A Novel Perceptual Hash Algorithm for Multispectral ...

algorithms Article

A Novel Perceptual Hash Algorithm for Multispectral Image Authentication Kaimeng Ding 1,2 1 2 3

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, Shiping Chen 1,3, *

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and Fan Meng 2

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School of Networks and Tele-Communications Engineering, Jinling Institute of Technology, Nanjing 211169, China; [email protected] State Key Laboratory of Resource and Environment Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Science, Beijing 100101, China; [email protected] Commonwealth Scientific and Industrial Research Organization (CSIRO), Data61, Sydney, NSW 1710, Australia Correspondence: [email protected]; Tel.: +61-2-9372-4663

Received: 21 December 2017; Accepted: 8 January 2018; Published: 14 January 2018

Abstract: The perceptual hash algorithm is a technique to authenticate the integrity of images. While a few scholars have worked on mono-spectral image perceptual hashing, there is limited research on multispectral image perceptual hashing. In this paper, we propose a perceptual hash algorithm for the content authentication of a multispectral remote sensing image based on the synthetic characteristics of each band: firstly, the multispectral remote sensing image is preprocessed with band clustering and grid partition; secondly, the edge feature of the band subsets is extracted by band fusion-based edge feature extraction; thirdly, the perceptual feature of the same region of the band subsets is compressed and normalized to generate the perceptual hash value. The authentication procedure is achieved via the normalized Hamming distance between the perceptual hash value of the recomputed perceptual hash value and the original hash value. The experiments indicated that our proposed algorithm is robust compared to content-preserved operations and it efficiently authenticates the integrity of multispectral remote sensing images. Keywords: multispectral remote sensing image; perceptual hash; integrity authentication; affinity propagation; feature fusion

1. Introduction Due to the rapid growth of remote sensing, multispectral (MS) remote sensing images have exhibited increasing potential for more and more applications ranging from independent land mapping services to government and military activities. However, with the development of image processing and network transmission techniques, it has become easier to tamper with or forge multispectral remote sensing images during the process of processing and transmission. For example, the widespread use of sophisticated image editing tools can make the authenticity and integrity of MS images suffer from a serious threat, even rendering the multispectral images useless. Therefore, ensuring the content integrity of the MS image is a major issue before the multispectral image can be used. A perceptual hash algorithm, also known as a robustness hash algorithm, is able to solve the problems of MS image content authentication, while the classic cryptographic authentication algorithms, such as MD5 and SHA1, are not suitable for this purpose since they are sensitive to each bit of the input image. A perceptual hash algorithm maps an input image into a compactible feature vector called perceptual hash value, which is a short summary of an image’s perceptual content. Perceptual hash algorithms have been developed as a frontier research topic in the field of digital media content security, and they can be applied for image content authentication, image retrieval, image registration, and digital watermarking. Similar to cryptographic hash functions, the perceptual hash algorithm Algorithms 2018, 11, 6; doi:10.3390/a11010006

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compresses the representation of the perceptual features of an image to generate a fixed-length sequence, which ensures that perceptually similar images produce similar sequences [1]. In recent years, a number of perceptual hash algorithms have been proposed to meet the requirements of different types of data [2–15]. Ahmed et al. [2] propose a perceptual hash algorithm for image authentication, which uses a secret key to randomly modulate image pixels to create a transformed feature space. It offers good robustness and it can detect minute tampering with localization of the tampered area, but it is not able be applied to an MS image with many more bands. Hadmi et al. [3] propose a novel perceptual image hash algorithm based on block truncation coding. Sun et al. [4] develop a perceptual hash based on compressive sensing and Fourier–Mellin transformation. The proposed method is robust to a wide range of distortions and attacks, and it yields better identification performances under geometric attacks such as rotation attacks and brightness changes. Yan et al. [5] propose a multi-scale image hashing method by using the location-context information of the features generated by adaptive and local feature extraction techniques. Cui et al. [6] propose a hash algorithm for 3D images by selecting suitable Dual-tree complex wavelet transform coefficients to form the final hash sequence. Qin et al. [7] propose a perceptual hash algorithm for images based on salient structure features, which can be applied in image authentication and retrieval. Chen et al. [8] propose a perceptual audio hash algorithm based on maximum-likelihood watermarking detection, which can be applied in a content-based search. Yang et al. [9] propose a wave atom transform (WAT) based image hash algorithm using distributed source coding to reduce the size of hash code, providing a better performance than existing WAT. Tang et al. [10] propose a perceptual hash algorithm with innovative use of discrete cosine transform and local linear embedding, which can be used in image authentication, image retrieval, copy detection and image forensics. Sun et al. [11] propose a video hash model based on a deep belief network, which generates the video hash from visual attention features. Chen et al. [13] propose a Discrete Cosine Transform (DCT) based perceptual hash scheme to track vehicle candidates and achieve a high level of robustness. Qin et al. [14] exploit the circle-based and the block-based strategies to extract the structural features. Fang et al. [15] adopt a gradient-based perceptual hash algorithm to encode invariant macro structures of person images to make the representation robust to both illumination and viewpoint changes. However, only a few researches on the perceptual hashing for multispectral remote sensing image have been carried out. The existing perceptual hash algorithms do not take the characteristics of MS images into consideration and they are not suitable for MS images. Therefore, new perceptual hash algorithms need to be introduced to solve the problems of MS image authentication. Different from MS remote sensing images, panchromatic (PAN) remote sensing images with the characteristics of high spatial resolution and low spectral resolution can be authenticated by the existing perceptual hash algorithms for normal images, as the digital form of PAN images is the same as normal images. In contrast, an MS remote sensing image is characterized by lower spatial resolution than PAN, but higher spectral resolution, which makes the existing perceptual hash algorithms for imaging unsuitable for multispectral remote sensing image authentication. An MS image obtains information from the visible and the near-infrared spectrum of reflected light; it is composed of a set of (more than three) monochrome images of the same scene, each of which is referred to as a band and is taken at a specific wavelength. Whereas the normal color image is composed of only three monochrome images, the PAN image has only one band. The bands of the MS remote sensing image represent the earth’s surface in different spectral sampling intervals and have clear physical meanings, while the existing perceptual hash algorithm does not take this into account and cannot perceive the content of each band. Moreover, multispectral images are generally of large sizes (some may be over several GB), while most existing perceptual hash algorithms compute the hash value from an image’s global features and are generally not sensitive to local modification in the multispectral remote sensing images. This paper addresses the above problems by presenting a novel perceptual hash algorithm for multispectral remote sensing image authentication. In this paper, we made the following contributions:

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(a) In the proposed hash algorithm, we adopt affinity propagation (AP) clustering to separate the Algorithms 2018, 11, 6 3 of 13 bands into several band subsets to reduce redundancy, in which mutual information (MI) is chosen measure the the similarity similarityofofthe thebands. bands.Therefore, Therefore,the the input image algorithm chosen to measure input image of of ourour algorithm cancan be be of an arbitrary band number to avoid setting number of band clusters. of an arbitrary band number to avoid setting thethe number of band clusters. (b) Based Based on on the analysis analysis of data characteristics characteristics of of the MS image and the basic principles of perceptual hash, technique to extract thethe principle features and and obtain compact hash hash,we weadopt adoptthe theband bandfusion fusion technique to extract principle features obtain compact values for each bandband subset, which overcomes thethe deficiencies hash values for each subset, which overcomes deficienciesininexisting existing perceptual perceptual hash algorithms algorithms for for mono-spectral mono-spectral images. images. (c) We introducegrid gridentropy-based entropy-based adaptive weighted fusion rules to comprehensive obtain comprehensive (c) We introduce adaptive weighted fusion rules to obtain features features of the grid in the same geographic region. This helps improve the preservation of of the grid in the same geographic region. This helps improve the preservation of detailed detailed information as possible. information as much as as much possible.

