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Stereoscopic Image Description With Trinion Fractional-Order Continuous Orthogonal Moments
Abstract
Some research progress has been made on fractional-order continuous orthogonal moments (FrCOMs) in the past two years. Compared with integer-order continuous orthogonal moments (InCOMs), FrCOMs increase the number of affine invariants and effectively improve numerical stability. However, the existing types of FrCOMs are still very limited, of which all are planar image oriented. No report on stereoscopic images is available yet. To this end, in this paper, FrCOMs corresponding to various types of InCOMs are first deduced, and then, they are combined with trinion theory to construct trinion FrCOMs (TFrCOMs) applicable to stereoscopic images. Furthermore, the reconstruction performance and geometric invariance of TFrCOMs are analyzed theoretically and experimentally. Finally, an application in the stereoscopic image zero-watermarking algorithm is investigated to verify the superior performance of TFrCOMs.
... With the widespread popularity of the Internet, more and more information is transmitted through the Internet, particularly the transmission of images [1]. As the carrier of information, the image has the characteristics of intuition, visuals, and vividness [2,3]. Images frequently contain some private personal information or confidential information, and the leakage of this information will cause huge losses to individuals and the country [4][5][6][7][8]. ...
... As can be seen in Fig. 6(a-c), the neighboring pixels in the three directions are highly correlated, while those in Fig. 6(d-f) have lower correlation strengths. Furthermore, the correlation of the images is quantitatively analyzed by equations (2)(3)(4)(5). From Table 3, the CC of plaintext images is near to 1, while the CC of ciphertext images is near to 0. In addition, the comparison with excellent cryptosystems in Table 4 reveal that the proposed cryptosystem can greatly decrease the correlation of images and has higher security performance. ...
In this paper, a new color image cryptosystem with cross-plane scrambling and cross-plane DNA mutation diffusion is proposed. First, the plaintext image is processed by a secure hash algorithm(SHA) to obtain small perturbations, and then these perturbations are added to the parameters of the memristor chaotic system, which generates chaotic sequences and matrices according to the initial conditions and the new parameters. Secondly, in the scrambling process, the position information is first obtained from the chaotic matrix, and the pixels of the RGB channels of the color image are swapped. Then the position information generated by the chaotic sequences changes the position of each image pixel, respectively. In the diffusion process, the DNA operation is first executed on the scrambled image, and then each pixel value is changed by cross-plane DNA mutation diffusion. Finally, the security performance of the proposed cryptosystem is evaluated by various test methods. The experimental results demonstrate the effectiveness and security of the cryptosystem.
... Toutefois, les transformées orthogonales permettent également d'analyser des signaux bidimensionnels (2D) comme les signaux d'images numériques [27]. Parmi les applications des transformées orthogonales dans l'analyse des signaux 2D (images), on trouve la reconnaissance de formes [28]- [30], la détection de contours [31], [32], compression [33]- [35], tatouage (tatouage) ...
... [36]- [39], zéro-tatouage [30], [40], [41], reconstruction [42], [43], cryptage [44]- [46], détection compressive [47] , détection de la falsification par copie-déplacement [48], [49] (I.6) À partir de l'Eq. (I.6), on peut montrer que la norme de x est préservée comme suit [55]: ...
The work presented in this thesis focuses on the theoretical development and practical applications of discrete orthogonal moment transforms in the field of digital signal analysis. Indeed, the contributions of this thesis can be divided into four main axes. In the first axis, we have presented new approaches to overcome the problem of numerical instability that limits the use of the discrete moment transforms of Charlier, Meixner, Hahn, Shmaliy, Dual Hahn and Racah in the field of digital signal analysis. The approaches proposed in this axis are based on the development of new recursive relations, modified recursive relations and on the use of methods that preserve the orthogonality property of the high-order polynomial basis, which constitute the kernel functions of the discrete moment transforms. In the second axis, we have introduced a new method based on meta-heuristic optimizers to address the problem of the optimal parameters selection of discrete moments. The relevance of this method is demonstrated through the performance improvement of three applications based on discrete moments, namely the reconstruction, the compression and the compressive sensing of large-size digital signals. In the third axis, our objective is focused on the development of new applications of discrete moment transforms in the field of digital signal analysis. Indeed, we have developed two new applications of discrete moments, namely the zero-watermarking of biosignals and the encryption of multichannel signals (biosignals and stereoscopic images). In the fourth axis, our objective is focused on the implementation of discrete moment applications on low cost, low power and portable embedded boards. To this end, we have presented a new security scheme dedicated to both the protection of confidential patient information and the copyright protection of bio-signals that are communicated in the Internet of Medical Things networks. Then, this scheme, which is based on discrete moments and a proposed chaotic systems is implemented on Raspbery Pi embedded board.
