Digital Signal Processing 43 (2015) 1727

Contents lists available at ScienceDirect

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secondary image and the embedding vector variances of LLE are used to form image hash. Hash similarity

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ht10E Lab color space is determined by correlation coecient. Many experiments are conducted to validate our eciency and the results illustrate that our hashing is robust to content-preserving operations and reaches a good discrimination. Comparisons of receiver operating characteristics (ROC) curve indicate that our hashing outperforms some notable hashing algorithms in classication between robustness and discrimination.

2015 Elsevier Inc. All rights reserved.

Introduction

Nowadays, the popularization of imaging device, such as smart ll phone, digital camera and scanner, provides us more and more gital images. Consequently, ecient techniques are needed for oring and retrieving hundreds of thousands of images. Mean-hile, it is easy to copy, edit and distribute images via powerful ols and the Internet. Therefore, digital right management (DRM) age authentication, image forensics, copyright protection, etc.)

in demand. All these practical issues lead to emergence of image shing. Image hashing is a novel technology for mapping input age into a short string called image hash. It not only allows to retrieve images from large-scale database, but also can be plied to DRM. In fact, it has been widely used in image authen-ation [1], digital watermarking [2], image copy detection, tamper tection, image indexing [3], image retrieval, image forensics [4], d image quality assessment [5].Generally, image hashing has two basic properties [68]. The st one is perceptual robustness. It requires that, for those vi-ally identical images, image hashing should generate the same very similar image hashes no matter whether their digital rep-

Corresponding author at: Department of Computer Science, Guangxi Normal iversity, No. 15 YuCai Road, Guilin 541004, PR China.E-mail address: tangzj230@163.com (Z. Tang).

resentations are the same or not. This means that image hashing must be robust against content-preserving operations, such as JPEG compression, brightness adjustment, contrast adjustment, water-mark embedding and image scaling. The second property is called discrimination. This implies that, image hashing should extract dif-ferent hashes from different images. In other words, similarity be-tween hashes of different images should be small enough. Note that the two properties contradict with each other [8]. The rst property requires robustness under small perturbations, whereas the second property amounts to minimization of collision proba-bility for images with different contents. High performance algo-rithms should reach a good trade-off between the two properties. In addition to the basic properties, image hashing should have another property when it is applied to specic applications. For example, it should be key-dependent for image authentication [9].

Due to the wide use of image hashing, many researchers have paid attention to hashing techniques. For example, Venkatesan et al. [10] exploited statistics of discrete wavelet transform (DWT) coecients to generate image hashes. This hashing is robust to JPEG compression and small-angle rotation, but sensitive to gamma correction and contrast adjustment. Lefebvre et al. [11] pioneered the use of Radon transform (RT) to hash extraction. This scheme can resist geometric transform, such as rotation and scaling, but its discriminative capability is limited. Kozat et al. [12] viewed im-ages and attacks as a sequence of linear operators and presented

tp://dx.doi.org/10.1016/j.dsp.2015.05.00251-2004/ 2015 Elsevier Inc. All rights reserved.Digital Signa

www.elsevier.c

obust image hashing with embedding ve

henjun Tang a,b,, Linlin Ruan b, Chuan Qin c, Xianquuangxi Key Lab of Multi-source Information Mining & Security, Guangxi Normal University, epartment of Computer Science, Guangxi Normal University, Guilin 541004, PR Chinachool of OpticalElectrical and Computer Engineering, University of Shanghai for Science andetwork Center, Guangxi Normal University, Guilin 541004, PR China

r t i c l e i n f o a b s t r a c t

ticle history:ailable online 9 May 2015

ywords:age hashingbust hashingcally linear embeddingta reduction

Locally linear embedding (LLidentication and face recogwe investigate the use of LLapproximately linearly changea novel LLE-based image hasby bilinear interpolation, coloThe normalized matrix is therocessing

/locate/dsp

or variance of LLE

Zhang a,b,d, Chunqiang Yu d

n 541004, PR China

hnology, Shanghai 200093, PR China

as been widely used in data processing, such as data clustering, video on, but its application in image hashing is still limited. In this work, image hashing and nd that embedding vector variances of LLE are y content-preserving operations. Based on this observation, we propose . Specically, an input image is rstly mapped to a normalized matrix ace conversion, block mean extraction, and Gaussian low-pass ltering. xploited to construct a secondary image. Finally, LLE is applied to the

18 Z. Tang et al. / Digital Signal Processing 43 (2015) 1727

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scrimination.The rest of this paper is organized as follows. Section 2 in-

oduces the proposed image hashing. Section 3 presents experi-ental results and Section 4 discusses performance comparisons. nally, conclusions are drawn in Section 5.

