Robust Perceptual Image Hashing Based on Ring ... - IEEE Xplore

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Robust Perceptual Image Hashing Based on Ring Partition and NMF Zhenjun Tang, Xianquan Zhang, and Shichao Zhang, Senior Member, IEEE Abstract—This paper designs an efficient image hashing with a ring partition and a nonnegative matrix factorization (NMF), which has both the rotation robustness and good discriminative capability. The key contribution is a novel construction of rotation-invariant secondary image, which is used for the first time in image hashing and helps to make image hash resistant to rotation. In addition, NMF coefficients are approximately linearly changed by content-preserving manipulations, so as to measure hash similarity with correlation coefficient. We conduct experiments for illustrating the efficiency with 346 images. Our experiments show that the proposed hashing is robust against content-preserving operations, such as image rotation, JPEG compression, watermark embedding, Gaussian low-pass filtering, gamma correction, brightness adjustment, contrast adjustment, and image scaling. Receiver operating characteristics (ROC) curve comparisons are also conducted with the state-of-the-art algorithms, and demonstrate that the proposed hashing is much better than all these algorithms in classification performances with respect to robustness and discrimination. Index Terms—Image hashing, multimedia security, nonnegative matrix factorization, ring partition

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INTRODUCTION

T

HE

Internet and multimedia devices, such as digital cameras, scanners, and smart cellphones, have made us easier and faster to capture, store, share, and convey hundreds of thousands of images, songs, and videos. While we are enjoying our life increasingly with multimedia products, there are still many challenging problems faced by academia and industries. For example, there may be multiple copies for an image in a PC, where the copies can be in different digital representations with visual contents the same as the original one. It is clearly an actual yet challenging issue to efficiently search for all similar versions (including the original one and its copies) of the image from large-scale multimedia data [1], [2]. In particular, while powerful multimedia tools make digital operations, such as editing and tampering, much easier than ever before, assurance of multimedia content security has been an important concern to multimedia community [3]. These real demands lead to an emerging multimedia technology, known as image hashing. We study a new yet robust image hashing in this paper. Image hashing not only allows us to quickly find image copies in large databases, but also can ensure content security of digital images. Image hashing maps an input image to a short string, called image hash, and has been widely used in image retrieval [1], image authentication [4], . Z. Tang and X. Zhang are with the Department of Computer Science, Guangxi Normal University, Guilin 541004, P.R. China. E-mail: [email protected], [email protected]. . S. Zhang is with the Department of Computer Science, Guangxi Normal University, Guilin 541004, China; and the Faculty of Information Technology, University of Technology, Sydney, NSW 2007, Australia. E-mail: [email protected]. Manuscript received 4 Sept. 2012; revised 10 Jan. 2013; accepted 25 Feb. 2013; published online 8 Mar. 2013. Recommended for acceptance by E. Ferrari. For information on obtaining reprints of this article, please send e-mail to: [email protected], and reference IEEECS Log Number TKDE-2012-09-0622. Digital Object Identifier no. 10.1109/TKDE.2013.45. 1041-4347/14/$31.00 ß 2014 IEEE

digital watermarking [5], image copy detection [6], tamper detection [7], image indexing [8], multimedia forensics [9], and reduced-reference image quality assessment [10]. There are some classical cryptographic hash functions, for example, SHA-1 and MD5, which can convert input message (document, image, graphic, text, video, etc.) into a fixed-size string. However, they are sensitive to bit-level changes and cannot be suitable for image hashing. This is because digital images often undergo normal digital processing, such as JPEG compression and image enhancement in real applications, without changing visual contents of images. This is the first one of the two basic properties of the image hash function, known as perceptual robustness, i.e., a hash function should be robust against contentpreserving operations, such as geometric transform, format conversion, and JPEG compression. In other words, hashes of an image and its processed versions are expected to be the same or very similar. Hash will be expected to be significantly changed only when visual content is altered by malicious operations, such as object deletion and object insertion. Another basic property is the discriminative capability, i.e., images with different contents should have different hashes. This means that hash distance between different images should be large enough. Moreover, an image hash function should satisfy additional properties when it is applied to some applications. For example, image hash must be dependent on one or several keys for application in digital forensics. Consequently, there are many image hashing algorithms successfully designed in last decade. From an applied context, there are still some limitations in image hashing. For example, image rotation is a useful operation. In the postprocessing of photographs, image rotation has frequently been exploited to correct those photographs with imperfect ground level. However, most of them are sensitive to rotation, mainly including, such as [4], [11], [12], [13], [14], and [15]. This means that they will falsely Published by the IEEE Computer Society

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identify those corrected photographs as different images. Some methods are robust against rotation, but their discriminative capabilities are not good enough, such as [16], [17], [18], [19], [20], and [21]. It is a challenging task to simultaneously satisfy both the requirements of rotation robustness and good discriminative capability in developing high-performance hashing algorithms. In this paper, we propose an efficient robust image hashing to meet both rotation robustness and good discriminative capability. This algorithm is based on a ring partition and a nonnegative matrix factorization (NMF). The key technique is a novel construction of secondary image achieved by the ring partition. The secondary image is invariant to image rotation, and then makes our algorithm resistant to rotation. In addition, the use of NMF provides the proposed algorithm with a good discriminative capability. This is because NMF is an efficient technique for learning parts-based representation, and the more information about local image content an image hash contains, the more discriminative the image hash. We conduct experiments for illustrating the efficiency with 346 images, including 146 images in the USC-SIPI Image Database [22], and 200 different color images, where 100 images are taken from the Ground Truth Database [23], 67 images are downloaded from the Internet, and 33 images are captured by digital cameras. Our experiments demonstrate that the proposed algorithm reaches a desirable tradeoff between the rotation robustness and the discriminative capability. The remainder of this paper is organized as follows: Section 2 briefly recalls the related work on image hashing. Section 3 describes the proposed image hashing. Section 4 and Section 5 present the experimental results and performance comparisons, respectively. Conclusions are finally drawn in Section 6.