The remainder of this paper is organized as follows. Section 2 gives a brief introduction to The remainder of this paper is organized as follows. Section 2 gives a brief introduction to perceptual hash algorithms and discusses the related work. Section 3 describes our proposed algorithm perceptual hash algorithms and discusses the related work. Section 3 describes our proposed algorithm in detail. Section 4 presents our experimental results and analysis. Finally, we draw conclusions in in detail. Section 4 presents our experimental results and analysis. Finally, we draw conclusions in Section 5. Section 5. 2. Preliminaries 2. Preliminaries 2.1. Overview Hash 2.1. Overview of of Perceptual Perceptual Hash As shown shown in in Figure Figure 1, 1, perceptual perceptual hash hash algorithms algorithms generally As generally consist consist of of the the following following stages: stages: preprocessing, feature feature extraction, extraction, feature feature quantification, quantification,hash hashgeneration. generation. preprocessing,

Figure 1. 1. Framework hash algorithms. algorithms. Figure Framework of of perceptual perceptual hash

Pre-processing generally removes redundant information in an image, making it easier to Pre-processing generally removes redundant information in an image, making it easier to extract extract features from the image later on. Feature extraction is to extract the principle features of the features from the image later on. Feature extraction is to extract the principle features of the image image using a specific extraction method. Feature compression is to fuzzy up the extracted features using a specific extraction method. Feature compression is to fuzzy up the extracted features in order to in order to enhance robustness. Hash generation is to make the quantitative characteristics more enhance robustness. Hash generation is to make the quantitative characteristics more abstract, because abstract, because the quantitative features may lead to a large amount of data being suitable as an the quantitative features may lead to a large amount of data being suitable as an output sequence. output sequence. For image authentication, a perceptual hash algorithm should possess the For image authentication, a perceptual hash algorithm should possess the following properties: following properties: 1. 1. 2. 3. 4.

Compactness: The The hash soso that it is to Compactness: hash value value of of the theimage imageshould shouldbe beasascompact compactasaspossible, possible, that it easier is easier transport, store and use. to transport, store and use. Sensitivity to to tampering: tampering: Visually Visuallydistinct distinctimages imagesshould shouldhave havesignificantly significantlydifferent differenthash hashvalues. values. Sensitivity Perceptual robustness: robustness: The The hash hash generation generation should be insensitive to a certain level of distortion Perceptual with respect to the input image. with Security: Security: Calculation Calculation of of image image hashing hashing depends depends on on aa secret secret key, key, that is, different secret keys can generate significantly different hash values for the same image. generate significantly

For the the authentication authentication of an MS MS image, image, the the perceptual perceptual hash hash algorithm algorithm has to be be sensitive sensitive to to For of an has to malicious tampering tampering operations operations and and to to be be robust robust to to content-preserving content-preserving ones. ones. Compared with normal normal malicious Compared with images, MS images have higher requirements for measurement accuracy, and their pixels with images, MS images have higher requirements for measurement accuracy, and their pixels with coordinates can be used for measuring geometrical locations after the image has been corrected and coordinates can be used for measuring geometrical locations after the image has been corrected processed, which means the authentication algorithm should havehave highhigh authentication precision and and processed, which means the authentication algorithm should authentication precision be able to detect micro-tampering of the image. and be able to detect micro-tampering of the image. The simplest way to generate multispectral image perceptual hashing is to generate the hash value for each band. However, this would lead to a huge data volume of hash values, while the perceptual hash values should be as compact as possible to be convenient for data authentication. In addition, there are some correlations between each band, which result in high redundancy and a great amount of computation time wasted in hash generation.

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The simplest way to generate multispectral image perceptual hashing is to generate the hash value for each band. However, this would lead to a huge data volume of hash values, while the perceptual hash values should be as compact as possible to be convenient for data authentication. In addition, there are some correlations between each band, which result in high redundancy and a great amount of computation time wasted in hash generation. In this paper, we separate the bands into several band subsets with a clustering algorithm to Algorithms 2018, 11, 6 4 of 13 reduce the content redundancy, and then we adopt a band fusion-based feature extraction technique to obtain In thethis compact feature of each band subset, which could be suitable for hashing computation. paper, we separate the bands into several band subsets with a clustering algorithm to reduce thegrid content redundancy, and then we adopt a band feature extraction technique Furthermore, division is adopted to divide each bandfusion-based into grids and make the hash value more to obtain the compact featureinofthe each band subset, which could be suitable for hashing computation. sensitive to local modification MS images. Furthermore, grid division is adopted to divide band into of grids make the hash value more On the other hand, feature extraction is each a key stage theand perceptual hash. For remote sensitive to local modification in the MS images. sensing image authentication, edge characteristics based on perceptual hash can achieve higher On the other hand, feature extraction is a key stage of the perceptual hash. For remote sensing precision [16]. The sensing images would have little value if the edge characteristics had been greatly image authentication, edge characteristics based on perceptual hash can achieve higher precision [16]. changed. Additionally, edge characteristics contain effective information for applications such as The sensing images would have little value if the edge characteristics had been greatly changed. objectAdditionally, extraction, edge image segmentation andeffective target recognition. Therefore, wesuch adopt edge extraction, features as the characteristics contain information for applications as object perceptual to generate perceptual hashTherefore, value. image feature segmentation and target recognition. we adopt edge features as the perceptual feature to generate perceptual hash value.

2.2. Affinity Propagation and Mutual Information-Based Band-Clustering 2.2. Affinity Propagation and Mutual Information-Based Band-Clustering

Different bands of a multispectral image have different spectral responses and can be Different a multispectral image have different responses andthere can be distinguished frombands each of other based on their grayscales. Evenspectral in the same image, are big distinguished from each other based on their grayscales. Even in the same image, there are bigband. grayscale differences between the bands, especially between the visible band and infrared grayscale differences between the instances bands, especially between visible(mountain band and infrared band.of the Figure 2 shows several comparison of different typethe regions and urban) Figure 2 shows several comparison instances of different type regions (mountain and urban) of the Landsat thematic mapper (TM) image data of Band 1 (InR1 ) and Band 4 (InR4 ). Obviously, there are Landsat thematic mapper (TM) image data of Band 1 (InR1) and Band 4 (InR4). Obviously, there are some differences between mountainous areas and the urban areas. Furthermore, even for the same some differences between mountainous areas and the urban areas. Furthermore, even for the same surface feature, the the difference between is obvious, obvious,asasshown shown Figure 2b,d. surface feature, difference betweendifferent different bands bands is in in Figure 2b,d.