... ... ... ...M1,1 M1,2 ... M1,M1

where i, j is the mean of the block in the i-th row and the j-th column of the L component (1 i M1, 1 j M1). This op-eration not only achieves initial compression, but also makes our Fig. 1. Block diagram o

image hashing with two singular value decompositions (SVDs). e SVDSVD hashing can tolerate geometric transform at the cost signicantly decreasing discrimination. In another study, Swami-than et al. [13] proposed to calculate image hashes based on ecients of FourierMellin transform. This algorithm is robust ainst moderate geometric transforms and ltering. Monga and ihcak [14] were the rst to use non-negative matrix factoriza-on (NMF) to derive image hashing. This method is robust against any popular digital operations, but sensitive to watermark em-dding. Tang et al. [15] found invariant relation in the NMF co-cient matrix and exploited it to design hashing. This scheme

resistant to JPEG compression and watermark embedding, but nsitive to image rotation. In another work, Ou et al. [16] used combining with discrete cosine transform (DCT) to generate age hashes. The RTDCT hashing is resilient to image rotation, t its discrimination is not good enough. Kang et al. [17] intro-ced a compressive sensing-based image hashing. This method

also sensitive to image rotation. Recently, Sun et al. [18] pre-nted a robust image hashing by using relations in the weight atrix of locally linear embedding (LLE). This LLE-based hashing n tolerate JPEG compression, but is fragile to rotation and its scrimination is also not good enough. Tang et al. [19] exploited ructural features to extract image hashes and introduced a novel milarity metric for tampering detection. This method is also sen-tive to image rotation. In [20], Li et al. extracted image hashes by ndom Gabor ltering (GF) and dithered lattice vector quantiza-on (LVQ). The GFLVQ hashing has better performances than the ell-known algorithms [13,17], but its discrimination is also not sirable enough. Zhao et al. [21] exploited Zernike moments (ZM) calculate image hashes. The ZM-based hashing only tolerates tation within 5 . Tang et al. [22] investigated the use of color ctor angle (CVA) and then exploited CVA and DWT to design age hashing. The CVADWT hashing is also robust to rotation ithin 5 , but its discrimination can be improved.Although many hashing algorithms have been reported, there

e still some problems in hashing design. For example, more ef-rts are still needed for developing high performance algorithms aching a desirable balance between robustness and discrimina-on. In this work, we propose a novel LLE-based image hashing, hich can achieve a good trade-off between robustness and dis-imination. The key technique of our work is an innovative use of E, which is based on the property that embedding vector vari-ces are approximately linearly changed by content-preserving erations. Since LLE can eciently learn global structure of non-ear manifolds and discover compact representations of high-mensional data, the use of LLE provides our hashing a good scrimination. Many experiments are conducted to validate the ciency of our hashing. The results illustrate that our hashing

robust against popular digital operations and reaches a good scrimination. Comparisons indicate that our hashing outperforms r image hashing.

Proposed image hashing

Our proposed image hashing is a three-step method, whose ock diagram is presented in Fig. 1. In the rst step, our hashing nverts input image into a normalized matrix by preprocessing. the second step, our method constructs a secondary image from e normalized matrix. Finally, we apply LLE to the secondary im-e and exploits LLE results to produce image hash. Details of these eps are described as follows.

1. Preprocessing

To make a normalized image for constructing secondary image, me digital operations are applied to the input image. Firstly, bi-ear interpolation is used to resize the input image to a standard ze M M , which makes our method robust against image rescal-g. For RGB color image, the resized image is then converted into E Lab color space and the L component is taken for rep-senting the resized image. Here, we choose L component for age representation. This is based on the consideration that, CIE ab color space is perceptually uniform and the L component osely matches human perception of lightness [23,24]. For each age pixel, let L be color lightness, a and b be chromaticity ordinates, respectively. Thus, color space conversion [23] can be ne by the following rules.

={116(Y1/Y0)1/3 16, if Y1/Y0 > 0.008856903.3(Y1/Y0), otherwise

(1)

= 500[ f (X1/X0) f (Y1/Y0)] (2)= 200[ f (Y1/Y0) f (Z1/Z0)] (3)here X0 = 0.950456, Y0 = 1.0 and Z0 = 1.088754 are the CIE YZ tristimulus values of the reference white point, f (t) is dened :

(t) ={t1/3, if t > 0.0088567.787t + 16/116, otherwise (4)

d X1, Y1 and Z1 are the CIE XYZ tristimulus values [24], which e calculated by the equation.