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RELATED WORK

The earliest work of image hashing is introduced by Schneider and Chang [24] at the Third International Conference on Image Processing (ICIP). At the Seventh ICIP, Venkatesan et al. [11] published their famous paper entitled “Robust image hashing”. From then on, many researchers have devoted themselves to developing image hashing algorithms. In terms of the underlying techniques, the existing hashing algorithms can be roughly classified into five categories as follows: The first class includes hashing algorithms based on discrete wavelet transform (DWT) [4], [11], [25], [26]. Venkatesan et al. [11] used statistics of wavelet coefficients to construct image hashes. This method is resilient to JPEG compression, median filtering, and rotation within 2 degrees, but fragile to gamma correction and contrast adjustment. Monga and Evans [25] exploited the end-stopped wavelet transform to detect visually significant feature points. To make a short hash, Monga et al. [26] proposed a heuristic clustering algorithm with a polynomial time for feature point compression. Ahmed et al. [4] gave a secure image hashing scheme for authentication by using DWT and SHA-1. It can be applied to tamper detection, but fragile to some normal digital processing, such as brightness adjustment and contrast adjustment.

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The second class is the use of discrete cosine transform (DCT) [12], [13]. Fridrich and Goljan [12] found that DCT coefficients can indicate image content, and then proposed a robust hashing based on this observation for application in digital watermarking. This hashing is robust against normal processing, but sensitive to image rotation. Lin and Chang [13] designed an image authentication system using robust hashing, which is based on invariant relation between DCT coefficients at the same position in separate blocks. The hashing method can distinguish JPEG compression from malicious attacks and is also fragile to rotation. The third class advocates the Radon transform (RT) [16], [18], [27]. Lefebvre et al. [16] are the first to exploit RT to construct robust hashes. Seo et al. [27] used autocorrelation of each projection in the RT domain to design image hashing. Motivated by RT, Roover et al. [18] designed a scheme called RASH method by dividing an image into a set of radial projections of image pixels, extracting the RAdial Variance (RAV) vector from these radial projections, and compressing the RAV vector by DCT. The RASH method is resilient to image rotation and rescaling, but its discriminative capability needs to be improved. The fourth class develops image hashing techniques with discrete Fourier transform (DFT) [14], [19], [21]. Swaminathan et al. [19] used the DFT coefficients to produce image hashes. This algorithm is resilient to several content-preserving modifications, such as moderate geometric transforms and filtering. Wu et al. [14] exploited RT combining with DWT and DFT to develop image hashing. Their algorithm is robust against print-scan attack and small angle rotation. Recently, Lei et al. [21] extracted moment features from RT domain and used significant DFT coefficients of the moments to produce hashes. The RT-DFT hashing is better than the methods [19], [27] in classification performances between the perceptual robustness and the discriminative capability. The last class proposes to employ the matrix factorization [7], [17], [20]. Kozat et al. [17] viewed images and attacks as a sequence of linear operators, and proposed to calculate hashes using singular value decompositions (SVDs). This method, called SVD-SVD hashing, is robust against geometric attacks, for example, rotation, at the cost of significantly increasing misclassification. Monga and Mihcak [20] pioneered the use of NMF to derive image hashing. They applied NMF to some subimages, used the combination coefficients in the matrix factorization to construct a secondary image, obtained its low-rank matrix approximation by using NMF again, and concatenated the matrix entries to form an NMF-NMF vector. To make a short hash, they calculated the inner product between the NMF-NMF vector and a set of weight vectors which have i.i.d. Gaussian components of zero mean and unit variance. The NMF-NMF-SQ hashing is resilient to geometric attacks, but it cannot resist some normal manipulations, for example, watermark embedding. Tang et al. [7] observed the invariant relation existing in the NMF coefficient matrix and used it to construct robust hashes. This method is robust against JPEG compression, additive noise, and watermark embedding, but also fragile to image rotation.