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Figure 2. Ground comparison in thematic mapper (TM) imagery: (a) City in band 1; (b) Coteau area

Figure 2. Ground comparison in thematic mapper (TM) imagery: (a) City in band 1; (b) Coteau area in in band 1; (c) City in band 4; (d) Coteau area in band 4. band 1; (c) City in band 4; (d) Coteau area in band 4.

Taking this into account, we adopt band clustering to separate the bands into several groups (band subsets). Band-clustering used band to identify the subset of bandsthe thatbands are as into independent as Taking this into account, we is adopt clustering to separate several groups andBand-clustering it is adopted to obtain compactable hash values in this algorithm. (bandpossible, subsets). is used to identify the subset of bands that are as independent as In this we use clustering [17,18] with MI values to divide bands into several band subsets. possible, and it paper, is adopted toAP obtain compactable hash inthe this algorithm. The AP algorithm is an exemplar-based clustering algorithm that uses max-sum belief propagation to In this paper, we use AP clustering [17,18] with MI to divide the bands into several band subsets. obtain an optimal exemplar which can determine the number of clusters automatically, with a The AP algorithm is an exemplar-based clustering algorithm that uses max-sum belief propagation to message exchange approach. The final clustering centers will be generated depending on the given obtain an optimal exemplar which can determine the number of clusters automatically, with a message dataset. Compared with traditional clustering algorithms, such as K-means clustering, AP clustering exchange approach. The clustering centers willit be generated depending on the dataset. does not need to set the final clustering number. Therefore, is an efficient clustering technique to given deal with Compared traditional clustering algorithms, such as performance K-means clustering, AP clustering datasetswith of many instances because of its better clustering over traditional methods.does not need to set the clustering number. Therefore, it is an efficient clustering technique to deal The AP clustering algorithm starts with the construction of a similarity matrix S  with R L L ,datasets in of many instances because of its better clustering performance over traditional methods. which the element s (i, j )(i  k ) measures the similarity between band k (InRk) and band i (InRi). In L× L , in which The AP clustering with the construction of a similarity S∈ our perceptual hashalgorithm algorithm, starts MI is chosen to construct the similarity matrix,matrix i.e., each s(i,Rj) denotes the element s(i,information j)(i 6= k) measures the between band k (InRkby ) and band i (InR the mutual between the i-thsimilarity and the j-th while L is determined the number of bands. i ). In our MI measures the statisticalMI dependence two random variables matrix, and can i.e., therefore to perceptual hash algorithm, is chosenbetween to construct the similarity eachbe s(i,used j) denotes evaluateinformation the relative utility of each to classification [19].L Given two random X and the mutual between the band i-th and the j-th while is determined by variables the number of Y bands. with marginal probability distributions p(X) and p(X) and joint probability distribution p(X, Y), their MI is defined as:

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MI measures the statistical dependence between two random variables and can therefore be used to evaluate the relative utility of each band to classification [19]. Given two random variables X and Y Algorithms 2018, 11, 6 5 of 13 with marginal probability distributions p(X) and p(X) and joint probability distribution p(X, Y), their MI is defined as: p( X, Y ) Y ) log p ( X , Y ) (1) ∑ pp(( X, I I((XX,, YY)) = ∑ X , Y ) log (1) P ( X ) p (Y ) X Y

 X

Y

P( X ) p(Y )

It follows that MI is related to entropy as: It follows that MI is related to entropy as: II((X, XY , Y) )= H H((XX) )+ HH((YY))− H H((X, X ,YY))

(2) (2)

where where H(X) H(X) and and H(Y) H(Y) are are respectively respectively the the entropies entropiesof ofXXand andY, Y,and andH(X, H(X,Y) Y)isistheir theirjoint jointentropy. entropy. Treating the band’s multispectral images as random variables, MI can be used to estimate Treating the band’s multispectral images as random variables, be used to estimate the the dependency dependency between between them, them, and and was was introduced introduced for for band band selection selection in in [20,21]. [20,21]. Using Using Equation Equation (2), (2), the the mutual mutual information information between each band of the the multispectral multispectral image can be be calculated, calculated, which which can can be be used used to to evaluate evaluate the the relative relative utility utility of of each each band bandto toclassification. classification. 2.3. 2.3. Band Band Fusion-Based Fusion-Based Edge Edge Feature Feature Extraction Extraction As achieve higher higher precision precision for As mentioned mentioned above, above, edge edge characteristics-based characteristics-based perceptual perceptual hash hash can can achieve for MS MS image image integrity integrity authentication, authentication, so so we we adopt adopt the the band band feature feature fusion fusion technique technique in in order order to to obtain obtain the the robust robust edge edge feature feature of of the the band bandsets setsseparated separatedby byband-clustering. band-clustering. So far, many fusion algorithms have been developed multispectral band fusion. the So far, many fusion algorithms have been developed forfor multispectral band fusion. One One of theofmost most important fusion techniques is the wavelet-based method, whichusually usuallyuses usesthe the discrete discrete wavelet important fusion techniques is the wavelet-based method, which wavelet transform (DWT) in the fusion [22]. Since the DWT of image signals produces a non-redundant transform (DWT) in the fusion [22]. Since the DWT of image signals produces a non-redundant image image representation, representation, it it can can provide provide better better spatial spatial and and spectral spectral localization localization of of image image information information as as compared compared to representations. Therefore, we adopt DWT-based fusionfusion techniques to obtain to other othermultiresolution multiresolution representations. Therefore, we adopt DWT-based techniques to the robust fusion features of the band subset. obtain the robust fusion features of the band subset. The The key key step step of of DWT-based DWT-based fusion fusion techniques techniques is is to to define define aa fusion fusion rule rule to to create create aa new new composite composite multiresolution representation, which uses different fusion rules to deal with various frequency bands. multiresolution representation, which uses different fusion rules to deal with various frequency bands. The process of applying the DWT can be represented as a set of filters. After first-level decomposition, The process of applying the DWT can be represented as a set of filters. After first-level decomposition, the the image image is is decomposed decomposed into into aa low lowfrequency frequency sub-image sub-image (LL (LL11)) which which is is the the approximation approximation of of the the original image and a group of high-frequency sub-images (LH , HH , and HL ) which contain abundant original image and a group of high-frequency sub-images (LH11, HH11, and HL11) which contain abundant edge as shown edge information, information, as shown in in Figure Figure 3a. 3a. The The low low frequency frequency sub-image sub-image is is the the approximation approximation of of the the original the desired desired resolution resolution is is reached. reached. original signals signals for for this this level level and and can can be be further further decomposed decomposed until until the Figure Figure 3b 3b illustrates illustrates wavelet wavelet decomposition decomposition of of an an image image at atlevel level2.2.In InFigure Figure3b, 3b,LL LL2 2, ,HL HL22,, LH LH22,, and and HH are the the sub-images sub-images produced produced after after the the LL LL11 sub-image sub-image that that are arebeing beingfurther furtherdecomposed. decomposed. Since Since HH22 are the the second-level second-level high-pass high-pass sub-images sub-images (also (also called called middle middle frequency frequency sub-images) sub-images)LH LH22,, HH HH22,, and and HL HL22 also contain abundant edge information, and are more robust than high frequency ones, but also contain abundant edge information, and are more robust than high frequency ones, but more more fragile fragile than than low low frequency frequency ones, ones, we we use use middle-frequency middle-frequencysub-images sub-imagesto toextract extractthe therobust robustbits. bits.