X1Y1Z1

=

0.4125 0.3576 0.18040.2127 0.7152 0.07220.0193 0.1192 0.9502

RG

B

(5)

here R , G and B are the red, blue and green components of each age pixel, respectively.Next, the L component is divided into non-overlapping blocks

ith a small size s1 s1. For simplicity, let M be the integral mul-ple of s1, and M1 = M/s1. Thus, to make an initial compression, e calculate block mean and use these means to construct a fea-re matrix as follows. 1,1 1,2 ... 1,M12,1 2,2 ... 2,M

Z. Tang et al. / Digital Signal Processing 43 (2015) 1727 19

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is kept unchanged during data reduction, a small vector number here is a given standard deviation of the Gaussian distribution. r example, if the lter size is 3 3, 1 i 1, and 1 j 1.g. 2 presents an instance of the preprocessing with M = 512, = 2, and 3 3 lter size, where (a) is the original input im-e, (b) is the resized image, (c) is the L component of (b), (d) is e matrix F, and (e) is its blurred version.

2. Secondary image construction

To construct a secondary image for data reduction, we ran-mly select N blocks sized n n from F under the control of secret key. We view each block as a high dimensional vector of ze n2 1 via concatenating block entries column by column. Let be the corresponding vector of the i-th block (1 i N). Thus, e can obtain the secondary image X as follows.

= [x1,x2, . . . ,xN ] (9)ote that, during block selection, there can exist overlapping re-on between blocks. However, the same selected blocks should be scarded since the same vectors are not expected in the secondary age. Compared with the input image, the secondary image has wer columns. As column number is equal to vector number that

helps to make a short image hash. Fig. 3 is the schematic diagram of secondary image construction.

2.3. Locally linear embedding

Locally linear embedding (LLE) [25] is a well-known algorithm for non-linear dimensionality reduction. It can eciently discover compact representations of high-dimensional data by computing low-dimensional, neighborhood-preserving embeddings and learn-ing global structure of nonlinear manifolds, such as those gener-ated by face images or text documents [25]. LLE has been indicated better performances than some popular methods, such as princi-pal component analysis (PCA) [26] and multidimensional scaling (MDS) [27]. Actually, LLE has been widely used in many applica-tions, such as data clustering [28], video identication [29], gait analysis [30] and face recognition [31].

The classical LLE algorithm [25] consists of three steps, i.e., neighbor selection, weight calculation, and low-dimensional em-bedding vector computation. For simplicity, suppose that xi is a vector of dimensionality D , where D = n2 and 1 i N . Thus, de-tails of these steps are illustrated as follows.

(1) Neighbor selection. For each vector xi (1 i N), its K near-est neighbors are chosen. This can be determined by Euclidean Fig. 2. Instance of t

ethod resistant to small-angle rotation, which can be understood follows. Although small-angle rotation will alter pixel positions, xels in a small region have similar values and then block means ill not be signicantly changed. Note that a big block size helps improve robustness against large-angle rotation. But a bigger ock size leads to fewer features in F, which will inevitably hurt scrimination. In experiments, we choose 2 2 as block size, hich can reach a desirable balance between robustness and dis-imination. Finally, a rotationally symmetric Gaussian low-pass ter is applied to the matrix F. This is to reduce the inuence of gital operations on F. In practice, the element of Gaussian low-ss lter can be calculated by:

(i, j) = G(1)(i, j)

i

j G

(1)(i, j)(7)

which G(1)(i, j) is dened as

(1)(i, j) = e (i2+ j2)22 (8)reprocessing.

Fig. 3. Schematic diagram of secondary image construction.

20 Z. Tang et al. / Digital Signal Processing 43 (2015) 1727

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tealthanplstance between xi and the other vector x j (1 j N and j = i) follows.

(xi,x j) = D

l=1

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]2(10)

here xi(l) and x j(l) are the l-th elements of xi and x j , respec-ely. Thus, those vectors corresponding to the K smallest dis-nces are the K nearest neighbors of xi .(2) Weight computation. Calculate the weight matrix W =i, j)NK . The weight matrix can best linearly reconstruct xi from

s nearest neighbors, and the reconstruction errors are computed the following cost function .

W) =N

i=1

xi j

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here Wi, j is the weight between xi and x j . In practice, W can be lculated by minimizing the Eq. (11) subject to two constraints as llows. First, Wi, j = 0 if x j is not a nearest neighbor of xi . Second, e sum of those neighbor weights of xi is 1, i.e.,

j Wi, j = 1.

(3) Low-dimensional embedding vector calculation. After theeight matrix is obtained, each high-dimensional vector xi is then apped to a low-dimensional vector yi of dimensionality d. This n be done by minimizing the cost function below.