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TABLE 1 Hashing Algorithms against Common Content-Preserving Operations

Besides the above five categories, there are also many other significant techniques for image hashing. For example, Mao and Wu [28] investigated the unicity distances of the hashing methods [11], [19] and concluded that the key reused several dozen times is no longer reliable. Khelifi and Jiang [29] proposed a robust image hashing algorithm by using the theory of optimum watermark detection. This method is resilient to rotation within 5 degrees. Lu and Wu [9] designed an image hashing for digital forensics using visual words. Tang et al. [15] proposed a lexicographical framework for image hashing and gave an implementation based on DCT and NMF. In another work, Tang et al. [30] used structural features to design image hashing and proposed a similarity metric for tamper detection. A common weakness of the algorithms [15], [30] is the fragility to rotation. Recently, Lv and Wang [31] designed a hashing algorithm using scale-invariant feature transform (SIFT) and Harris detector. Tang et al. [32] converted an RGB color image into YCbCr and HSI color spaces, and extracted invariant moments [33] from each component to construct hashes. This method is resistant to image rotation with arbitrary degree, but will falsely identify 0.43 percent different images as similar images when 98 percent visually identical images are correctly detected. In another study, Li et al. [34] proposed a robust image hashing based on random Gabor filtering (GF) and dithered lattice vector quantization (LVQ), where GF is used to extract image features resilient to rotation and LVQ is exploited to conduct compression. The GF-LVQ hashing is also robust

against image rotation with arbitrary degree and has a fast speed. In [35], Tang et al. exploited histogram of color vector angles to generate hashes. This algorithm is robust against rotation with arbitrary degree, but will mistakenly view 17.05 percent different images as identical images when the ratio of correct detection is 98 percent. Zhao et al. [36] used Zernike moments to design image hashing, which only tolerates rotation within 5 degrees. Robustness performances of some typical hashing algorithms against common content-preserving operations are summarized in Table 1, where the word “Yes” means that the algorithm is robust against such operation, the word “No” implies that the algorithm is sensitive to the operation, and the word “Unknown” represents that such robustness result has not been reported in the literature as far as we know. From the results, we observe that some state-of-the-art algorithms are robust against image rotation with arbitrary degree, such as [17], [18], [20], [21], [32], and [34]. However, we also find that these algorithms are not good enough in discrimination. Therefore, more efforts on developing high-performance algorithms with rotation robustness and good discrimination are in demand.

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PROPOSED IMAGE HASHING

Our image hashing consists of three steps, as shown in Fig. 1. In preprocessing, the input image is converted to a normalized image with a standard size. In the second step, the normalized image is partitioned into different rings,

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Fig. 2. Ring partition of an image and its rotated version. Fig. 1. Block diagram of our image hashing.

which are then used to construct a secondary image. In the third step, NMF is applied to the secondary image, and image hash is finally formed by NMF coefficients. In the following sections, we will present an NMF, the scheme of ring partition, and the illustration of our image hashing.

3.1 NMF NMF is an efficient technique of dimensionality reduction, which has shown better performance than principal components analysis (PCA) and vector quantization (VQ) in learning parts-based representation [37]. In fact, NMF has been successfully used in face recognition [38], image representation [39], image analysis [40], signal separation [41], data clustering [42], and so on. A nonnegative matrix V ¼ ðVi;j ÞMN is generally viewed as a combination of N vectors sized M  1. NMF results of V are two nonnegative matrix factors, i.e., B ¼ ðBi;j ÞMK and C ¼ ðCi;j ÞKN , where K is the rank for NMF and K < minðM; NÞ. The matrices B and C are called the base matrix and the coefficient matrix (or encoding matrix), respectively. They can be used to approximately represent V such that: V  BC:

ð1Þ

In the literature, various algorithms [43], [44] have been proposed to achieve NMF. In this paper, we employ the multiplicative update rules [43] to find B and C as follows: PN 8 Ck;j Vi;j =ðBCÞi;j > > Bi;k Bi;k j¼1PN > > Ck;j < PM j¼1 ð2Þ Bi;k Vi;j =ðBCÞi;j > Ck;j Ck;j i¼1PM > > B > : i¼1 i;k i ¼ 1; . . . ; M; j ¼ 1; . . . ; N; k ¼ 1; . . . ; K:

them to form a secondary image invariant to rotation. Fig. 3 is a schematic diagram of secondary image construction, where (a) is a square image divided into seven rings, and (b) is the secondary image formed by these rings. Detailed scheme of secondary image construction is as follows: Let the size of square image be m  m; n be the total number of rings, and Rk be a set of those pixel values in the kth ring (k ¼ 1; 2; . . .; n). In here, we only use the pixels in the inscribed circle of the square image and divide the inscribed circle into rings with equal area. This is because each ring is expected to be a column of the secondary image. The ring partition can be done by calculating the circle radii and the distance between each pixel and the image center. As shown in Fig. 3a, the pixels of each ring can be determined by two neighbor radii except those of the innermost ring. Suppose that rk is the kth radius (k ¼ 1; 2; . . .; n), which is labeled from small value to big value. Thus, r1 and rn are the radii of the innermost and outmost circles, respectively. Clearly, rn ¼ bm=2c for the m  m images, where bc means downward rounding. To determine other radii, the area of the inscribed circle A and the average area of each ring A are first calculated as follows: A ¼ r2n ;

ð4Þ

A ¼ bA=nc:

ð5Þ

So r1 can be computed by r1 ¼

rffiffiffiffiffiffi A : 

The above rules correspond to minimizing the generalized Kullback-Leibler (KL) divergence as follows: " # M X N X Vi;j F ¼ Vi;j log  Vi;j þ ðBCÞi;j : ð3Þ ðBCÞi;j i¼1 j¼1

3.2 Ring Partition In general, rotation manipulation takes image center as origin of coordinates. Fig. 2a shows a central part of Airplane, and Fig. 2b shows the corresponding part of the rotated Airplane. Obviously, visual contents in the corresponding rings of Figs. 2a and 2b are kept unchanged after image rotation. Thus, to make image hash resilient to rotation, we can divide an image into different rings and use

Fig. 3. Schematic diagram of secondary image construction.