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(b)

Figure 3. 3. Two-dimensional Two-dimensional discrete discrete wavelet wavelet transform transform of of 2D 2D signals: signals: (a) (a) One-level One-level discrete discrete wavelet wavelet Figure transform (DWT); (b) Two-level DWT. transform (DWT); (b) Two-level DWT.

3. Our Perceptual Hash Algorithm Design The proposed perceptual hash algorithm for MS sensing image authentication consists of three main stages: (a) bands clustering, (b) feature extraction, and (c) hash value generation. The schematic diagram of the proposed algorithm is given in Figure 4.

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3. Our Perceptual Hash Algorithm Design The proposed perceptual hash algorithm for MS sensing image authentication consists of three main stages: (a) bands clustering, (b) feature extraction, and (c) hash value generation. The schematic Algorithms 11,proposed 6 6 of 13 diagram 2018, of the algorithm is given in Figure 4.

Figure 4. Framework of the proposed perceptual hash algorithm.

3.1. Band-Clustering We employ AP AP clustering clustering to to divide divide the the original original MS MS image image I into into several several band band groups, groups, and we We employ and we is constructed, constructed, where each do not need need to to set setthe theclustering clusteringnumber. number.Firstly, Firstly,the thesimilarity similaritymatrix matrixSS is matrix element element isisthe themutual mutualinformation informationbetween betweenInR InR k and InR i and the matrix size is determined k and InRi and the matrix size is determined by are updated repeatedly until by number of bands. Then, messages of similarity matrix thethe number of bands. Then, the the messages of similarity matrix S areSupdated repeatedly until some some stop aafter a fixed number of iterations, at which we need setdamping the damping factor λ and stop after fixed number of iterations, at which pointpoint we need to settothe factor λ and the the maximum number of iterations in advance. maximum number of iterations in advance. After the step step of of band-clustering, band-clustering,the thebands bandsare aredivided dividedinto intoband bandclusters clusters (band subsets). That (band subsets). That is is to say, the L bands are divided into N clusters, and each cluster is denoted as IC n (n < N). For each to say, the L bands are divided into N clusters, and each cluster is denoted as ICn (n < N). band cluster ICnn:: n o ICn =

IC1 , IC2 , ...ICi

ICn  {ICnn1 , ICnn2 ,...ICnni }

(3) (3)

where ICni i∈ I; therefore, the original MS image can also be expressed as: where ICn  I ; therefore, the original MS image can also be expressed as: I = { IC1 , IC2 , ..., ICN }

I  {IC1 , IC2 ,..., ICN }

(4) (4)

3.2. Band Fusion-Based Edge Feature Extraction The band fusion-based featureExtraction extraction is intended for encoding the perceptual information 3.2. Band Fusion-Based Edge Feature from source bands into a single one containing the best aspects of the original bands, which includes The band fusion-based feature extraction is intended for encoding the perceptual information two steps: grid division and feature extraction. The details of band fusion-based edge feature extraction from source bands into a single one containing the best aspects of the original bands, which includes on the band subsets are described as follows. two steps: grid division and feature extraction. The details of band fusion-based edge feature extraction the band subsets are described as follows. 3.2.1. Grid on Division make the hash value more sensitive to local modification in the MS images, each band is 3.2.1.To Grid Division k in which w = 1, 2, . . . , M, h = 1, 2, ..., N, partitioned into M × N grids, and the grid is denoted as Gwh To make the hash value more sensitive to local modification in the MS images, each band is and k denote the band number. Thus, the grids in different bands of the same position composed a k partitioned intoisM × N grids, the grid is denoted as Gwh in which w = 1, 2, …, M, h = 1, 2, ..., N, grid set which denoted Gwhand , as follows. and k denote the band number. Thus, the grids in different bands of the same position composed a 1 2 n Gwh = { Gwh , Gwh , . . . , Gwh } (5) grid set which is denoted G , as follows. wh

1 the 2resolution n of the grid division, the higher the As the tamper location ability G is based = { Gon (5) wh wh , Gwh ,…, Gwh } resolution of the grid division, the more fine-grained the authentication granularity can be. While the computational cost would raisedisatbased higheronresolutions, we need segment the remote sensing As the tamper locationbeability the resolution of thetogrid division, the higher the resolution of the grid division, the more fine-grained the authentication granularity can be. While the computational cost would be raised at higher resolutions, we need to segment the remote sensing image into more grids in order to increase both the time for computing perceptual hash values, as well as comparing the values. The choice of the grid division resolution thus presents a trade-off between the cost and tamper location ability. Our work aims at designing such an authentication model with

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image into more grids in order to increase both the time for computing perceptual hash values, as well as comparing the values. The choice of the grid division resolution thus presents a trade-off between 3.2.2. Feature Extraction the cost and tamper location ability. Our work aims at designing such an authentication model with goodSelecting balance between costrules and is performance. the fusion of great importance; it directly affects the fusion quality and the

sensitivity of the perceptual hash algorithm. For each grid set Gwh , the features are extracted and 3.2.2. Feature Extraction fused based on discrete wavelet transform (DWT) with adaptive weighted rules. Selecting the fusion rules is of great importance; it directly affects the fusion quality and the The whole process can be divided into the following steps: sensitivity of the perceptual hash algorithm. For each grid set Gwh , the features are extracted and fused k basedToonobtain discretethe wavelet with adaptive weighted rules. Gwh is firstly conducted with the 1. fixed transform length of (DWT) hash values, each grid The whole process can be divided into the following steps: normalization of bilinear interpolation to resize with the size of m × m. 2. 1. 2.

3.

4. 3. 4.

Two-level DWT is applied to each resized grid, which is decomposed into different kinds of k is firstly To obtain the fixed length of hash values, each grid Gwh conducted with the normalization coefficients at different scales. To extract more robust detailed information for generating hash of bilinear interpolation to resize with the size of m × m. values, we choose the two-level high-pass coefficients LH2, HH2, and HL2 as the basic perceptual Two-level DWT is applied to each resized grid, which is decomposed into different kinds of feature. coefficients at different scales. To extract more robust detailed information for generating For each grid, the three sub-bands LH2, HH2, and HL2 are fused into one matrix though the hash values, we choose the two-level high-pass coefficients LH2 , HH2 , and HL2 as the basic k fusion rule of maximum, and the fusion result is expressed as a matrix denoted by M wh . perceptual feature. k M wh n, the adaptive madeinto on the of the grid For cluster For each each band grid, the threeICsub-bands LH2 , weighted HH2 , and fusion HL2 areisfused onematrix matrix though the fusion k rule of maximum, a matrix denoted by Mwh . should satisfy FM in different bands, and and the the fusion fusion result matrixisisexpressed denoted as wh . The fusion process For each band cluster IC , the adaptive weighted fusion is made on the matrix Mk of the grid in the followed conditions,ni.e., the preservation of as much detailed information aswh possible. To do different bands, and the fusion matrix is denoted FM . The fusion process should satisfy the this, the fusion coefficient of each matrix is as follows: wh followed conditions, i.e., the preservation of as much detailed information as possible. To do this, k k the fusion coefficient of each matrix is as E follows: Ewh wh

k =

Total Ewh Ek

αk =

where

k



wh Total Ewh

n

(6) (6)