... On the other hand, the global zero-watermarking schemes (C. Wang et al., 2021aWang et al., , 2021bR. Wang et al., 2020;Xia et al., 2021a;Yang et al., 2020) generally use the whole image and a binary message (watermark) to generate an unique zero-watermark. ...
... Wang et al., 2019), (H. Chen et al., 2012), (C.Wang et al., 2021b),, and(Fang et al., 2022) are superb gray-scale stereo image zerowatermarking schemes. ...
Abstract
Discrete orthogonal moments (DOMs) are widely applied in the field of image processing. However, most existing DOMs are used for flat image analysis and are less suitable for color stereo image processing. In light of this limitation, this paper firstly presents a moments type called octonion Hahn moments (OHMs) for the compact analysis of color stereo images, and also for preserving the internal relations between all the color channels of the stereo image. OHMs are introduced in both Cartesian and polar coordinates. Secondly, we present a modified version of 2D Henon map that exhibits improved chaotic behavior over its original version. This version is introduced for potential deployment in the field of information security. Thirdly, we present an efficient color stereo image encryption scheme in the transform domain using the modified Henon's map and OHMs that are defined in Cartesian space. This scheme guarantees a perfect reconstruction of the stereo image. Finally, we present a local zero-watermarking scheme for color stereo image copyrighting based on the proposed version of Henon's map and OHMs that are defined in the polar coordinate space. This scheme is originally designed to be robust against image rotation attack. Compared to excellent existing encryption schemes, our scheme shows superior performance in terms of high security level and good robustness to various attacks (classical, statistical, noise addition, cropping, etc.). Moreover, the proposed zero-watermarking method shows stronger resistance to different types of attacks (geometric, common image processing, noise, desynchronization, etc.) in comparison to recent zero-watermarking methods.
... Image recognition under various geometric conditions is an important area in several real applications. In general, the orthogonal invariant moments have become the most used in pattern recognition and signal processing applications such as image and signal reconstruction [1], edge detection [2,3], image encryption and watermarking [4], reversible data hiding [5], image description [6], stereoscopic image description [7], action recognition from point cloud patches [8], image denoising [9], face recognition [10], color images representation and recognition [11], resilient image watermarking [12], 3D image recognition [13], content-based image retrieval [14], image analysis [15], robust copy-move forgery-detection [16], object recognition and pattern classification [17], 2D/3D object recognition through sketches [18], scene matching [19], etc. ...
... Finally, we have the two inclusions, so we have equality (7).To understand well we present the following example for p 3. ...
Images recognition require an extraction technique of feature vectors of these images. These vectors must be invariant to the three geometric transformations: rotation, translation and scaling. In this context, there are several authors who used the theory of orthogonal moments, which are become an indispensable tool in a wide range of pattern recognition applications. In this paper, we generalize the notions of orthogonality and orthogonal moments by introducing the property «p-orthogonality» and «p-orthogonal moments». We show that a p-orthogonal set of functions is composed of p orthogonal subsets. We prove that the set of linear shape functions or hat functions, used in the finite element method (FEM), is 2-orthogonal. Based in these functions we present four types of moments: the set of 2-orthogonal radial shape moments (2ORSMs), the set of orthogonal radial shape moments (1ORSMs) for gray-level images, the set of multi-channel 2-orthogonal radial shape moments (2MRSMs) and the set of multi-channel orthogonal radial shape moments (1MRSMs) for color images. Invariants to translation, scaling and rotation (TSR) of the four proposed moments are derived for image representation and recognition. We present a set of numerical experiments in the field of classification and pattern recognition to evaluate the performance of the proposed invariant moments. From a comparative study with the recent invariant moments, we conclude that our approach is very promising in the pattern recognition field and image analysis.
... For example, discrete trinion Fourier transform was introduced in [16] and applied to multiple images encryption [17]. Wang et al. proposed trinion fractional-order continuous orthogonal moments for stereoscopic image zero-watermarking [18]. Shao et al. proposed trinion discrete cosine transform and developed a cryptosystem for color image [19]. ...