ð6Þ

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Thus, other radii rk ðk ¼ 2; 3; . . .; n  1) can be obtained by the following equation: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A þ r2k1 : ð7Þ rk ¼  Let p(x, y) be the value of the pixel in the yth row and the xth column of the image (1  x; y  m). Suppose that (xc ; yc ) are the coordinates of the image center. Thus, xc ¼ m=2 þ 0:5 and yc ¼ m=2 þ 0:5 if m is an even number. Otherwise, xc ¼ ðm þ 1Þ=2 and yc ¼ ðm þ 1Þ=2. So the distance between pðx; yÞ and the image center (xc ; yc ) can be measured by the euclidean distance as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð8Þ dx;y ¼ ðx  xc Þ2 þ ðy  yc Þ2 : Having obtained the circle radii and pixel distances, we can classify these pixel values into n sets as follows: R1 ¼ fpðx; yÞ j dx;y  r1 g; Rk ¼ fpðx; yÞ j rk1 < dx;y  rk gðk ¼ 2; 3; . . .; nÞ:

ð9Þ ð10Þ

Next, we rearrange the elements of Rk ðk ¼ 1; 2; . . .; nÞ to make a sorted vector uk in ascending order. This operation guarantees that uk is unrelated to rotation. As pixel coordinates are discrete, the pixel number of each set is not always equal to A . Since the pixels of each ring are expected to form a column of the secondary image, uk is then mapped to a new vector vk sized A  1 by linear interpolation. Thus, the secondary image V is obtained by arranging these new vectors as follows: V ¼ ½v1 ; v2 ; v3 ; . . .; vn :

ð11Þ

As vk is unrelated to rotation, V is also invariant to this operation. Except the rotation-invariant merit, the secondary image has another advantage that it has fewer columns than the original image. Since each column is viewed as a high-dimensional vector and will be compressed by NMF, fewer columns are helpful to compact hash.

3.3 Illustrating Our Approach Below our image hashing is illustrated with an example step by step as follows: 1.

Preprocessing. The input image is first mapped to a normalized size m  m by bilinear interpolation. This ensures that our hashing is resilient to scaling operation and hashes of different size images have the same length. For an RGB color image, we convert it into YCbCr color space by the following equation: 2 3 2 32 3 65:481 128:553 24:966 R Y 4 Cb 5 ¼ 4 37:797 74:203 112 54 G 5 Cr B 2 112 3 93:786 18:214 16 þ 4 128 5 128 ð12Þ where R, G, and B represent the red, green, and blue components of a pixel, and Y ; Cb , and Cr are

Fig. 4. A pair of visually identical images.

the luminance, blue-difference chroma, and reddifference chroma, respectively. After color space conversion, we take the luminance component Y for representation. 2. Ring partition. Divide Y into n rings and exploit them to produce a secondary image V by using the scheme described in the Section 3.2. The aim of this step is to construct a rotation-invariant matrix for dimensionality reduction. 3. NMF. Apply NMF to V, and then the coefficient matrix C is available. Concatenate the matrix entries and obtain a compact image hash. Thus, the hash length is L ¼ nK, where n is the number of rings and K is the rank for NMF. To measure similarity between two image hashes, we take correlation coefficient as the metric. Let hð1Þ ¼ ð1Þ ð1Þ ð1Þ ð2Þ ð2Þ ð2Þ ½h1 ; h2 ; . . .; hL  and hð2Þ ¼ ½h1 ; h2 ; . . .; hL  be two image hashes. Thus, the correlation coefficient is defined as  PL  ð1Þ ð2Þ i¼1 hi  1 ½hi  2 ; ð13Þ S ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffiqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi PL  ð2Þ PL  ð1Þ h h þ "     1 2 i i i¼1 i¼1 where " is a small constant to avoid singularity when PL PL ð1Þ ð2Þ 2 2 i¼1 ½hi  1  ¼ 0 or i¼1 ½hi  2  ¼ 0, 1 and 2 are ð1Þ ð2Þ the means of h and h , respectively. The range of S is [1; 1]. The more similar the input images, the bigger the S value. If S is bigger than a predefined threshold T , the images are viewed as visually identical images. Otherwise, they are different images or one is a tampered version of the other. The reason of choosing correlation coefficient as the metric is based on the observation that NMF coefficients are approximately linearly changed by content-preserving manipulations. This will empirically be validated in Section 4.1. We now present two examples of our image hashing algorithm. Fig. 4a is an image with imperfect ground level. Fig. 4b is a similar version of Fig. 4a, which undergone a sequence of digital processing, including image rotation with 4 degrees, JPEG compression with quality factor 50, brightness adjustment with the Photoshop’s scale 50, and Gaussian white noise of mean 0 and variance 0.01. Both the image sizes of Figs. 4a and 4b are 760  560. We employed our image hashing with parameters of m ¼ 512, n ¼ 32, and K ¼ 2 to generate the image hashes of Figs. 4a and 4b. The results are illustrated in Table 2. We calculated similarity between the hashes of Figs. 4a and 4b, and found that S ¼ 0:9957, indicating that Figs. 4a and 4b are a pair of visually identical images.

