A Review of Hashing based Image Copy Detection Techniques <s> Receiver Operating Characteristics (ROC) <s> In this paper we suggest viewing images (as well as attacks on them) as a sequence of linear operators and propose novel hashing algorithms employing transforms that are based on matrix invariants. To derive this sequence, we simply cover a two dimensional representation of an image by a sequence of (possibly overlapping) rectangles R/sub i/ whose sizes and locations are chosen randomly/sup 1/ from a suitable distribution. The restriction of the image (representation) to each R/sub i/ gives rise to a matrix A/sub i/. The fact that A/sub i/'s will overlap and are random, makes the sequence (respectively) a redundant and non-standard representation of images, but is crucial for our purposes. Our algorithms first construct a secondary image, derived from input image by pseudo-randomly extracting features that approximately capture semi-global geometric characteristics. From the secondary image (which does not perceptually resemble the input), we further extract the final features which can be used as a hash value (and can be further suitably quantized). In this paper, we use spectral matrix invariants as embodied by singular value decomposition. Surprisingly, formation of the secondary image turns out be quite important since it not only introduces further robustness (i.e., resistance against standard signal processing transformations), but also enhances the security properties (i.e. resistance against intentional attacks). Indeed, our experiments reveal that our hashing algorithms extract most of the geometric information from the images and hence are robust to severe perturbations (e.g. up to %50 cropping by area with 20 degree rotations) on images while avoiding misclassification. Our methods are general enough to yield a watermark embedding scheme, which will be studied in another paper. <s> BIB001 </s> A Review of Hashing based Image Copy Detection Techniques <s> Receiver Operating Characteristics (ROC) <s> In this paper, we propose the use of non-negative matrix factorization (NMF) for image hashing. In particular, we view images as matrices and the goal of hashing as a randomized dimensionality reduction that retains the essence of the original image matrix while preventing intentional attacks of guessing and forgery. Our work is motivated by the fact that standard-rank reduction techniques, such as QR and singular value decomposition, produce low-rank bases which do not respect the structure (i.e., non-negativity for images) of the original data. We observe that NMFs have two very desirable properties for secure image hashing applications: 1) The additivity property resulting from the non-negativity constraints results in bases that capture local components of the image, thereby significantly reducing misclassification and 2) the effect of geometric attacks on images in the spatial domain manifests (approximately) as independent identically distributed noise on NMF vectors, allowing the design of detectors that are both computationally simple and, at the same time, optimal in the sense of minimizing error probabilities. Receiver operating characteristics analysis over a large image database reveals that the proposed algorithms significantly outperform existing approaches for image hashing. <s> BIB002 </s> A Review of Hashing based Image Copy Detection Techniques <s> Receiver Operating Characteristics (ROC) <s> In order to design the image hash from human being's view, we capture the perceptual characters of the image using Gabor filter which can sense the directions in the image just like human's primary visual cortex. For a given image, we compute the reference scale, direction and block to make sure the final hash can resist against RST (Rotation, Scale, Translation) attacks while maintain the sensitivity to local malicious manipulations. In addition, it has another promising ability to locate the tampered image blocks, approximately determined tamper methods (delete, add, modify) and the original direction of each block. The ability is very useful in forensics. The experimental results show that the strategy of the reference metrics works quite well and it is much more effective than the other state of art image hash method. <s> BIB003 </s> A Review of Hashing based Image Copy Detection Techniques <s> Receiver Operating Characteristics (ROC) <s> The perceptual image hashing is an emerging technique which can be used in image authentication and content-based image retrieval. Recently, several image hashing schemes based on Radon transform are proposed for image authentication and retrieval. These schemes have no random information to strengthen the security with image hashing. In this paper, we propose a simple key-based secure image hashing scheme by using radon transform and 1-D Discrete Cosine Transform (DCT). Particularly, we introduce a randomization on Radon transform and make the image hash more secure and more robust. Moreover, the discriminative capability is also confirmed in our experimental results. <s> BIB004 </s> A Review of Hashing based Image Copy Detection Techniques <s> Receiver Operating Characteristics (ROC) <s> A robust image hashing using locally linear embedding (LLE) is presented. The image is first rescaled to a fixed size. Then the image is divided into key-dependent overlapping blocks. Every blocks are reshaped to vectors and combined to the matrix. The LLE algorithm is applied to the matrix. The reconstruction weights coefficients reflect the intrinsic geometric properties of image and are invariant basicly to ordinary image processing and several geometric transformation. The quantization scheme is devised to compress the coefficients matrix and form the binary image hash. Test results indicate that the proposed method is robust against content-preserving modifications such as JPEG compression, filtering and affine transformation. Hashes of different images have very low collision probability. <s> BIB005 </s> A Review of Hashing based Image Copy Detection Techniques <s> Receiver Operating Characteristics (ROC) <s> Abstract Conventional image hash functions only exploit luminance components of color images to generate robust hashes and then lead to limited discriminative capacities. In this paper, we propose a robust image hash function for color images, which takes all components of color images into account and achieves good discrimination. Firstly, the proposed hash function re-scales the input image to a fixed size. Secondly, it extracts local color features by converting the RGB color image into HSI and YCbCr color spaces and calculating the block mean and variance from each component of the HSI and YCbCr representations. Finally, it takes the Euclidian distances between the block features and a reference feature as hash values. Experiments are conducted to validate the efficiency of our hash function. Receiver operating characteristics (ROC) curve comparisons with two existing algorithms demonstrate that our hash function outperforms the assessed algorithms in classification performances between perceptual robustness and discriminative capability. <s> BIB006 </s> A Review of Hashing based Image Copy Detection Techniques <s> Receiver