For the analysis of color images, the single-channel processing method fails to consider the internal correlation between color components, while the quaternion matrix representation is not compact enough. To avoid these, this paper introduces trinion gyrator transform for color face image and develop a cancelable recognition scheme by jointing with randomized nonlinear PCANet. Firstly, color face images are precoded into trinion matrices and followed by a random binary amplitude mask for non-reversible. The nonlinear trinion correlation is proposed for selecting the optimal ratio. Next, the sampled matrix is modulated by using trinion gyrator transform and logistic-based random phase mask for increasing discriminability. Afterwards, the randomized nonlinear principal component analysis network is employed for extracting features. The recognition accuracy of the proposed algorithm on VIS, Aberdeen, GT and YMU datasets are up to 99.00%, 99.23%, 99.68% and 97.88%, which outperforms several existed methods. On top of that, the correlation index of generated face templates is no more than 0.26, indicating the revocability and security of the proposal.
... Moment-based watermarking methods have become more popular in recent years. They have robust geometric invariance and favorable image description capability, such as PHFMs (polar harmonic Fourier moments) [8] and TFrCOMs (trinion fractional-order continuous orthogonal moments) [9]. In this regard, quaternion-type orthogonal image moments, which are particularly promising tools, have been studied, such as QRHFMs (quaternion radial harmonic Fourier moments) [10], QZMs (quaternion Zernike moments) [11], QPHTs (quaternion polar harmonic transforms) [12], QPCET (quaternion polar complex exponential transform) [13], and QGPCET (quaternion generic polar complex exponential transform) [14]. ...
Digital image watermarking, as an important image content security protection technology, has higher research value. It is well-known that imperceptibility, robustness, and watermark payload are three paramount factors to evaluate model performance. Recent methods based on statistical modeling strategy effectively trade-off between imperceptibility and robustness. However, capacity and time complexity are not allowed to ignore. Furthermore, how to select robust modeling objects, appropriate statistical models, and decision rules is one of the major issues in statistical watermark detection. To this end, we propose a color image watermark detector in robust fast quaternion generic polar complex exponential transform (FQGPCET) magnitudes domain, which fully considers the human visual system (HVS) and the statistical properties of image signals. Specifically, we adopt the Cauchy-Rayleigh distribution to model the probability density function of the FQGPCET magnitudes. Then, local high entropy image blocks are used as a new embedding domain for watermark messages due to their strong robustness. Furthermore, we develop a novel optimum multibit watermark decoder based on maximum likelihood theory. Experimental results are evaluated employing a set of standard color images in terms of watermark capacity, imperceptibility, and robustness. The proposed scheme provides better performance against all types of attacks in comparison with other existing methods.
... In the field of watermarking, Fractional-order continuous orthogonal moments (FrCOMs) is a recent research topic, limited to planar images. One of the approaches extends the application to stereoscopic images by combination with Trinion theory [3]. ...
This paper proposes a cryptographic technique on images based on the Sudoku solution. Sudoku is a number puzzle, which needs applying defined protocols and filling the empty boxes with numbers. Given a small size of numbers as input, solving the sudoku puzzle yields an expanded big size of numbers, which can be used as a key for the Encryption/Decryption of images. In this way, the given small size of numbers can be stored as the prime key, which means the key is compact. A prime key clue in the sudoku puzzle always leads to only one solution, which means the key is always stable. This feature is the background for the paper, where the Sudoku puzzle output can be innovatively introduced in image cryptography. Sudoku solution is expanded to any size image using a sequence of expansion techniques that involve filling of the number matrix, Linear X-Y rotational shifting, and reverse shifting based on a standard zig-zag pattern. The crypto key for an image dictates the details of positions, where the image pixels have to be shuffled. Shuffling is made at two levels, namely pixel and sub-pixel (RGB) levels for an image, with the latter having more effective Encryption. The brought-out technique falls under the Image scrambling method with partial diffusion. Performance metrics are impressive and are given by a Histogram deviation of 0.997, a Correlation coefficient of 10⁻² and an NPCR of 99.98%. Hence, it is evident that the image cryptography with the sudoku kept in place is more efficient against Plaintext and Differential attacks.
... However, such encryption schemes cannot be used to cipher digital image since there are some significant intrinsic features differences between text information and digital images [1,2]. In this regard, various technologies for image processing have been investigated [3][4][5][6][7][8][9][10]. As a branch of digital image processing, data hiding is a critical technology to guarantee the security of confidential information. ...