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TABLE 2 Hash Values of the Images Illustrated in Fig. 4

4

EXPERIMENTAL RESULTS

In the experiments, the input image is resized to 512  512, the used number of rings is 32, and the rank for NMF is 2, i.e., m ¼ 512; n ¼ 32, and K ¼ 2. Thus, the hash length is L ¼ nK ¼ 64 decimal digits. To validate our hashing performances, experiments about perceptual robustness and discriminative capability are conducted in the next two sections, respectively. Section 4.3 will evaluate sensitivity to visual content changes. Effect of different parameters on hash performances, i.e., numbers of rings and ranks for NMF, will be discussed in the final section.

4.1 Perceptual Robustness All images in the USC-SIPI Image Database [22] were taken as test images, except those in the fourth volume, i.e., “Sequences,” which are often used for sequence image retrieval. This means, there are totally 146 test images selected in our experiments. We attacked these images by normal content-preserving operations with different parameters, and calculated similarities between hashes of the

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original and their attacked images. The experiments demonstrated that the proposed hashing is robust against the test operations except a few cases. For space limitation, typical examples are exemplified in this paper, where Airplane, Baboon, House, Lena, and Peppers are the test images sized 512  512. We exploited StirMark benchmark 4.0 [45] to attack them, where JPEG compression, watermark embedding, scaling, and rotation are all used. The parameters are set as follows: quality factors for JPEG compression are 30; 40; . . . ; 100; strengths of watermark embedding are 10; 20; . . . ; 100; scaling ratios are 0.5, 0.75, 0.9, 1.1, 1.5, and 2.0; and rotation angles are 1; 2; 5; 10; 15; 30; 45; 90; 1; 2; 5; 10; 15; 30; 45, and 90 degrees. Since rotation operation will expand the sizes of the attacked images, only the center parts sized 361  361 are taken from the original and the attacked images for hash generation. Brightness adjustment and contrast adjustment with Photoshop are also applied to the test images. Their parameters are both 10, 20 and 10; 20. Moreover, gamma correction and 3  3 Gaussian low-pass filtering in MATLAB are also used to produce processed versions. The  values for gamma correction are 0.75, 0.9, 1.1, 1.25, and the standard deviations for Gaussian blur are 0:3; 0:4; . . . ; 1:0. The settings of our experiments are summarized in Table 3. Therefore, each test image has 60 attacked versions. We extracted image hashes of the test images and their attacked versions, and calculated their correlation coefficients. The results are presented in Fig. 5, where the abscissa is the parameter values of each operation and the ordinate represents the correlation coefficients. It is observed that all correlation coefficients in Figs. 5a, 5b, 5c, and 5e are bigger than 0.98. In Figs. 5d, 5f, and 5g, each has one value below 0.98. They are 0.9653, 0.9790, and 0.9763, respectively. In Fig. 5h, two values, i.e., 0.9797 and 0.9573, are smaller than 0.98 when the Photoshop’s scales are 20 and 20. Therefore, we can choose T ¼ 0:98 as a threshold to resist most of the above content-preserving operations. In this case, 5=300  100% ¼ 1:67% pairs of visually identical images are falsely considered as different images. As the threshold decreases to 0.95, no pair of visually identical images is viewed as distinct images. Moreover, we validated our hashing performances under the combined attacks between rotation and other

TABLE 3 The Used Content-Preserving Operations and Their Parameter Values

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Fig. 5. Robustness test based on five standard test images.

content-preserving operations. Here, we took Airplane as test image, and further attacked the rotated Airplane with 30 degrees by JPEG compression with quality factor 30, 3  3 Gaussian low-pass filtering with a unit standard deviation, gamma correction with  ¼ 1:1, brightness adjustment with the Photoshop’s scale 20, and contrast adjustment with the Photoshop’s scale 20, respectively. The S values of the five combined attacks are 0.98516, 0.99020, 0.98699, 0.99133, and 0.98801, respectively, which are all bigger than the above-mentioned thresholds. Note that correlation coefficient S is a useful metric to measure linearity between two vectors. Its range is [1, 1], where S ¼ 1 means that the hash vectors are completely linearly dependent. The above S values are all bigger than 0.95. Those S values close to 1 indicate strong linear dependences, and therefore empirically verify that NMF coefficients are approximately linearly changed by contentpreserving manipulations.

4.2 Discriminative Capability To validate the discrimination, 200 different color images were collected to form an image database, where 100 images were taken from the Ground Truth Database [23], 67 images were downloaded from the Internet, and 33 images

were captured by digital cameras. These image contents include buildings, human beings, sport, landscape, and so on. The image sizes range from 256  256 to 2;048  1;536. Fig. 6 presents typical examples of the image database. We calculated image hashes of these 200 images, computed correlation coefficient S between each pair of different

Fig. 6. Typical images in the test database.