Operating Characteristics (ROC) <s> We proposed a scheme to fast retrieval similar images.SIFT features are converted to binary strings to shorten the time needed for feature matching.A fast retrieval method using hash technique is proposed.The proposed scheme possesses corresponding distinguishing ability as compared to the original SIFT method. The well-known SIFT is capable of extracting distinctive features for image retrieval. However, its matching is time consuming and slows down the entire process. In the SIFT matching, the Euclidean distance is used to measure the similarity of two features, which is expensive because it involves taking square root. Moreover, the scale of the image database is usually too large to adopt linear search for image retrieval. To improve the SIFT matching, this paper proposes a fast image retrieval scheme transforms the SIFT features to binary representations. The complexity of the distance calculation is reduced to bit-wise operation and the retrieval time is greatly decreased. Moreover, the proposed scheme utilizes hashing for retrieving similar images according to the binarized features and further speeds up the retrieval process. The experiment results show the proposed scheme can retrieve images efficiently with only a little sacrifice of accuracy as compared to SIFT. <s> BIB007 </s> A Review of Hashing based Image Copy Detection Techniques <s> Receiver Operating Characteristics (ROC) <s> We investigate the use of LLE in image hashing.We find that embedding vector variances of LLE are approximately linearly changed by content-preserving operations.We propose a robust image hashing based on this LLE property.Our hashing outperforms some notable algorithms in classification performances. Locally linear embedding (LLE) has been widely used in data processing, such as data clustering, video identification and face recognition, but its application in image hashing is still limited. In this work, we investigate the use of LLE in image hashing and find that embedding vector variances of LLE are approximately linearly changed by content-preserving operations. Based on this observation, we propose a novel LLE-based image hashing. Specifically, an input image is firstly mapped to a normalized matrix by bilinear interpolation, color space conversion, block mean extraction, and Gaussian low-pass filtering. The normalized matrix is then exploited to construct a secondary image. Finally, LLE is applied to the secondary image and the embedding vector variances of LLE are used to form image hash. Hash similarity is determined by correlation coefficient. Many experiments are conducted to validate our efficiency and the results illustrate that our hashing is robust to content-preserving operations and reaches a good discrimination. Comparisons of receiver operating characteristics (ROC) curve indicate that our hashing outperforms some notable hashing algorithms in classification between robustness and discrimination. <s> BIB008 </s> A Review of Hashing based Image Copy Detection Techniques <s> Receiver Operating Characteristics (ROC) <s> Perceptual image hash has been widely investigated in an attempt to solve the problems of image content authentication and content-based image retrieval. In this paper, we combine statistical analysis methods and visual perception theory to develop a real perceptual image hash method for content authentication. To achieve real perceptual robustness and perceptual sensitivity, the proposed method uses Watson’s visual model to extract visually sensitive features that play an important role in the process of humans perceiving image content. We then generate robust perceptual hash code by combining image-block-based features and key-point-based features. The proposed method achieves a tradeoff between perceptual robustness to tolerate content-preserving manipulations and a wide range of geometric distortions and perceptual sensitivity to detect malicious tampering. Furthermore, it has the functionality to detect compromised image regions. Compared with state-of-the-art schemes, the proposed method obtains a better comprehensive performance in content-based image tampering detection and localization. <s> BIB009 </s> A Review of Hashing based Image Copy Detection Techniques <s> Receiver Operating Characteristics (ROC) <s> Robustness and discrimination are two of the most important objectives in image hashing. We incorporate ring partition and invariant vector distance to image hashing algorithm for enhancing rotation robustness and discriminative capability. As ring partition is unrelated to image rotation, the statistical features that are extracted from image rings in perceptually uniform color space, i.e., CIE L*a*b* color space, are rotation invariant and stable. In particular, the Euclidean distance between vectors of these perceptual features is invariant to commonly used digital operations to images (e.g., JPEG compression, gamma correction, and brightness/contrast adjustment), which helps in making image hash compact and discriminative. We conduct experiments to evaluate the efficiency with 250 color images, and demonstrate that the proposed hashing algorithm is robust at commonly used digital operations to images. In addition, with the receiver operating characteristics curve, we illustrate that our hashing is much better than the existing popular hashing algorithms at robustness and discrimination. <s> BIB010
Majority of hashing algorithms employ the ROC curve to indicate classification performance between robustness and discrimination. However, parameters used to draw the ROC curve along with the thresholds can vary [18, BIB007  BIB005 . Table 9 below lists the different ROC parameters adopted by various image hashing techniques reviewed in this paper. It is important here to emphasize that different authors used different terms for the same set of parameters. From the table, it is evident that most of the reported techniques employed TPR vs FPR values to draw the ROC curve for different thresholds. Ideally, the ROC curve should pass through (0, 1) where 0 is for false positive rate and 1 is for true positive rate. Consequently BIB008 BIB006 BIB010 BIB003 exhibit the best ROC curves among the reviewed techniques. Table 9 . ROC parameters used by reviewed algorithms. n1 is the number of different images detected as identical images; n2 is the number of identical images detected as different images; n3 is the number of similar images considered as visually identical images; N1 is the total number of different images; N2 is the total number of identical images. ROC Zernike moments and local features    BIB009 Performance evaluation and comparison with the state-of-the-art is an essential step in verifying the efficacy of a proposed technique. This comparison can be either based on all performance parameters mentioned above or on a subset of them. The performance of reviewed hashing algorithms is evaluated by comparing it with some of the state-of-the-art techniques BIB001 BIB002 BIB004 . Table 10 above gives a list of state-ofthe-art techniques used by the reviewed techniques for comparison. It can be observed that the techniques NMF-NMF-SQ and SVD-SVD are most frequently used as a benchmark for comparative analysis.