In this work, a fast and effective chaos-based image cryptosystem is proposed. Collaborated with a dynamical state variables selection mechanism (DSVSM) and (7, 4) Hamming code, discrete fractional-order system with high computation complexity is innovatively introduced in this paper. In our scheme, the chaotic system only needs to be pre-iterated once and different combinations of state variables produced by DSVSM are used to encrypt different images. What’s more, these combinations of state variables are extremely sensitive to pixel changes and can introduce differential pixels into the confusion and diffusion process. Therefore, with the help of the proposed pixel-selecting-exchanging based confusion strategy, an excellent differential spreading effect can be generated to accelerate our block diffusion efficiency. Finally, in order to further advance the performance of the proposed cryptosystem, the transmission of state variables will be hidden in the corresponding cipher image through (7, 4) Hamming coding. Simulation results and performance analysis substantiate that the proposed cryptosystem has superior security, high efficiency and more in line with the real-time secure image communication.
... This type of watermarking still poses a problem, as it does not prove the authorship of the document, even if it confirms that a document has been altered. Robust watermarking [6][7][8], on the other hand, must withstand various attacks and have two key properties: 1) resistance to known attacks such as resampling, JPEG compression, cropping, and noise, and 2) easy recognizability of the watermark after extraction, despite damage inflicted by various attacks. ...
... On the other side, a limited number of computational algorithms were proposed to accelerate the moment computation of color images. Wang et al. [57] proposed ternary polar harmonic Fourier moments (TPHFMs) for processing stereoscopic images and applied the TPHFMS to the zero-watermarking algorithm. Yao et al. [58] proposed effective quaternion radial harmonic Fourier moments (Q-RHFMs) for color image representation. ...
Image moments are image descriptors widely utilized in several image processing, pattern recognition, computer vision, and multimedia security applications. In the era of big data, the computation of image moments yields a huge memory demand, especially for large moment order and/or high-resolution images (i.e., megapixel images). The state-of-the-art moment computation methods successfully accelerate the image moment computation for digital images of a resolution smaller than 1K × 1K pixels. For digital images of higher resolutions, image moment computation is problematic. Researchers utilized GPU-based parallel processing to overcome this problem. In practice, the parallel computation of image moments using GPUs encounters the non-extended memory problem, which is the main challenge. This paper proposed a recurrent-based method for computing the Polar Complex Exponent Transform (PCET) moments of fractional orders. The proposed method utilized the symmetry of the image kernel to reduce kernel computation. In the proposed method, once a kernel value is computed in one quaternion, the other three corresponding values in the remaining three quaternions can be trivially computed. Moreover, the proposed method utilized recurrence equations to compute kernels. Thus, the required memory to store the pre-computed memory is saved. Finally, we implemented the proposed method on the GPU parallel architecture. The proposed method overcomes the memory limit due to saving the kernel's memory. The experiments show that the proposed parallel-friendly and memory-efficient method is superior to the state-of-the-art moment computation methods in memory consumption and runtimes. The proposed method computes the PCET moment of order 50 for an image of size 2K × 2K pixels in 3.5 seconds while the state-of-the-art method of comparison needs 7.0 seconds to process the same image, the memory requirements for the proposed method and the method of comparison for the were 67.0 MB and 3.4 GB, respectively. The method of comparison could not compute the image moment for any image with a resolution higher than 2K × 2K pixels. In contrast, the proposed method managed to compute the image moment up to 16K × 16K pixels image.
... Besides, the work [16] engineered a concealed attack using generative adversarial network and perceptual losses for a potent watermarking. Apart from that, the research [17] did a novel stereoscopic image description using the theory of Trinion fractional-order continuous orthogonal moments. An other study [18] developed a 3D model encryption method using 2D chaos map built through the fusion of semi-tensor product (STP) theory, infinite collapse (2D-LAIC) and logistic map. ...