Ei  = En whwh k

i 1

i ∑ Ewh is the weighted coefficient of the matrix M wh of the grid in the kth band, and ik=1

k Ewh is

the entropy the corresponding grid. Obviously,  k kdepends on the entropy of the gridk and is where αof k is the weighted coefficient of the matrix M wh of the grid in the kth band, and Ewh is the entropy of the other corresponding grid. αkmatrix depends on wh thecan entropy of the grid is different FM be computed as and follows: different from areas. Then, theObviously, pixel of the from other areas. Then, the pixel of the matrix FMwh can be computed as follows: n

k n  k M wh (i , j ) FM wh (i, j )   k

FMwh (i, j) =

(7) (7)

k 1 α k Mwh (i, j ) ∑

k =1

A fusion example of sub-band HL2 is given in Figure 5, where Figure 5a–c show the intermediate A fusion example ofofsub-band given in4 Figure 5, 7where Figure 5a–c the5d intermediate frequency components the gridsHLin2 is InR 3, InR and InR respectively, andshow Figure shows the frequency components of the grids in InR , InR and InR respectively, and Figure 5d shows thegrid fusion 3 4 7 fusion result. It is observed that the fusion result retains the obvious edge features of the in result. It is observed that the fusion result retains the obvious edge features of the grid in several bands. several bands.

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(d)

Figure 5. A of the Figure 5. A fusion fusion example example of of the the sub-band: sub-band: (a) (a) the the intermediate intermediate frequency frequency components components of the grid grid in in grid in in InR InR4;; (c) the intermediate intermediate frequency frequency InR InR33;; (b) (b) the the intermediate intermediate frequency frequency components components of of the the grid (c) the 4 components of the the grid grid in in InR InR77;; (d) components of (d) the the fusion fusion result. result.

3.3. Data Compaction Based on Self-Adaptive PCA Since the hash value has to be as compact as possible in order to keep the content-preserving ones robust, we apply principal component analysis (PCA) on the fused feature fusion matrix

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3.3. Data Compaction Based on Self-Adaptive PCA Since the hash value has to be as compact as possible in order to keep the content-preserving ones robust, we apply principal component analysis (PCA) on the fused feature fusion matrix FMwh for noise reduction and data compaction. The PCA algorithm reduces the large dimensionality of image data in order to reduce the dimensionality of independent feature space. It is widely used in data reduction and data compression, as it is able to discover the relationships among the variables [23,24]. By using PCA on matrix FMwh , the linear correlation of the matrix element can be removed. This means that the noise can be effectively removed and the extracted feature achieves data compression. The grid’s principal components are then standardized in order to obtain the fixed-length string which is then encrypted by using a cryptographic encryption algorithm that takes RC4 as an example k . to enhance the security. The encrypted string is the hash value of the grid denoted as PHw,j k are put together as the hash value of the clustering, All of the grid’s perceptual hash values PHw,j

denoted as PHk : PH k = PH0,0 || PH0,1 || . . . || PHw,h

(8)

Finally, the hash value of the original multispectral is denoted PH as follows. PH =

n

PH 1 , PH 2 , ..., PH N

o

(9)

where N is the number of band clusters. Clearly, the hash length depends on band clusters and grid division. 3.4. Integrity Authentication At the receiver, the authentication process is implemented via the comparison between the reconstructed perceptual hash value and the original one: the higher the perceptual hash values’ difference, the greater the corresponding images’ difference. Although the hamming distance is frequently used to evaluate the difference between two sequences, it is not suitable for this purpose, because the length of the hash value may vary along with the change of algorithm parameters. We have adopted the followed “Normalized Hamming Distance” [25] to evaluate the difference between two hash values: ! L

Dis =

∑ |h1(i) − h2(i)|

/L

(10)

i =1

where h1 and h2 are perceptual hash values with L length. It is observed that the normalized hamming distance Dis is a float between 0 and 1. If the Dis of two perceptual hash values of the same area is lower than the threshold Th , it means that the corresponding area is content-preserving; otherwise, it means that the content of the corresponding area has been tampered with. Furthermore, the tampering can be located in the corresponding geographic regions by comparing each hash value of each grid. The higher the resolution of the grid division, the more fine-grained the authentication granularity can be. To obtain higher resolutions, we need to divide the image into more grids, compute more unit perceptual hash values, and compare more hash values. 4. Experiments and Discussion In this section, we evaluate the robustness of our proposed perceptual hash algorithms from two aspects. The first one is the robustness against content-preserving manipulations, wherein perceptually identical images under distortions would have similar hashes, which is important for content-based image identification. The other is the sensitivity to tampering of the image, whereby the image that has been tampered with would have different hashes to the corresponding original image.

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All experiments were implemented on a computer with a 2.40 GHz Intel i7 processor and 4.00 GB memory running Windows 10 operating system. The test software was developed using Microsoft Visual Studio 2013 Algorithms 2018, 11, 6 in C++. 9 of 13 Algorithms 2018, 11, 6

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4.1. Perceptual Perceptual Hash Hash Values Values Generation Generation 4.1. 4.1. Perceptual Hash Values Generation There are in the hash algorithm, and we we describe the parameter There are several several parameters parameters in the perceptual perceptual hash algorithm, and describe the parameter There are several parameters in the perceptual hash algorithm, and we describe the parameter settings used used in in our our experimental experimental results results in in the the following. following. Referring Referring to to the the existing existing research research [17,18], settings [17,18], settings used in our experimental results inthe themaximum following. number Referringoftoiterations the existing research [17,18], we set the damping factor λ as 0.5 and as 100 during we set the damping factor λ as 0.5 and the maximum number of iterations as 100 during the the we set the damping factor λ as 0.5 and the numbernumber. of iterations asthe 100grid during the band-clustering. The clustering clustering process need notmaximum set the the clustering clustering During division band-clustering. The process need not set number. During the grid division band-clustering. The clustering process need128 not set thepixels. clustering number. During the grid division process, 128 process, the the size size of of non-overlapping non-overlapping grids grids is is 128 × × 128 pixels. process, the size of non-overlapping grids is 128 × 128 pixels. We opted We opted for for the the Landsat Landsat TM TM image image as as an an example example to to validate validate robustness robustness performances performances and and We opted for the Landsat TM image as an example to validate robustness performances and tamper sensitivity. sensitivity. Figures Figures 66 and and 77 present present several several bands bands of of the the typical typical TM TM images images to show tamper to show the the tamper sensitivity. Figures 6 and 7 present several bands of the typical TM images to show the comparison between the bands of the same area, in which the content of the same geographical comparison between the bands of the same area, in which the content of the same geographical comparison between the bands of the same area, in which the content of the same geographical location in ofof thethe mutual information between thethe bands of the location in each eachband bandisisquite quitedifferent. different.The Thedetails details mutual information between bands of location in each band is quite different. The details of the mutual information between the bands of above twotwo images are given in Tables 1 and 2. 2. the above images are given in Tables 1 and the above two images are given in Tables 1 and 2.