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Fig. 7. Discrimination test based on 200 different images.

images, and then obtained 19,900 values. Distribution of these results is presented in Fig. 7, where the abscissa is the correlation coefficient S and the ordinate represents the frequency of S. In Fig. 7, the minimum and maximum S values are 0:6836 and 0.9717, and the mean and the standard deviation of all S values are 0.3910 and 0.3014, respectively. If T ¼ 0:95 is selected as a threshold, 0.12 percent pairs of different images are falsely considered as visually similar images. As the threshold reaches 0.98, false judgment will not occur.

4.3 Sensitivity to Visual Content Changes When some operations, such as object deletion and object insertion, are applied to an image, the meaning of the attacked image is different from that of its original image. In other words, the original image and the attacked images are perceptually different. Generally, these operations are viewed as image tampering and are expected to be significantly reflected in image hash [7], [9], [13], [19], [21], [30]. This means that image hashing should be sensitive to image tampering. To validate sensitivity to visual content changes, we simulated image tampering by deleting objects or inserting objects using Photoshop, and generated dozens of tampered images. We applied the proposed hashing to the original images and their tampered images, calculated similarity S between each pair of hashes, and found that all S values are smaller than the above mentioned thresholds. For space limitation, four typical results are exemplified here. Figs. 8a, 8c, 8e, and 8g are four original images, and Figs. 8b, 8d, 8f, and 8h are their tampered versions, respectively. Hash similarity between each pair of images is given in Table 4. From the results, we observed that all S values are smaller than 0.90. Therefore, the proposed hashing can distinguish tampered images from the processed images by using the above threshold 0.95 or 0.98. 4.4 Effect of Number of Rings and Rank for NMF The receiver operating characteristics (ROC) graph [46] was exploited to visualize classification performances with respect to the robustness and the discriminative capability under different parameters. Thus, both true positive rate (TPR) PTPR and false positive rate (FPR) PFPR can be calculated as follows: PTPR ¼

n1 ; N1

ð14Þ

Fig. 8. Original images and their tampered versions.

PFPR ¼

n2 ; N2

ð15Þ

where n1 is the number of the pairs of visually identical images considered as similar images, N1 is the total pairs of visually identical images, n2 is the number of the pairs of different images viewed as similar images, and N2 is the total pairs of different images. Obviously, TPR and FPR indicate the perceptual robustness and the discriminative capability, respectively. In the experiments, all images are mapped to 512  512, i.e., m ¼ 512. The used ranks for NMF are 2 and 3, i.e., K ¼ 2 and K ¼ 3. For each rank, four numbers of rings are tested, i.e., n ¼ 8; n ¼ 16; n ¼ 32, and n ¼ 64. The test TABLE 4 Similarity S between the Original and Tampered Images

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TABLE 5 Average Time of Hash Generation under Different Parameters

Fig. 9. ROC curves under different parameters.

images used in the Sections 4.1 and 4.2 are also adopted here. For each group of parameter values, robustness validation and discrimination test are both calculated. We choose a threshold and calculate TPR and FPR. This process is repeated for different thresholds and the ROC curve is then obtained. The used thresholds are 0.940, 0.950, 0.960, 0.970, 0.980, 0.985, 0.988, 0.990, 0.995, and 0.998. Fig. 9 is the ROC curves under different parameters. It is observed that, for a fixed rank, the whole hashing performances will be improved when the number of rings increases. In fact, the number of rings is equal to column number of the secondary image. Fewer columns will lead to fewer features in the final hash, which will inevitably hurt the discriminative capability. For a fixed number of rings, a bigger rank will make better hashing performances. This is because a bigger rank means more elements in the hash, which not only preserve the perceptual robustness, but also improve the discriminative capability. In fact, hashing performances are related to hash length. Generally, a short image hash will have good robustness, but makes poor discrimination. As hash length increases, discriminative capability is strengthened, while perceptual robustness slightly decreases. Note that image hash is a compact representation, meaning that hash length is expected to be short enough. Thus, a tradeoff is needed in choosing the hash length, i.e., the values of K and n. In the experiments, we find that, for 512  512 normalized images, hash lengths ranging from 40 to 100 can reach a desirable compromise between the robustness and the discrimination, for example, 1) K ¼ 2 and n ¼ 32, 2) K ¼ 3 and n ¼ 16, and 3) K ¼ 3 and n ¼ 32.

To compare average time of hash generation under different parameters, we recorded the total time of calculating 200 different image hashes in discrimination tests and then computed the consumed time for generating a hash. Our algorithm was implemented in MATLAB language, running on a PC with 2.61-GHz AMD Athlon 64 X2 Dual CPU and 1.87-GB RAM. The results are presented in Table 5. We observe from the table that, for a fixed K, average time slightly increases when the n value becomes large. Similarly, for a fixed n, as the K value increases, consumed time will also increase.