Plethora of image encryption schemes exist in literature based on the construct of magic square for realizing the purpose of image obfuscation. This magic square carries out the scrambling project of the encryption. In these schemes, normally single and static magic square is implied. To render greater scrambling effects, this study proposes a novel image encryption scheme using all order-4 magic squares whose frequency reaches to the tune of 880. These magic squares have been dynamically selected to carry out the scrambling project. As the color image is input, it is broken into its gray scale red, green and blue components. These components are joined together to make a big gray scale image. Intertwining logistic map (ILM) has been used for the generation of random data. Besides, one more stream has been created through the arithmetic manipulation of the generated three streams. Streams generated by ILM has been used to realize the effects of confusion and diffusion. First and second streams out of the four streams randomly select the address from the big gray scale image to apply the randomly selected magic square by the third stream, in order to create the scrambling effects. The fourth and last stream of random numbers is used to create the diffusion effects in the scrambled image. Plaintext senstivity has been introduced by tempering the one initial value of the chaotic system through the usage of a characteristic of the given input color image. The experimentation and security analyses sections vividly demonstrate the strength, immunity from the diverse attacks and prospects for the real world application of the proposed image cipher. In particular, we got very promising stats of information entropy (7.9974) and computational time (0.9865 seconds). No doubt, they suggest the potential application of the proposed image cipher in some real world setting.
... Besides, the work [16] engineered a concealed attack using generative adversarial network and perceptual losses for a potent watermarking. Apart from that, the research [17] did a novel stereoscopic image description using the theory of Trinion fractional-order continuous orthogonal moments. An other study [18] developed a 3D model encryption method using 2D chaos map built through the fusion of semi-tensor product (STP) theory, infinite collapse (2D-LAIC) and logistic map. ...
Plethora of image encryption schemes exist in literature based on the construct of magic square for realizing the purpose of image obfuscation. This magic square carries out the scrambling project of the encryption. In these schemes, normally single and static magic square is implied. To render greater scrambling effects, this study proposes a novel image encryption scheme using all order-4 magic squares whose frequency reaches to the tune of 880. These magic squares have been dynamically selected to carry out the scrambling project. As the color image is input, it is broken into its gray scale red, green and blue components. These components are joined together to make a big gray scale image. Intertwining logistic map (ILM) has been used for the generation of random data. Besides, one more stream has been created through the arithmetic manipulation of the generated three streams. Streams generated by ILM has been used to realize the effects of confusion and diffusion. First and second streams out of the four streams randomly select the address from the big gray scale image to apply the randomly selected magic square by the third stream, in order to create the scrambling effects. The fourth and last stream of random numbers is used to create the diffusion effects in the scrambled image. Plaintext senstivity has been introduced by tempering the one initial value of the chaotic system through the usage of a characteristic of the given input color image. The experimentation and security analyses sections vividly demonstrate the strength, immunity from the diverse attacks and prospects for the real world application of the proposed image cipher. In particular, we got very promising stats of information entropy (7.9974) and computational time (0.9865 seconds). No doubt, they suggest the potential application of the proposed image cipher in some real world setting.
... Chaos theory has been applied in various areas of science and engineering such that found in nonlinear oscillatory systems [1,2], biological modelling [3,4], circuits [5][6][7][8][9][10], artificial neural network modelling [11,12], chemical modelling [13,14], fuzzy modelling [15,16], robotics [17], cryptosystem [18], audio encryption [19,20], image encryption [21][22][23][24], data hiding [25][26][27], watermarking [28], and Field Programmable Gate Array (FPGA) implementation [29]. A system is said to be chaotic when exhibiting high sensitivity to even small changes in the initial conditions [30]. ...
In recent years, there are numerous studies on chaotic systems with special equilibrium curves having various shapes such as circle, butterfly, heart and apple. This paper describes a new 3-D chaotic dynamical system with a capsule-shaped equilibrium curve. The proposed chaotic system has two quadratic, two cubic and two quartic nonlinear terms. It is noted that the proposed chaotic system has a hidden attractor since it has an infinite number of equilibrium points. It is also established that the proposed chaotic system exhibits multi-stability with two coexisting chaotic attractors for the same parameter values but differential initial states. A detailed bifurcation analysis with respect to variations in the system parameters is portrayed for the new chaotic system with capsule equilibrium curve. We have shown MATLAB plots to illustrate the capsule equilibrium curve, phase orbits of the new chaotic system, bifurcation diagrams and multi-stability. As an engineering application, we have proposed a speech cryptosystem with a numerical algorithm, which is based on our novel 3-D chaotic system with a capsule-shaped equilibrium curve. The proposed speech cryptosystem follows its security evolution and implementation on Field Programmable Gate Array (FPGA) platform. Experimental results show that the proposed encryption system utilizes 33% of the FPGA, while the maximum clock frequency is 178.28 MHz.
... Kang et al. [10] proposed a robust and distinguishable color image zero-watermarking algorithm based on PHTs and compound chaotic map. Wang et al. [38] proposed a stereo image zero-watermarking algorithm based on novel trinion fractional-order continuous orthogonal moments (TFrCOMs). Yamni et al. [53] proposed a robust zero-watermarking algorithm based on quaternion radial fractional Charlier moments (QRFrCMs) for copyright protection of color medical images. ...