(a) (b) (c) (d) (a) (b) (c) (d) Figure Different Image A for testing: testing: (a) (b) band 4; (c) band 5; (d) band band 7. Figure 6. 6. Different bands bands of of (a) band band 1; 1; Figure 6. Different bands of Image Image A A for for testing: (a) band 1; (b) (b) band band 4; 4; (c) (c) band band 5; 5; (d) (d) band 7. 7.

(a) (b) (c) (d) (a) (b) (c) (d) Figure 7. Different bands of Image B for testing: (a) band 1; (b) band 4; (c) band 5; (d) band 7. Figure 7. Different of Image Image B B for for testing: testing: (a) 1; (b) (b) band band 4; 4; (c) (c) band band 5; 5; (d) (d) band band 7. 7. Figure 7. Different bands bands of (a) band band 1;

Band Band InR 1 Band InR 1 InR 2 InR InR 2 1 InR 3 InR InR3 2 InR InR 4 3 InR 4 InR InR 5 4 InR 5 InR InR6 5 InR InR 6 6 InR 7 InR InR7 7

Table 1. The mutual information between the bands of the TM image A. Table 1. The The mutual mutual information information between between the the bands bands of of the the TM TM image image A. A. Table 1.

InR1 InR1 3.2901 InR1 3.2901 1.4594 3.2901 1.4594 1.0248 1.4594 1.0248 1.0248 1.3750 1.3750 1.3750 0.4729 0.4729 0.4729 0.3153 0.3153 0.3153 0.5264 0.5264 0.5264

InR2 InR2 1.4594 InR2 1.4594 2.8759 1.4594 2.8759 1.3769 2.8759 1.3769 1.3769 0.5142 0.5142 0.5142 0.6558 0.6558 0.6558 0.4224 0.4224 0.4224 0.6977 0.6977 0.6977

InR3 InR3 1.0248 InR3 1.0248 1.3769 1.0248 1.3769 3.3143 1.3769 3.3143 3.3143 0.4844 0.4844 0.4844 0.8609 0.8609 0.8609 0.5246 0.5246 0.5246 1.0225 1.0225 1.0225

InR4 InR4 0.3750 InR 4 0.3750 0.5142 0.3750 0.5142 0.4844 0.5142 0.4844 0.4844 3.8516 3.8516 3.8516 0.8623 0.8623 0.8623 0.4968 0.4968 0.4968 0.5814 0.5814 0.5814

InR5 InR5 0.4729 InR 5 0.4729 0.6558 0.4729 0.6558 0.8609 0.6558 0.8609 0.8609 0.8623 0.8623 0.8623 4.5497 4.5497 4.5497 0.6991 0.6991 0.6991 1.5869 1.5869 1.5869

InR6 InR6 0.3153 InR 6 0.3153 0.4224 0.3153 0.4224 0.5246 0.4224 0.5246 0.5246 0.4968 0.4968 0.4968 0.6991 0.6991 0.6991 2.8549 2.8549 2.8549 0.6597 0.6597 0.6597

InR7 InR7 0.5264 InR 7 0.5264 0.6977 0.5264 0.6977 1.0225 0.6977 1.0225 1.0225 0.5814 0.5814 0.5814 1.5869 1.5869 1.5869 0.6597 0.6597 0.6597 3.9207 3.9207 3.9207

Table 2. The mutual information between the bands of the TM image B. Table 2. The mutual information between the bands of the TM image B.

Band Band InR1 InR1 InR2 InR2 InR3 InR3 InR4 InR4 InR5 InR5 InR6 InR6 InR7 InR7

InR1 InR1 3.8032 3.8032 1.3787 1.3787 1.2635 1.2635 0.1976 0.1976 0.2785 0.2785 0.2564 0.2564 0.7383 0.7383

InR2 InR2 1.3787 1.3787 3.6052 3.6052 1.6015 1.6015 0.1938 0.1938 0.3104 0.3104 0.2085 0.2085 0.7552 0.7552

InR3 InR3 1.2635 1.2635 1.6015 1.6015 4.1446 4.1446 0.2561 0.2561 0.3137 0.3137 0.2488 0.2488 0.8458 0.8458

InR4 InR4 0.1976 0.1976 0.1938 0.1938 0.2561 0.2561 4.5152 4.5152 0.5029 0.5029 0.1878 0.1878 0.4335 0.4335

InR5 InR5 0.2785 0.2785 0.3104 0.3104 0.3137 0.3137 0.5029 0.5029 4.6314 4.6314 0.1555 0.1555 0.9323 0.9323

InR6 InR6 0.2564 0.2564 0.2085 0.2085 0.2488 0.2488 0.1878 0.1878 0.1555 0.1555 3.1426 3.1426 0.3227 0.3227

InR7 InR7 0.7383 0.7383 0.7552 0.7552 0.8458 0.8458 0.4335 0.4335 0.9323 0.9323 0.3227 0.3227 4.3498 4.3498

The results of band clustering for each TM image are the same as below: IC1  {I 11, I 22 , I 33} , The results of band clustering for each TM image are the same as below: IC1  {I , I , I } , IC  {I 66} , IC  {I 5 , I 7 } . Thus, InR1, InR2 and InR3 would be divided into a band group and be

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Table 2. The mutual information between the bands of the TM image B. Band

InR1

InR2

InR3

InR4

InR5

InR6

InR7

InR1 InR2 InR3 InR4 InR5 InR6 InR7

3.8032 1.3787 1.2635 0.1976 0.2785 0.2564 0.7383

1.3787 3.6052 1.6015 0.1938 0.3104 0.2085 0.7552

1.2635 1.6015 4.1446 0.2561 0.3137 0.2488 0.8458

0.1976 0.1938 0.2561 4.5152 0.5029 0.1878 0.4335

0.2785 0.3104 0.3137 0.5029 4.6314 0.1555 0.9323

0.2564 0.2085 0.2488 0.1878 0.1555 3.1426 0.3227

0.7383 0.7552 0.8458 0.4335 0.9323 0.3227 4.3498

 The results of band clustering for each TM image are the same as below: IC1 = I 1 , I 2 , I 3 ,   IC3 = I 6 , IC4 = I 5 , I 7 . Thus, InR1 , InR2 and InR3 would be divided into a band group and be generated as the perceptual hash value. Similarly, InR5 and InR7 would be generated as the perceptual hash value as a group. 4.2. Performance of Perceptual Robustness Perceptual robustness is the most significant difference between perceptual hash and cryptography hash. An ideal perceptual hash algorithm should be resistant to commonly-used remote sensing image content-preserving manipulations, which means that the normalized Hamming distance between the two hash values of the original image and the processed one by the content-preserving manipulation should be under the pre-determined threshold T. In this paper, the threshold T is set as 0.05. In order to evaluate the performance of perceptual robustness for the algorithm, we utilized data compaction and digital watermark embedding as examples of content-preserving manipulations for testing, in which data compaction involves lossy compression (90% JPEG compression) and lossless compression, and digital watermark embedding adopts least significant bit (LSB) embedding. In this paper, to describe the perceptual robustness, we adopt the percentage of the grid’s hash values in which no changes occurred that exceed the threshold T; the results are shown in Table 3. It can be seen from Table 3 that this algorithm can maintain its robustness with respect to the lossless compression of multi-spectral images and LSB watermark embedding, and can maintain near-robustness to lossy compression. Table 3. The results of the robustness test. Manipulation