(Y) =N

i=1

yi j

Wi, jy j

2

(12)

here Y = [y1, y2, . . . , yN ] is a matrix forming by all low-dimensional bedding vectors. For more details of LLE algorithm, please refer

[25,32]. The MATLAB code of LLE algorithm can be downloaded om the personal website of Roweis [33].Having obtained these low-dimensional embedding vectors, we lculate statistics of each embedding vector to produce a short age hash. Here we choose variance as the feature for represent-g low-dimensional embedding vector. This is because variance n eciently measure the uctuation of vector elements, and we so nd the LLE property that embedding vector variances are proximately linearly changed by content-preserving operations. is LLE property will be validated in Section 3.1. The reason of the E property is that the effect of content-preserving operations on e change of embedding vector variances is relatively small and e Gaussian noise disturbance. Note that the use of LLE in our ork is different from that of [18], which used LLE weight matrix construct hash but cannot acquire good classication between bustness and discrimination. The variance of yi is dened as fol-ws.

= 1d 1

dl=1

[yi(l) i

]2(13)

here yi(l) is the l-th element of yi and i is the mean calculated the below equation.

i = 1d

dl=1

yi(l) (14)

reduce storage, each variance is quantized to an integer as fol-ws.

i) = Round(2i 1000) (15)here Round() is the rounding operation, and 1 i N . Next, a pseudo-random generator, we scramble the integer sequence = [c(1), c(2), . . . , c(N)] to make a secure image hash. Specically, e can set a secret key as the seed of pseudo-random genera-r and create N random numbers. Then, we sort these N random mbers and use an array P [N] to record the original positions of e sorted elements. Therefore, the i-th hash element is obtained the below equation.

i) = c(P [i]) (16)nally, our image hash h is obtained as follows.

= [h(1), h(2), . . . , h(N)] (17) is clear that our hash consists of N integers. In experiment, we d that each integer only requires 11 bits at most for storage. erefore, the length of our hash is 11N bits. This will be validated Section 3.3.

4. Hash similarity evaluation

Let h1 = [h1(1), h1(2), . . . , h1(N)] and h2 = [h2(1), h2(2), . . . ,(N)] be a pair of hashes of two images. In this study, the well-own correlation coecient is exploited to evaluate similarity tween h1 and h2. Specically, the used correlation coecient

dened as follows.

(h1,h2) =N

l=1[h1(l) m1][h2(l) m2]Nl=1[h1(l) m1]2

Nl=1[h2(l) m2]2 + s

(18)

here s is a small constant to avoid zero denominator, and m1d m2 are the means of h1 and h2, respectively. The range of rrelation coecient is [1, 1]. The greater the correlation coef-ient, the more similar the evaluated hashes and then the more milar the corresponding images. If the correlation coecient is eater than a threshold, the two images of the input hashes are nsidered as visually identical images. Otherwise, they are the ages with different contents. Here, correlation coecient is cho-n as the similarity metric. This is based on the observation that ntent-preserving operations approximately linearly change the riances of low-dimensional embedding vectors. Section 3.1 will pirically verify this.

Experimental results

In the experiments, our parameter settings are as follows. In the eprocessing, the input image is resized to 512 512, the L com-nent of the input image is divided into 2 2 non-overlapping ocks, and a 3 3 Gaussian low-pass lter with zero mean and a it standard deviation is taken. During secondary image construc-

on, 50 blocks of size 50 50 are randomly chosen. For LLE, 30 arest neighbors are selected for each vector and the dimension-ity of low-dimensional embedding vector is 30. In other words, e used parameters of our hashing are: M = 512, s1 = 2, n = 50, = 50, K = 30 and d = 30. Thus, our hash length is 50 integers. validate eciency of our hashing, robustness and discrimination e tested in Sections 3.1 and 3.2, respectively. Section 3.3 presents sh length analysis and Section 3.4 discusses the effect of differ-t parameter settings on hash performances.

1. Robustness validation

Many images in the USC-SIPI Image Database [34] are taken as st images, including 8 standard color images sized 512 512 and l color images, i.e., 37 images sized 512 512 2250 2250, in e Aerials volume. Fig. 4 illustrates these standard color images d Fig. 5 presents typical images in the Aerials volume. We ex-oit Photoshop, MATLAB and StirMark [35] to generate visually

Z. Tang et al. / Digital Signal Processing 43 (2015) 1727 21

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lanspFig. 4. Standard color images for robustness validation.

Fig. 5. Typical images in the Aerials volume.

ble 1gital operations and their parameter settings.