In this paper, we propose a new zero-watermarking algorithm for copyright protection of color image based on a new type of fractional-order quaternion moments called quaternion radial fractional Hahn moments (QRFrHMs), the artificial bee colony (ABC) algorithm, and a chaotic system that uses a mixed linear–nonlinear coupling based on two-dimensional CML (2DCML). The proposed QRFrHMs are defined by the projection of the color image on an orthogonal basis formed by a quaternion circular function and the fractional version of discrete orthogonal Hahn polynomials which depends on an additional fractional parameter α∈R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \in {\mathbb{R}}$$\end{document}. The proposed zero-watermarking algorithm computes the QRFrHMs of the original image and then uses the ABC algorithm to choose the optimal parameters of the QRFrHMs. After that, the QRFrHMs with optimal parameters are used to construct a feature image called zero-watermark. The zero-watermark is used later to verify the copyright of the protected color image in a blind way. The combination of QRFrHMs and ABC algorithm gives the proposed zero-watermarking algorithm a high robustness with a bit error rate (BER) less than 0.03 for various attacks. In addition, the proposed zero-watermarking algorithm uses the chaotic 2DCML system to improve the security requirement so that only authorized persons can verify the copyright of the protected color image. The experimental results indicate the superiority of the proposed zero-watermarking algorithm.
... The steps and techniques used to decrypt the data must be the same as the encrypted time. Only authorized users can access this data if cryptography is implemented on cloud data [26]. Encryption is always done on the sender side, while decryption is always done on the receiver side [27]. ...
There are many cloud data security techniques and algorithms available that can be used to detect attacks on cloud data, but these techniques and algorithms cannot be used to protect data from an attacker. Cloud cryptography is the best way to transmit data in a secure and reliable format. Various researchers have developed various mechanisms to transfer data securely, which can convert data from readable to unreadable, but these algorithms are not sufficient to provide complete data security. Each algorithm has some data security issues. If some effective data protection techniques are used, the attacker will not be able to decipher the encrypted data, and even if the attacker tries to tamper with the data, the attacker will not have access to the original data. In this paper, various data security techniques are developed, which can be used to protect the data from attackers completely. First, a customized American Standard Code for Information Interchange (ASCII) table is developed. The value of each Index is defined in a customized ASCII table. When an attacker tries to decrypt the data, the attacker always tries to apply the predefined ASCII table on the Ciphertext, which in a way, can be helpful for the attacker to decrypt the data. After that, a radix 64-bit encryption mechanism is used, with the help of which the number of cipher data is doubled from the original data. When the number of cipher values is double the original data, the attacker tries to decrypt each value. Instead of getting the original data, the attacker gets such data that has no relation to the original data. After that, a Hill Matrix algorithm is created, with the help of which a key is generated that is used in the exact plain text for which it is created, and this Key cannot be used in any other plain text. The boundaries of each Hill text work up to that text. The techniques used in this paper are compared with those used in various papers and discussed that how far the current algorithm is better than all other algorithms. Then, the Kasiski test is used to verify the validity of the proposed algorithm and found that, if the proposed algorithm is used for data encryption, so an attacker cannot break the proposed algorithm security using any technique or algorithm.
... Many image protection methods have been proposed, such as image steganography technology, image encryption technology, image watermarking technology [8][9][10][11][12], and so on. Image encryption is one of the most widely used image protection methods. ...
In this paper, a new one-dimensional chaotic system is proposed, which is called one-dimensional sine-fractional-adjusted-cosine-fractional (1D-SFACF). The dynamic behavior of the 1D-SFACF is analyzed by LE, bifurcation graph, trajectory, and cobweb plot. Compared to most one-dimensional chaotic systems, the 1D-SFACF has good cryptographic properties, such as larger parameter space and better chaotic behavior. Based on the excellent expressiveness of the 1D-SFACF, we design a secure image encryption algorithm using 1D-SFACF, called the image encryption algorithm based on 1D-SFACF (SFACF-IE). SFACF-IE is divided into four steps. First, the control parameters and initial values of 1D-SFACF are generated through a natural noise using a hash function. Secondly, an adaptive diffusion strategy is proposed. The starting position of the plaintext diffusion is adaptively changed according to the characteristics of the plaintext. Then, use a cross-cyclic shift to scramble. Finally, a hash function is used to generate a feedback key, the scrambled image is the input of the hash function, and the ciphertext is obtained by diffusing again. Experimental evaluations show that the algorithm is resistant to common attacks.