Lossless Compression

Digital Watermarking

JPEG Compression (90%)

Image A (12 × 8 partition) Image B (4 × 4 partition)

100% 100%

100% 100%

87.5% 93.75%

The robustness of the algorithm can be adjusted by the pre-determined threshold T, i.e., the greater the threshold T is, the stronger the robustness of the algorithm. However, the relationship between robustness and sensitivity to tampering is contradictory, and may directly affect sensitivity to tampering if the robustness is overemphasized. In contrast, cryptographic authentication methods cannot achieve better certification, since they treat the above manipulation as illegal operations and their hash value would be changed dramatically after content-preserving manipulations. We utilized SHA-256 (Secure Hash Algorithm 256) as an example of cryptographic algorithms to compare with our proposed algorithm. Figure 8 shows examples of content-preserving manipulations; Figure 8a shows the original grid and Figure 8b–c show the results of content-preserving manipulations. Obviously, there are almost no differences between each of them, while the hash values of SHA-256 are very different, as shown in Table 4. By contrast, our proposal keeps the content-preserving manipulations robust, and the perceptual hash values remain unchanged. On the other hand, as the conventional perceptual hash algorithms for images do not take

after content-preserving manipulations. We utilized SHA-256 (Secure Hash Algorithm 256) as an example of cryptographic algorithms to compare with our proposed algorithm. Figure 8 shows examples of content-preserving manipulations; Figure 8a shows the original grid and Figure 8b–c show the results of content-preserving manipulations. Obviously, there are almost no differences between each of them, while the hash values of SHA-256 are very different, as shown in Table 4. By contrast, Algorithms 2018, 11, 6 11 of 14 our proposal keeps the content-preserving manipulations robust, and the perceptual hash values remain unchanged. On the other hand, as the conventional perceptual hash algorithms for images thenot multiband of MS images accountinto andaccount cannot be to MS images, do take thecharacteristic multiband characteristic of into MS images andapplied cannotdirectly be applied directly to we do not compare them with our proposed algorithm. MS images, we do not compare them with our proposed algorithm.

(a)

(b)

(c)

Figure Figure 8. 8. Examples Examples of of content-preserving content-preserving manipulations: manipulations: (a) (a)Original Originalgrid; grid;(b) (b)After Afterlossy lossycompression; compression; (c) After watermark embedded. (c) After watermark embedded. Algorithms 2018, 11, 6 Table 4. Comparison

11 of 13 of the hash values before and after content-preserving manipulations.

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of the hash values before afterCompression content-preserving manipulations. HashTable Value4. Comparison Original Hash Value After and Lossless After Watermark Embedded Table 4. Comparison of the hash values before and after content-preserving manipulations. f8f718effc12faee f8f718effc12faee Hash Value Originalf8f718effc12faee Hash Value After Lossless Compression After Watermark Embedded Our proposed f21ef6faf005f4f3 f21ef6faf005f4f3 f21ef6faf005f4f3 Hash Value Original Hash Value After Lossless Compression After Watermark Embedded f8f718effc12faee f8f718effc12faee f8f718effc12faee algorithm eef2001c08fafe0a eef2001c08fafe0a eef2001c08fafe0a Our proposed f21ef6faf005f4f3 f21ef6faf005f4f3 f21ef6faf005f4f3 f8f718effc12faee f8f718effc12faee f8f718effc12faee 5b0902fdf0f4f4fd 5b0902fdf0f4f4fd 5b0902fdf0f4f4fd algorithm eef2001c08fafe0a eef2001c08fafe0a eef2001c08fafe0a Our proposed f21ef6faf005f4f3 f21ef6faf005f4f3 f21ef6faf005f4f3 7ab724d6a78b5b70 b45d4e47cbf18b2d acbe3194602df9e2 5b0902fdf0f4f4fd 5b0902fdf0f4f4fd 5b0902fdf0f4f4fd algorithm eef2001c08fafe0a eef2001c08fafe0a eef2001c08fafe0a 1d005c1a13de6cdc 6427e04022c9bc4a 5d7f1e560f472ab5 5b0902fdf0f4f4fd 5b0902fdf0f4f4fd 5b0902fdf0f4f4fd SHA-256 7ab724d6a78b5b70 b45d4e47cbf18b2d acbe3194602df9e2 7b8a890c98204380 149397fb054156d2 dfcb813d6c073fb3 1d005c1a13de6cdc 6427e04022c9bc4a 5d7f1e560f472ab5 7ab724d6a78b5b70 b45d4e47cbf18b2d acbe3194602df9e2 4df7abff96d38f8c dc2f965424c285ae e2fca9f5295e9f58 SHA-256 7b8a890c98204380 149397fb054156d2 dfcb813d6c073fb3 1d005c1a13de6cdc 6427e04022c9bc4a 5d7f1e560f472ab5 SHA-256 4df7abff96d38f8c dc2f965424c285ae e2fca9f5295e9f58 7b8a890c98204380 149397fb054156d2 dfcb813d6c073fb3 Performance of Sensitivity to Tampering 4df7abff96d38f8c dc2f965424c285ae e2fca9f5295e9f58

4.3. Performance of Sensitivity to Tampering The authentication process of a multi-spectral image should be able to detect the local tampering 4.3. Performance of Sensitivity to Tampering The authentication a multi-spectral image should be able to detect local tampering of the bands, which meansprocess that theoftampered and original images should havethe significantly different The authentication process ofofatampered multi-spectral image should beshould able tohave detect the local of the bands, which means that the andwith original images significantly differentkinds hashes. To test the performance sensitivity respect to tampering, we take tampering several of the bands, which means that the original images should have significantly different hashes. Tooperations, test the performance of tampered sensitivityand with respect toand tampering, we the take object, several as kinds of in of tampering including removing, appending changing shown hashes. To operations, test the performance of sensitivity with respect to tampering, we take severalinkinds of tampering including removing, appending and changing the object, as shown Figures Figures 9–11. When the band of the image is tampered with, the regenerated perceptual hash values of tampering appending and changing the object, as shown in the Figures 9–11. Whenoperations, the band ofincluding the imageremoving, is tampered with, the regenerated perceptual hash values of grid the grid and thethe whole image would be changed, and the malicious tampering can be detected. Take 9–11. When the image is tampered with, regenerated perceptual values ofTake the grid and the whole band imageofwould be changed, and thethe malicious tampering can hash be detected. the the tampering of InR11ofofthe the original image Aanasexample, an example, as shown in Figure 9a,b, the perceptual and the whole would beimage changed, the malicious tampering can be the detected. Take the tampering of InRimage original A asand as shown in Figure 9a,b, perceptual hash hash values values of the image and grid cell would be changed tremendously, as shown in Table 5. tampering of image InR1 ofand the original aschanged an example, as shown inasFigure the perceptual hash of the grid cellimage wouldAbe tremendously, shown9a,b, in Table 5. values of the image and grid cell would be changed tremendously, as shown in Table 5.