Tool Operation Parameter Parameter setting Number of operations

Photoshop Brightness adjustment Photoshops scale 10, 20 4Photoshop Contrast adjustment Photoshops scale 10, 20 4MATLAB Gamma correction 0.75, 0.9, 1.1, 1.25 4MATLAB 3 3 Gaussian low-pass ltering Standard deviation 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0 8MATLAB Speckle noise Variance 0.001,0.002, . . . ,0.01 10MATLAB Salt and pepper noise Density 0.001,0.002, . . . ,0.01 10StirMark JPEG compression Quality factor 30, 40, 50, 60, 70, 80, 90, 100 8StirMark Watermark embedding Strength 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 10StirMark Image scaling Ratio 0.5, 0.75, 0.9, 1.1, 1.5, 2.0 6StirMark Rotation, cropping and rescaling Angle in degree 0.25, 0.5, 0.75, 1.0, 1.25, 1.5 12Total 76

entical versions of these test images. The adopted digital opera-ns include brightness adjustment, contrast adjustment, gamma rrection, 3 3 Gaussian low-pass ltering, speckle noise, salt d pepper noise, JPEG compression, watermark embedding, im-e scaling, and the operation of rotation, cropping and rescaling. r the operation of rotation, cropping and rescaling, each test im-e is rstly rotated, the rotated version is then cropped to remove ose padded pixels introduced by rotation, and the cropped ver-on is nally resized to the original size of the test image. Detailed rameter settings of each operation are listed in Table 1. It is ob-rved from Table 1 that total number of the used operations is 76. is means that each test image has 76 visually similar versions. erefore, there are (8 + 37) 76 = 3420 pairs of visually similar ages.We extract image hashes of the test images and their simi-

r versions, calculate similarity between each pair of hashes, and d that our hashing is robust to the used digital operations. For ace limitation, only the results of 8 typical standard color im-

ages are plotted here. Fig. 6 presents the robustness results under various digital operations. Clearly, all results are bigger than 0.70. To demonstrate the robustness performance of our hashing on a big dataset, we calculate statistics of correlation coecients based on the above mentioned 3420 pairs of visually similar images. The results are listed in Table 2. It is observed from these results that, the means of correlation coecients for all digital operations are bigger than 0.87, and all standard deviations are very small. Note that correlation coecient is an effective metric for mea-suring the linearity. These big correlation coecients empirically verify that the variances of LLE results are approximately linearly changed by content-preserving operations. In addition, the mini-mum values of correlation coecients for all digital operations are bigger than 0.75, except the operation of rotation, cropping and rescaling. The minimum value of rotation, cropping and rescaling is 0.4572, which is much smaller than those values of other opera-tions. This is because it is a combinational operation, which causes more changes in the attacked images than other operations. Con-

22 Z. Tang et al. / Digital Signal Processing 43 (2015) 1727

sesemthfeth

3.

dataSpFig. 6. Robustness results under various digital operations.

quently, if there are no rotated images in application, we can lect 0.75 as the threshold. In this case, all similar images are al-ost correctly detected. If there exists some rotated images, the reshold should be lowered. From Fig. 6(j), we nd that only a w cases are smaller than 0.75. Therefore, we can choose 0.70 as e threshold to resist most of the above used operations.

2. Discrimination test

To test discrimination of our hashing, we collect a large tabase with 200 different color images via Internet and digi-l camera, whose sizes range from 256 256 to 2048 1536. ecically, we download 67 images from Internet, take 100 im-

ages from a well-known public database, i.e., the Ground Truth Database [36], and capture 33 images with camera. We apply our hashing to the image database, extract 200 image hashes, cal-culate similarity between each pair of hashes, and then reach 200 (200 1)/2 = 19900 correlation coecients. Distribution of these results is shown in Fig. 7, where the x-axis is the cor-relation coecient and the y-axis is its frequency. It is observed that the minimum and the maximum of correlation coecients are 0.6891 and 0.6967, respectively. And further, the mean and stan-dard deviation of the distribution in Fig. 7 are 0.0066 and 0.1905, respectively. Clearly, if we choose 0.80 or 0.70 as the threshold, no images will be falsely considered as similar images. If the thresh-

Z. Tang et al. / Digital Signal Processing 43 (2015) 1727 23

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Table 2Statistics of correlation coecients based on 3420 pairs of similar images.

Operation Maximum Minimum Mean Standard deviation

Brightness adjustment 1 0.8426 0.9694 0.0240Contrast adjustment 0.9977 0.8457 0.9667 0.0227Gamma correction 1 0.7765 0.9713 0.02593 3 Gaussian low-pass ltering 1 0.9198 0.9825 0.0160Speckle noise 0.9986 0.8677 0.9706 0.0218Salt and pepper noise 0.9983 0.8173 0.9701 0.0219JPEG compression 0.9999 0.9031 0.9691 0.0200Watermark embedding 1 0.7569 0.9765 0.0269Image scaling 0.9980 0.8626 0.9765 0.0269Rotation, cropping and rescaling 0.9914 0.4572 0.8717 0.0781

d is 0.60, only 0.05% different images will be mistakenly detected visually identical images. Actually, a big threshold will improve scrimination, but will also inevitably decrease robustness. Table 3ustrates our detection performances under different thresholds, here robustness is described by the percentage of similar images dged as identical images and discrimination is indicated by the rcentage of different images detected as similar images. In prac-e, we can choose a threshold in terms of specic applications.