... It is a transform that can represent a function and capture its local or global significant features (depending on the type of moments) with 5 a minimum of moment coefficients. The moment transform has been widely used in many applications, including image analysis [16], image recognition [17], [18], [19], audio and image watermarking [4], [20], [21], signal and image encryption [22], stereo image analysis [7], [23], image retrieval [24], bio-signals reconstruction [25], etc. ...
This paper proposes a novel Octonion Krawtchouk Moments (OKMs) transform to deal with a set of images in a compact manner, and based on this transform, a local zero-watermarking scheme is proposed to protect the copyright of CT medical images. The scheme first annotates regions of interest (ROIs) on seven medical images and then uses the OKMs of these ROIs to construct a single feature image called zero-watermark. This scheme adopts the Grey Wolf Optimizer (GWO) algorithm to have a blind nature and to improve robustness against common image processing manipulations and attacks (zero-watermarking requirements). In addition, our scheme uses the trained U-net (R231) model to reduce the search space for the GWO algorithm and prevent this algorithm from getting stuck in a local optimal solution. The experimental results show that the proposed method is very robust against common image processing manupilations and attacks and has superiority compared with superb other zero-watermarking methods.
... A safe and efficient image encryption algorithm must thus use the chaotic system with other encryption techniques [21][22][23]. Even while several image encryption techniques have been presented up to this point, most of them only use a single grayscale image as the study object, and it is impossible to ensure either the safety or the efficiency of the algorithm [24][25][26]. ...
... The ensuing transmission process brings many security risks. Many image protection algorithms have been proposed nowadays [4][5][6][7][8]. Chaos and cryptography have many similarities and connections [9][10][11]. ...
... This includes noise attacks, filtering attacks, sharpening processes, compression attacks, brightness and contrast changes, and blurring processes, among others. To counteract these traditional attack methods, researchers have proposed a variety of watermarking algorithms, most notably those based on the image spatial-domain [5,6] and transform-domain [7,8] and watermarking strategies such as geometric invariants [9], simultaneous correction, and local feature regions [10]. Watermarking attacks and digital watermarking algorithms operate similarly to a game, where they promote and complement one another. ...
Digital watermarking technology is widely used in today’s copyright protection, data monitoring, and data tracking. Digital watermarking attack techniques are designed to corrupt the watermark information contained in the watermarked image (WMI) so that the watermark information cannot be extracted effectively or correctly. While traditional digital watermarking attack technology is more mature, it is capable of attacking the watermark information embedded in the WMI. However, it is also more damaging to its own visual quality, which is detrimental to the protection of the original carrier and defeats the purpose of the covert attack on WMI. To advance watermarking attack technology, we propose a new covert watermarking attack network (CWAN) based on a convolutional neural network (CNN) for removing low-frequency watermark information from WMI and minimizing the damage caused by WMI through the use of deep learning. We import the preprocessed WMI into the CWAN, obtain the residual feature images (RFI), and subtract the RFI from the WMI to attack image watermarks. At this point, the WMI’s watermark information is effectively removed, allowing for an attack on the watermark information while retaining the highest degree of image detail and other features. The experimental results indicate that the attack method is capable of effectively removing the watermark information while retaining the original image’s texture and details and that its ability to attack the watermark information is superior to that of most traditional watermarking attack methods. Compared with the neural network watermarking attack methods, it has better performance, and the attack performance metrics are improved by tens to hundreds of percent in varying degrees, indicating that it is a new covert watermarking attack method.
... They are ensuring that privacy is not leaked, and the safe transmission of images in the network has become a significant research problem in the field of information security [4][5][6][7]. Many image protection methods have been proposed, such as image steganography, image encryption technology, image watermarking technology, and so on [8][9][10][11][12][13]. Image encryption technology is one of the most widely used technologies. ...