5

PERFORMANCE COMPARISONS

To show advantages of the proposed hashing, we compared it with some state-of-the-art algorithms: The RASH method [18], RT-DFT hashing [21], SVD-SVD hashing [17], NMFNMF-SQ hashing [20], invariant moment-based hashing [32], and GF-LVQ hashing [34]. To make fair comparisons, the same images were adopted for robustness validations and discrimination tests. All images were resized to 512  512 before hash generation [17, 20]. The luminance components in YCbCr color space were also taken for representation. The original similarity metrics of the assessed algorithms were also adopted, i.e., the peak of cross correlation (PCC) for the RASH method, the modified L1 norm for the RT-DFT hashing, the L2 norm for the SVDSVD hashing, the NMF-NMF-SQ hashing, and the invariant moment-based hashing, and the normalized Hamming distance for the GF-LVQ hashing. The used parameters for the SVD-SVD hashing are as follows: the first number of overlapping rectangles is 100, rectangle size is 64  64, the second number of overlapping rectangles is 20 and the rectangle size is 40  40. For the NMF-NMF-SQ hashing, the used parameters are: subimage number is 80, height and width of subimages are 64, rank of the first NMF is 2, and rank of the second NMF is 1. For the GF-LVQ hashing, image size is also normalized to 512  512 and other parameter values are the same with those used in [34]. For the proposed hashing, experimental results under the parameters K ¼ 2 and n ¼ 32 were taken for comparisons. Therefore, the hash lengths of the RASH method, the RTDFT hashing, the SVD-SVD hashing, the NMF-NMF-SQ hashing, the invariant moment-based hashing, and the

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Fig. 10. Performance comparisons.

proposed hashing are 40, 15, 1,600, 64, 42, and 64 decimal digits, respectively. And the hash length of the GF-LVQ hashing is 120 bits. We exploited the RASH method, the RT-DFT hashing, the SVD-SVD hashing, the NMF-NMF-SQ hashing, the invariant moment-based hashing, and the GF-LVQ hashing to generate image hashes and calculated their hash similarities by using the respective metrics. The results are shown in Fig. 10, where the results of robustness validation and discrimination test are both presented for viewing classification performances. Fig. 10a is the results of the RASH method. The authors of the RASH method [18] take 0.87 as the threshold. If PCC  0:87, the images are viewed as visually identical images. Otherwise, they are different images. It is observed that the minimum PCC of visually identical images is 0.649 and the maximum PCC of different images is 0.962. This means that PCC 2 [0.649, 0.962] will

be inevitably misclassified. Fig. 10b presents the results of the RT-DFT hashing, where the minimum modified L1 norm of different images is 0.023, but the maximum distance of visually identical images is 0.144. So the values in [0.023, 0.144] will be misclassified. Fig. 10c shows the L2 norms of the SVD-SVD hashing. The minimum value of different images is 0.105 and the maximum value of similar images is 0.806. Thus, the overlapping interval between the L2 norms of similar images and different images is [0.105, 0.806]. It implies that, for those L2 norms in this interval, misclassification cannot be avoided. The results of the NMF-NMF-SQ hashing are given in Fig. 10d, where the minimum L2 norm of different images is 3,184 and the maximum value of visually identical images is 14,634. Therefore, distances in the interval [3,184, 14,634] will be falsely classified. The results of the invariant moment-based hashing are illustrated in Fig. 10e, where the minimum L2

TANG ET AL.: ROBUST PERCEPTUAL IMAGE HASHING BASED ON RING PARTITION AND NMF

TABLE 6 Thresholds of the Respective Algorithms for ROC Curves

norm of different images is 6.5 and the maximum value of visually identical images is 12.1. Thus, the overlapping interval is [6.5, 12.1]. The results of the GF-LVQ hashing are illustrated in Fig. 10f, where the minimum normalized Hamming distance of different images is 0 and the maximum distance of visually identical images is 0.5417. Therefore, the overlapping interval is [0, 0.5417]. The results of the proposed hashing are presented in Fig. 10g. It is found that the minimum S of similar images is 0.957 and the maximum S of different images is 0.972. So the overlapping interval is [0.957, 0.972]. Clearly, all the above hashing algorithms cannot find a threshold which can divide their values into two subsets without misclassification. It is also observed that the image pair number of the proposed hashing in the overlapping interval is smaller than those of other algorithms in their respective intervals. Therefore, we can intuitively conclude that the proposed hashing outperforms the compared algorithms in classification performances. To make theoretical analysis of the above results, ROC graphs were used again. For those algorithms with the same FPR, the method with big TPR outperforms the one with small value. Similarly, for those algorithms with the same TPR, the hashing with small FPR is better than that with big FPR. We exploited the thresholds of respective algorithms given in Table 6 to calculate their TPR and FPR values, and obtained the ROC curves as shown in Fig. 11, where (a), (b), (c), (d), (e), (f), and (g) are the results of the RASH method, the RT-DFT hashing, the SVD-SVD hashing, the NMF-NMFSQ hashing, the invariant moment-based hashing, the GFLVQ hashing, and the proposed hashing, respectively. From the results, we observe that, when FPR is close to 0, the TPRs of the RASH method, the RT-DFT hashing, the SVD-SVD hashing, the NMF-NMF-SQ hashing, the invariant momentbased hashing, the GF-LVQ hashing, and the proposed hashing are 0.9100, 0.8767, 0.1259, 0.8133, 0.9300, 0.5167, and 0.9833, respectively. When TPR reaches 1, the optimal FPRs of the RASH method, the RT-DFT hashing, the SVD-SVD hashing, the NMF-NMF-SQ hashing, the invariant momentbased hashing, the GF-LVQ hashing, and the proposed