3. Hash length analysis

A short length is a basic requirement for image hash. To ana-ze the required bits for storing our hash, we take the 200 image shes extracted in discrimination as the sample data. As each im-e hash contains 50 elements, the total number of hash elements 50 200 = 10 000. Fig. 8 is the distribution of these hash el-

ements, where the x-axis is the value of hash element and the y-axis is its frequency. It is found that the minimum value is 4 and the maximum value is 1666. This means that storage of hash element only requires 11 bits, which can represent integers rang-ing from 0 to 211 1 = 2047. Therefore, the length of our hash is 50 11 = 550 bits, reaching a reasonable short length. As a ref-erence, the lengths of the SVDSVD hashing [12], the ZM-based hashing [21], and the CAV-DWT hashing [22] are 1600 digits, 560 bits, and 960 bits, respectively.

3.4. Effect of parameters on hash performances

To evaluate the effect of parameter settings on our hash perfor-mances, we use different parameter values to validate robustness and discrimination. To make visual comparisons between the re-sults of different settings, the notable tool, i.e., receiver operating

24 Z. Tang et al. / Digital Signal Processing 43 (2015) 1727

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ble 3tection performances under different thresholds.

Threshold Similar images judged as identical images

Different images detected as similar images

0.90 89.91% 00.80 97.16% 00.75 98.92% 00.70 99.53% 00.60 99.91% 0.05%0.55 99.94% 0.12%0.50 99.97% 0.37%0.45 100% 0.87%

Fig. 8. Distribution of hash elements based on 200 different images.

aracteristics (ROC) graph [37], is adopted here. In the ROC graph, e x-axis is generally dened as false positive rate (FPR) P1 and e y-axis is used to represent true positive rate (TPR) P2. The two tes are calculated by the below equations.

1 = n1N1

(19)

2 = n2N2

(20)

Table 4Time comparison under different K values.

K 5 1

Computational time (second) 0.62 0Fig. 9. ROC curve comparisons under different K values when d = 30.

here n1 is the number of visually different images detected as milar images, and N1 is the total number of different images, is the number of visually similar images judged as identical im-es, N2 is the total number of similar images. Clearly, P1 and P2e indicators of discrimination and robustness, respectively. The aller the P1 value, the better the discrimination performance. d the bigger the P2 value, the better the robustness perfor-ance. Since ROC curve is formed by a set of points (P1, P2), the rve close to the top-left corner (a small P1 and a big P2) is bet-r than the one far away from the top-left corner.Here, we mainly discuss the key parameters, i.e., the number

nearest neighbors K and the dimensionality of low-dimensional ctor d for LLE. Firstly, we only vary the K value and keep other rameters unchanged. The used K values include 5, 15, 25, 30, , and 40. Fig. 9 is the ROC curve comparisons among different Klues. It is observed that all ROC curves are close to the top-left rner, indicating that our hashing reaches a satisfactory balance tween robustness and discrimination. To view differences, the C curves around the top-left corner are enlarged in the right-ttom part of Fig. 9. It is found that, a moderate K value, such 30 or 35, can reach a slightly better classication performance an those small K values (such as 5 or 15) and big K values (e.g., ). This can be understood as follows. In LLE algorithm, K nearest ighbors are used to reconstruct a vector. A small K value can-t make a good reconstruction due to the lack of enough nearest ighbors. But a big K value will bring some unnecessary neigh-rs, leading to a larger reconstruction error. In the experiments, e nd that, for 512 512 images, K = 30 or K = 35 can reach a od classication performance between robustness and discrim-ation. Moreover, computational time is also compared. To this d, the total consumed time for extracting 200 hashes in discrim-ation test is recorded, and then the average time for generat-g a hash is acquired. Our hashing is implemented with MATLAB 012a, running in a desktop PC with 3.4 GHz Intel Core i5-3570 U and 4.0 GB RAM. We observe that the running time under dif-rent K values is around 0.61 seconds, and the time under K = 40 a little more than those of other values. Table 4 summarizes the mparison of computational time under different K values.Secondly, we only change the d value. The adopted values of are 25, 30, 35, and 40. Fig. 10 presents the ROC curve compar-

25 30 35 40

0.61 0.61 0.62 0.64

Z. Tang et al. / Digital Signal Processing 43 (2015) 1727 25

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ble 5e comparison under different d values.