(a) (b) (c) (d) (a) (b) (c) (d) Figure 9. Tampering Test 1 (removing the object): (a) InR1 of the original image A; (b) InR1 of the Figure 9. Tampering Test 1 (removing the object): (a) InR1 of the original image A; (b) InR1 of the ofthe thetampered original image Figure 9. Tampering theimage object): (a) InR InR11 of the original B; (d) image A; B. (b) InR1 of the tampered image A; (c)Test InR11of(removing tampered image A; (c) InR1 of the original image B; (d) InR1 of the tampered image B. tampered image A; (c) InR1 of the original image B; (d) InR1 of the tampered image B.

(a) (b) (c) (d) (a) (b) (c) (d) Figure 10. Tampering Test 2 (appending the object): (a) InR3 of the original image A; (b) InR3 of the 3 of thetampered original image B. A; (b) InR3 of the Figure 10.image Tampering the object): (a) InR 52 of(appending the original B; (d) 5 of the tampered A;Test (c) Test InR Figure 10. Tampering 2 (appending theimage object): (a)InR InR 3 of the original image A; (b) InR3 of the tampered image A; (c) InR5 of the original image B; (d) InR5 of the tampered image B.

tampered image A; (c) InR5 of the original image B; (d) InR5 of the tampered image B.

(a) (a)

(b) (b)

(c) (c)

(d) (d)

(a)

(b)

(c)

(d)

Figure 10.11, Tampering Test 2 (appending the object): (a) InR3 of the original image A; (b) InR3 of the Algorithms 2018, 6 12 of 14 tampered image A; (c) InR5 of the original image B; (d) InR5 of the tampered image B.

(a)

(b)

(c)

(d)

of the the original original image image A; A; (b) (b) InR InR7 of of the the Figure 11. 11. Tampering Test 33 (changing (changing the the object): object): (a) (a) InR InR7 of Figure Tampering Test 7 7 7 of the original image B; (d) InR7 of the tampered image B. tampered image A; (c) InR tampered image A; (c) InR7 of the original image B; (d) InR7 of the tampered image B. Table 5. The The normalized normalized hamming hamming distance distance of of the the tampered tampered grid. grid. Table 5.

Compared images Figure 8a,b Figure 8a,b The normalized hamming distance 0.1016 Compared Images

The normalized hamming distance

0.1016

Figure 8c,d Figure 8c,d 0.1484 0.1484

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For the above above tampering tampering example, used to to For the example, the the comparison comparison of of the the hash hash values values of of each each grid grid can can be be used locate with respect to thetocorresponding geographic region, and the location granularity locate the thetampering tampering with respect the corresponding geographic region, and the location will depend on the resolution of the grid divisions. Figure 12 shows the tamper location of Test 1 as granularity will depend on the resolution of the grid divisions. Figure 12 shows the tamper location of an example. Test 1 as an example.

(a)

(b)

(c)

(d)

the tampered image A; (b) Tamper location of Image Figure 12. 12. Tamper location of of Test Test 1: 1: (a) (a) InR InR1 of Figure Tamper location 1 of the tampered image A; (b) Tamper location of Image 1 of the tempered image B; (d) Tamper location of Image B. A; (c) InR A; (c) InR1 of the tempered image B; (d) Tamper location of Image B.

4.4. Security Analysis 4.4. Security Analysis As described in Section 3, the performance of the security of the hash values is dependent on the As described in Section 3, the performance of the security of the hash values is dependent on the security of the cryptographic encryption algorithm. The security of the chosen RC4 in this paper is security of the cryptographic encryption algorithm. The security of the chosen RC4 in this paper is widely researched and recognized, so that the security of our algorithm is guaranteed. widely researched and recognized, so that the security of our algorithm is guaranteed. 5. Conclusions 5. Conclusions In this this paper, paper, we we have have proposed proposed aa perceptual perceptual hash hash algorithm algorithm for for multispectral multispectral remote remote sensing sensing In image authentication. In order to compactly represent the perceptual features of the multispectral image authentication. In order to compactly represent the perceptual features of the multispectral image, we have adopted adopted an an affinity affinity propagation propagation algorithm algorithm to classify the the MS MS images images into into several several image, we have to classify clusters based on the mutual information of the bands of these images. Dividing each band into clusters based on the mutual information of the bands of these images. Dividing each band into aa grid, grid, the features features of the grid grid cell cell at at the the same same location location within within the the cluster cluster are are extracted extracted and and fused fused based based on on the of the DWT, while onon thethe fused feature helps reduce the the influence of noise. The DWT, while PCA-based PCA-baseddata datacompression compression fused feature helps reduce influence of noise. final perceptual hash value can be acquired after the compressed feature has been encrypted by the The final perceptual hash value can be acquired after the compressed feature has been encrypted cryptographic encryption algorithm. Experimental results have shown that the proposed by the cryptographic encryption algorithm. Experimental results have shown that the algorithm proposed is robust against normal content-preserving manipulations, such as data compaction and digital algorithm is robust against normal content-preserving manipulations, such as data compaction and watermark embedding, and has good sensitivity to detect local detailed tampering of the multispectral digital watermark embedding, and has good sensitivity to detect local detailed tampering of the image. Thus, image. the algorithm the content of multispectral remote multispectral Thus, theefficiently algorithmauthenticates efficiently authenticates theintegrity content integrity of multispectral sensing images, and overcomes the defects of the existing perceptual hash algorithms which not remote sensing images, and overcomes the defects of the existing perceptual hash algorithms do which consider multispectral remote sensing images. do not consider multispectral remote sensing images. The aims of future works are outlined as follows: firstly, to improve the robustness against JPEG compression; secondly, to expand the algorithm to include hyperspectral remote sensing images which contain many more bands than multispectral images. Acknowledgments: This study is supported by grants from the State Key Laboratory of Resource and Environment Information System Open Funding Program (Grant No. 201604), the Jiangsu Province Science and Technology Support Program (Grant No. BK20170116), the National Natural Science Foundation of China (Grant Nos. 41601396,

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The aims of future works are outlined as follows: firstly, to improve the robustness against JPEG compression; secondly, to expand the algorithm to include hyperspectral remote sensing images which contain many more bands than multispectral images. Acknowledgments: This study is supported by grants from the State Key Laboratory of Resource and Environment Information System Open Funding Program (Grant No. 201604), the Jiangsu Province Science and Technology Support Program (Grant No. BK20170116), the National Natural Science Foundation of China (Grant Nos. 41601396, 41501431) and the Scientific Research Hatch Fund of Jinling Institute of Technology (Grant Nos. jit-fhxm-201604, jit-fhxm-201605, jit-b-201520). Author Contributions: The manuscript was written by Kaimeng Ding under the guidance of Shiping Chen. Fan Meng participated in designing the experiments. All authors reviewed the manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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