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hashing are 0.2691, 0.1454, 0.9451, 0.5347, 0.0311, 0.9113, and 0.00116, respectively. It is clear that the proposed hashing outperforms the RASH method, the RT-DFT hashing, the SVD-SVD hashing, the NMF-NMF-SQ hashing, the invariant moment-based hashing, and the GF-LVQ hashing. We also evaluated content sensitivities of the compared algorithms. To do so, we applied the compared algorithms to those image pairs in Fig. 8, calculated their similarity values, and obtained the results as shown in Table 7. We took the optimum threshold of each algorithm when FPR  0 to make fair comparisons. In this case, the optimum threshold of the proposed hashing is 0.98. With this threshold, the proposed hashing can correctly identify all tampered images. The optimum thresholds of the compared algorithms are listed in Table 7. It is observed that, the RASH method cannot correctly identify the image pairs of Figs. 8a and 8 b, and Figs. 8g and 8h. Similarly, the RT-DFT hashing cannot correctly identify the image pairs of Figs. 8a and 8b, and Figs. 8c and 8d. However, the SVD-SVD hashing can successfully detect all tampered images. For the NMF-NMF-SQ hashing, it only finds a pair of the original and tampered images. The invariant moment-based hashing is insensitive to content changes, and therefore cannot discover any tampered image. For the GF-LVQ hashing, it can successfully detect the image pairs of Figs. 8a and 8b, and Figs. 8c and 8d, but fails to identify the image pairs of Figs. 8e and 8f, and Figs. 8g and 8h. In Table 7, the texts in bold indicate those results which cannot be correctly detected by the corresponding algorithms. Moreover, we compared the run time of the seven algorithms. To this end, we recorded the total time of the respective discrimination test to find average time of hash generation. The average time of the RASH method, the RTDFT hashing, the SVD-SVD hashing, the NMF-NMF-SQ hashing, the invariant moment-based hashing, the GF-LVQ hashing, and the proposed hashing are 9.6, 12.8, 1.5, 2.4, 2.6, 0.67, and 2.8 seconds, respectively. Table 8 summarizes the performance comparisons among different algorithms. We find that the proposed hashing is better than the compared algorithms in classification performances between perceptual robustness and discrimination. The proposed hashing and the SVD-SVD hashing are both sensitive to visual content changes, showing better performances than other algorithms. As to hash length and time complexity of hash generation, the proposed hashing has moderate performances, and the best algorithm is the GF-LVQ hashing.

6

CONCLUSIONS

In this paper, we have proposed a robust image hashing based on ring partition and NMF, which is robust against image rotation and has a desirable discriminative capability. A key component of our hashing is the construction of secondary image, which is used for the first time in image hashing. The secondary image is rotation-invariant, and therefore makes our hashes resistant to rotation. Discriminative capability of the proposed hashing is attributed to the use of NMF, which is good at learning parts-based representation. Experiments have been conducted to validate our hashing performances, and showed that our hashing is robust against content-preserving

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Fig. 11. ROC curve comparisons among different hashing algorithms.

manipulations, such as image rotation, JPEG compression, watermark embedding, Gaussian low-pass filtering, gamma correction, brightness adjustment, contrast adjustment, and

image scaling, and reaches good discrimination. The ROC curve comparisons have indicated that the proposed hashing is better than some well-known hashing algorithms

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TABLE 7 Similarity Results between Each Pair of Images in Fig. 8 under Different Algorithms

TABLE 8 Performance Comparisons among Different Algorithms

in classification performances between the perceptual robustness and the discriminative capability. Research on image hashing is still under way. Future works are mainly focused on the use of the rotationinvariant secondary image in combination with other techniques. Issues being considered include the capability of tamper detection in small region, tamper localization, efficient color feature extraction, and so on.

[2]

[3]

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ACKNOWLEDGMENTS The authors are grateful for the anonymous reviewers’ insightful comments and valuable suggestions sincerely, which can substantially improve the quality of this paper. Many thanks for Dr. Y. Li’s source code. This work is supported in part by the Australian Research Council (ARC) under large grant DP0985456; the China 863 Program under grant 2012AA011005; the China 973 Program under grant 2013CB329404; the Natural Science Foundation of China under grants 61300109, 61363034, 61165009, 60963008, 61170131; Guangxi “Bagui Scholar” Teams for Innovation and Research; the Guangxi Natural Science Foundation under grants 2012GXNSFGA060004, 2012GXNSFBA053166, 2011GXNSFD018026; the Training Project for Excellent Middle-aged/Young Teachers in Guangxi Higher Education Institutions; and the Scientific Research and Technological Development Program of Guangxi under grant 10123005-8. Shichao Zhang is the corresponding author.

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Shichao Zhang received the PhD degree in computer science from Deakin University, Australia. He is currently a China 1000-Plan distinguished professor with the Department of Computer Science, Guangxi Normal University, China. His research interests include information quality and pattern discovery. He has published about 60 international journal papers and more than 60 international conference papers. He has won more than 10 nation class grants. He served/is serving as an associate editor for the IEEE Transactions on Knowledge and Data Engineering, Knowledge and Information Systems, and the IEEE Intelligent Informatics Bulletin. He is a senior member of the IEEE and the IEEE Computer Society, and a member of the ACM.

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