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ons among different d values. From the results, we nd that all C curves reach the top-left corner. This implies that the d value s little effect on classication performances of our hashing. To ew more details, the right-bottom region of Fig. 10 shows the agnied part of the ROC curves around the top-left corner. We serve that the curves of d = 30 and d = 35 are almost the same, d the curves of d = 25 and d = 40 is a little below them. There-re, for 512 512 images, we can choose d = 30 or d = 35 to hieve a good classication between robustness and discrimina-n. In addition, we calculate the average time of hash generation d nd that the time under different d values is also around 0.61 conds. The comparison of computational time is presented in Ta-e 5.

Performance comparisons with notable algorithms

To illustrate our superiority in classication performances, we mpare our hashing with some notable image hashing algorithms cluding LLE-based hashing [18], RTDCT hashing [16], GFLVQ shing [20] and CVADWT hashing [22]. To ensure fair compar-ons, the test images used in Sections 3.1 and 3.2 are also taken re. In the comparisons, all images are converted to 512 512, d other parameters are the same with the default settings of e assessed algorithms. The original metrics for measuring hash milarity are also adopted here, i.e., Hamming distance for LLE-sed hashing and RTDCT hashing, the normalized Hamming dis-nce for GFLVQ hashing, and L2 norm for CVADWT hashing. us, hash lengths of LLE-based hashing, RTDCT hashing, GFLVQ shing, and CVADWT hashing are 300, 240, 120, 960 bits, re-ectively.We exploit the compared algorithms to generate hashes of the ove images and then calculate hash similarity with respective etric. For our hashing, the results of K = 30 and d = 30 is taken re. To make theoretical analysis, the ROC graph is used again. the ROC graph, if some algorithms reach the same TPR, the gorithm with small FPR is better than the algorithm with big R. Similarly, the algorithm with big TPR outperforms the algo-thm with small TPR when they have the same FPR. Intuitively, e larger the area under ROC curve, the better the classication rformance. Fig. 11 is the ROC curve comparisons among the as-Fig. 11. ROC curve comparisons among different hashing algorithms.

ssed algorithms. Clearly, our ROC curve is above those curves of e compared algorithms. In other words, the area under our ROC rve is much larger than others. This means that our hashing has tter classication performance than other image hashing algo-thms. For example, when TPR 1.0, the best FPRs of LLE-based shing, RTDCT hashing, GFLVQ hashing, CVADWT hashing, and r hashing are 0.5569, 0.9963, 0.7040, 0.1033, and 0.0087, re-ectively. And when FPR 0, the optimum TPRs of LLE-based shing, RTDCT hashing, GFLVQ hashing, CVADWT hashing, and r hashing are 0.8959, 0.7018, 0.7827, 0.9406, and 0.9953, respec-ely.In fact, the good classication performance of our hashing

contributed by our well-designed steps, including the similar- metric. Specically, our preprocessing reduces inuences of ntent-preserving operations and thus helps to achieve good ro-stness. Our second step provides a secondary image suitable for ta reduction with LLE. The use of LLE in the third step makes our shing discriminative since it can eciently learn global struc-re of nonlinear manifolds and discover compact representations. nally, according to the LLE property, we select the correlation co-cient as similarity metric, which can effectively measure the early changed variances of embedding vectors and thus make r algorithm reach a desirable tradeoff between robustness and scrimination.Moreover, computational time of generating a hash is also com-red. This is done by recording the total consumed time of ex-acting 200 hashes in respective discrimination test. The average e of LLE-based hashing, RTDCT hashing, GFLVQ hashing and ADWT hashing is 0.04, 3.04, 0.42 and 0.27 seconds, respec-ely. Our average time is about 0.61 seconds, which is slower an those of LLE-based hashing, RTDCT hashing and CVADWT shing, but is much faster than that of RTDCT hashing. The low eed of RTDCT hashing is due to the high complexity of RT. rformance comparisons are summarized in Table 6. Our hash-g outperforms the compared algorithm in classication with re-ect to robustness and discrimination. As to computational time d hash length, our hashing reaches moderate performances. The stest algorithm is the LLE-based hashing, and the GFLVQ hash-g has the shortest length.

Conclusions

In this work, we have proposed a robust image hashing based LLE. The key contribution of our work is the innovative use of E. As LLE is good at discovering compact representation by learn-g global structure of input data, it provides our image hashing a

26 Z. Tang et al. / Digital Signal Processing 43 (2015) 1727

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[31] F. Lefebvre, B. Macq, J.-D. Legat RASH, Radon soft hash algorithm, in: Proc. of European Signal Processing Conference, 2002, pp. 299302.

2] S.S. Kozat, R. Venkatesan, M.K. Mihcak, Robust perceptual image hashing via matrix invariants, in: Proc. of IEEE International Conference on Image Process-ing, 2004, pp. 34433446.

3] A. Swaminathan, Y. Mao, M. Wu, Robust and secure image hashing, IEEE Trans. Inf. Forensics Secur. 1 (2) (2006) 215230.

