly evaluated how the CMFD
approach compared with the existing CMFD methods. This
approaches perform under ideal conditions (no post-
table indicates that the forgery detection result of the
processing). Here, we used the 48 forgery color images
proposed approach is better than that of the existing state-
from Christlein’s dataset without any additional mod-
of-the-art CMFD methods when under plain copy–move.
ification to evaluate the detection performance. Note
that we calibrated the thresholds for all approaches in a
way that yields very competitive (comparable) detec- 5.4 Detection results at image level
tion performances.
2. JPEG compression We introduced a common local Area-based pixel-level performance measures such as
disturbance on the copied regions, lossy JPEG com- Precision, Recall, and F rates are useful when we know that
pression, for which the quality factors varied between the tested color images are forgeries. Yet, in practice, they
30 and 90 in steps of 10. For each evaluated quality are usually not known a priori. In the next section, we test
level, we applied the same JPEG compression to the the overall image-level detection performance of our
copied regions of the 48 forgeries images, so a total of approach. Specifically, for a forgery color image, a suc-
48 9 8 = 384 forgeries images are tested. For very cessful detection is deemed when our approach detects a
low quality factors, the visual quality of the color duplicated region larger than the area threshold. For an
image is strongly affected. But, we consider at least untampered color image, a true negative occurs when our
quality levels down to 70 as reasonable assumptions approach does not detect any duplicated region.
for real-world image forgeries. We split these image-level experiments in a series of
3. Additive white Gaussian noise (AWGN) We applied separate evaluations. We firstly evaluate the proposed
additive white Gaussian noise to the copied regions of approach under ideal conditions (plain copy–move). Here,
the 48 forgeries images. The strength of distortion is we have 48 original color images and 48 forgery color

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Pattern Anal Applic

Fig. 5 Detection results on some test images from Christlein’s dataset [2]: a original images, b tempered images, c ground-truth forgery regions,
d detected forgery regions using Ryu’s method [11], e detected forgery regions using our approach

images, in which a one-to-one copy–move is implemented. 1. Plain copy–move We firstly evaluated the proposed
We must distinguish the original and forgery color images approach under ideal conditions. Here, 48 original
in this case. Then, our copy–move forgery approach is color images and 48 forgery color images are used, and
evaluated under different types of attacks, including the per-method optimal thresholds are chosen for classi-
geometric transforms such as rotation and scaling, and fying these 96 images. Similarly to the experiment at
common signal processing such as JPEG compression and pixel level, all regions have been copied and pasted
additive white Gaussian noise. without additional disturbances.
Figure 8 shows the average CMFD performance at 2. JPEG compression We used the same experimental
image level on some test images from Christlein’s dataset setup as in the pixel-level evaluation, i.e., added JPEG
[2] under various attacks.

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 Pattern Anal Applic

Fig. 6 Detection results on some test images from Christlein’s dataset [2]: a original images, b tempered images, c ground-truth forgery regions,
d detected forgery regions using Ryu’s method [11], e detected forgery regions using our approach

compression between quality levels 30 and 100 in steps also tested three larger rotation angles of 20°, 60°, and
of 10. 180°. We assumed them to be the reasonable ranges.
3. Additive white Gaussian noise (AWGN) We again used 5. Scaling The experimental setup is the same as on the
the same experimental setup as in the pixel-level pixel-level analysis. The copied regions are scaled
evaluation, i.e., zero-mean AWGN with standard between 91 and 109% of their original size in steps of
deviation 2, 4, 6, and 8, as well as average filters of 2%. Additionally, more extreme scaling parameters
radius 0.5, 1, 1.5, 2, and 2.5, has been inserted snippets were evaluated, including 50, 80, 120, and 200%.
before splicing.
From the above experimental results, we can see that the
4. Rotation We evaluated cases where the copied matches
newly proposed approach can achieve much better
have been rotated between 2° and 10° in steps of 2° and

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Pattern Anal Applic

Fig. 7 Average CMFD performance (F-measure) at pixel level on some test images from Christlein’s dataset [2]: a JPEG compression,
b additive white Gaussian noise, c rotation, d scaling

Table 6 Average detection results under plain copy–move at pixel blocks, which are robust to geometrical transformations
level and image level (e.g., scaling, rotation); (3) the E2LSH based image block
Methods Average F-measure Average AUC matching is introduced. It can effectively detect the image
block pairs with similar feature vectors; (4) QEMs mag-
Image level Pixel level
nitudes are incorporate into the false matching reduction
Pun [9] 0.9611 0.7973 0.8975 procedure, which can effectively remove false positives
Ryu [11] 0.9494 0.7586 0.8723 and enhance the detection accuracy significantly.
Cozzolino [13] 0.9470 0.8740 0.8710 Despite the present advances, there is still much room
Our scheme 0.9696 0.8826 0.9268 for improvements. As an example, the proposed copy–
move forgery approach is computationally more
demanding, which makes the proposed approach cannot
detection results for copy–move forgery color images
be used effectively in real-time applications.
under various challenging conditions, such as JPEG com-
pression, geometric transforms, and additive white Gaus-
sian noise, compared with the state-of-the-art CMFD
schemes. This is because that (1) image blocks are repre- 6 Conclusion
sented by QEMs holistically as a vector field. The accurate
and invariant property of QEMs magnitude makes these Copy–move forgeries are a common type of forgery where
moments particularly promising CMFD features; (2) cir- parts of an image are replaced with other parts from the
cular image blocks are adopted instead of rectangular same image. The copied and pasted regions may be sub-

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 Pattern Anal Applic

Fig. 8 Average CMFD performance (F-measure) at image level on some test images from Christlein’s dataset [2]: a JPEG compression,
b additive white Gaussian noise, c rotation, d scaling

jected to various image transformations in order to conceal superpixel theory. Also, we will investigate the use of our
the tampering better. Conventional techniques of detecting approach in detecting regions which have undergone non-
copy–paste forgeries usually suffer from the problems of affine transformations and/or are multiply copied.
false positives and susceptibility to many image processing
operations. In this work, we describe a new copy–move
forgery detection method, which is based on circular image References
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