4] V. Monga, M.K. Mihcak, Robust and secure image hashing via non-negative ma-trix factorizations, IEEE Trans. Inf. Forensics Secur. 2 (3) (2007) 376390.

in 2010. He is now a professor with the Department of Computer Science, Guangxi Normal University. His research interests include image processing and mul-timedia security. He has contributed more than 30 pa-pers in international journals such as IEEE Transactions

on Knowledge and Data Engineering, Signal Processing, Applied Mathematics and Computation, IET Image Processing, Fundamenta Informaticae, Multimedia Tools and Applications, Imaging Science Journal, Applied Mathematics & Infor-mation Sciences, AE-International Journal of Electronics and Communications, ble 6rformance comparisons among different algorithms.

PerformanceAlgorithm GFLVQ hashing RTDCT hashing

Classication Moderate BadComputational time (second) 0.42 3.04Hash length (bit) 120 240

sirable discrimination. More specically, we have observed the E property that embedding vector variances are approximately early changed by content-preserving operations, so as to mea-re hash similarity with correlation coecient. Many experiments ve been conducted to validate eciency of our image hashing. e results have shown that our image hashing is robust to many mmon digital operations and reaches a good discrimination. ROC rve comparisons with some well-known algorithms have illus-ated that our hashing outperforms the compared algorithms in assication performances with respect to robustness and discrim-ation.

knowledgments

This work is partially supported by the National Natural ience Foundation of China (61300109, 61363034, 61303203), e Guangxi Natural Science Foundation (2012GXNSFBA053166, 12GXNSFGA060004), Guangxi Bagui Scholar Teams for Inno-tion and Research, the Scientic and Technological Research ojects in Guangxi Higher Education Institutions (YB2014048, 2014005), the Project of the Guangxi Key Lab of Multi-source In-rmation Mining & Security (14-A-02-02, 13-A-03-01), the Project Outstanding Young Teachers Training in Higher Education In-itutions of Guangxi, and Guangxi Collaborative Innovation Center Multi-source Information Integration and Intelligent Processing. e authors would like to thank the anonymous referees for their luable comments and suggestions.

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861874.

Zhenjun Tang received the B.S. and M.Eng. de-grees from Guangxi Normal University, Guilin, P.R. China, in 2003 and 2006, respectively, and the Ph.D. degree from Shanghai University, Shanghai, P.R. China,

Z. Tang et al. / Digital Signal Processing 43 (2015) 1727 27

anChTrananIEan

wAdted Optik-International Journal for Light and Electron Optics. He holds three ina patents. He is a reviewer of some reputable journals such as IEEE ansactions on Image Processing, IEEE Transactions on Information Forensics d Security, IEEE Transactions on Multimedia, IEEE Transactions on Circuits d Systems for Video Technology, Signal Processing, Digital Signal Processing, T Image Processing, IET Computer Vision, Neurocomputing, Multimedia Tools d Applications, and Imaging Science Journal.

Linlin Ruan received the B.S. degree from Wuhan University of Science and Engineering, Wuhan, P.R. China, in 2009. Currently, he is pursuing the M.Eng. degree at the Department of Computer Science,Guangxi Normal University. His research interests in-clude image processing and multimedia security.

Chuan Qin received the B.S. and M.S. degrees in electronic engineering from Hefei University of Tech-nology, Anhui, China, in 2002 and 2005, respectively, and the Ph.D. degree in signal and information pro-cessing from Shanghai University, Shanghai, China, in 2008. Since 2008, he has been with the faculty of the School of Optical-Electrical and Computer Engineer-ing, University of Shanghai for Science and Technol-ogy, where he is currently an Associate Professor. He as with Feng Chia University at Taiwan as a Postdoctoral Researcher and junct Assistant Professor from July 2010 to July 2012. His research in-rests include image processing and multimedia security.

Xianquan Zhang received the M.Eng. degree from Chongqing University, Chongqing, P.R. China, in 1996. He is currently a Professor with the Department of Computer Science, Guangxi Normal University. His re-search interests include image processing and com-puter graphics. He has contributed more than 70 pa-pers.

Chunqiang Yu received the M.Eng. degree fromGuangxi Normal University in 2013. His research in-terests include image processing and information hid-ing.

Robust image hashing with embedding vector variance of LLE1 Introduction2 Proposed image hashing2.1 Preprocessing2.2 Secondary image construction2.3 Locally linear embedding2.4 Hash similarity evaluation

3 Experimental results3.1 Robustness validation3.2 Discrimination test3.3 Hash length analysis3.4 Effect of parameters on hash performances

4 Performance comparisons with notable algorithms5 ConclusionsAcknowledgmentsReferences