The generation method of the key stream and the structure of the algorithm determine the security of the cryptosystem. The classical chaotic map has simple dynamic behavior and few control parameters, so it is not suitable for modern cryptography. In this paper, we design a new 2D hyperchaotic system called 2D simple structure and complex dynamic behavior map (2D-SSCDB). The 2D-SSCDB has a simple structure but has complex dynamic behavior. The Lyapunov exponent verifies that the 2D-SSCDB has hyperchaotic behavior, and the parameter space in the hyperchaotic state is extensive and continuous. Trajectory analysis and some randomness tests verify that the 2D-SSCDB can generate random sequences with good performance. Next, to verify the excellent performance of the 2D-SSCDB, we use the 2D-SSCDB to generate a keystream for color image encryption. In the encryption algorithm, the encryption algorithm scrambles and diffuses simultaneously, increasing the cryptographic system’s security. The horizontal correlation, vertical correlation, and diagonal correlation of ciphertext are −0.0004, −0.0004 and 0.0007, respectively. The average information entropy of the ciphertext is 7.9993. In addition, the designed encryption algorithm reduces the correlation between the three channels of the color image. Security analysis shows that the color image encryption algorithm designed using 2D-SSCDB has good security, can resist standard attack methods, and has high efficiency.
... Therefore, researchers are interested in fractional-order OMs. Several applications of fractional-order OMs have recently been discovered through research, such as image analysis, pattern recognition, copy-move image forgery, image reconstruction, watermarking of biomedical signals and images, plant disease recognition, color face recognition, robust and zerowatermarking of digital images, and color image encryption [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. ...
Volumetric images have a three-dimensional (3D) view, in which viewers can examine their characteristics from any angle. The more accurate the digital representation of volumetric images, the more precise and valuable the assessment of what these images represent. The representation of volumetric images is a significant area of study in pattern recognition and computer vision. Recently, volumetric image analysis using orthogonal moments with fractional order has opened up a new study pathway, which has led scholars to discover many real-life applications through investigating efficient algorithms to represent the features of 3D images. In this study, a new set of 3D shifted fractional-order Gegenbauer moments (FrGMs) for volumetric image representation is proposed. First, a mathematical description of the shifted Gegenbauer moments for 3D images is presented. Second, a fast, highly accurate method for calculating the fractional-order shifted Gegenbauer moments of 3D images is introduced. Finally, the efficiency of the proposed FrGMs is evaluated through various suitable experiments and compared with existing methods in terms of the reconstruction of 3D images, the invariability property, sensitivity to noise, and computation time. The experimental results clearly show that FrGMs outperform existing related algorithms.
... It is a hot issue to ensure the safe transmission of images on the Internet. Many encryptions, steganography, watermarking, and other algorithms for image protection have been proposed [1][2][3]. Image encryption technology is one of the important means to protect image transmission [4,5]. Traditional algorithms for encrypting text information are mature, such as DES, AES, and 3DES. ...
Face recognition is a relatively common method humans use to confirm their identity. Protecting the safe transmission of face images has become a hot issue. This paper proposes an encryption method for face images, EFR-CSTP. The EFR-CSTP is very efficient because it only encrypts the facial in the face image. Firstly, the secret keys are generated by Hash. They are the parameters and the initial values of the two-dimensional logistic tent modular map (2D-LTMM), the chaotic sequence required for encryption by 2D-LTMM. Secondly, facial information is recognized by the histogram of oriented gradients (HOG). Note that the entire algorithm only encrypts this facial image. Finally, the facial image is used as the input of the EFR-CSTP, and the ciphertext image is generated by scrambling, STP combined with the XOR diffusion method. We evaluated our algorithm in the IMDB-WIKI dataset. We also evaluate the EFR-CSTP and other algorithms on the same datasets. The evaluation results show that the EFR-CSTP has excellent performance and efficiency.
... With the rapid development of Internet technology, multimedia information such as images, audio, and texts can be exchanged frequently in an open and shared environment, which also exposes many information security problems [1][2][3][4]. Many multimedia information protection methods have been proposed, such as watermarking technology, encryption technology, steganography technology, etc. [5][6][7][8]. Among them, encryption technology is one of the most widely used technologies [9][10][11]. ...
Audio information strongly correlates in adjacent times, and the data type of the audio is float, so the traditional encryption algorithms for the image are unsuitable for audio encryption. This paper proposes an audio encryption algorithm based on Chaos, named AEA-NCS. Most 1D maps have a control parameter, and the parameter space in the chaotic state is small. Therefore, a 2D-Logistic-nested-infinite-collapse (2D-LNIC) is proposed by combining an infinite collapse map (1D-ICM) and a logistic map. There are two control parameters in 2D-LNIC, and it exhibits good chaotic performance through the Lyapunov exponent and attractor phase diagram. In the audio encryption algorithm, 2D-LNIC generates the keystream, and the encryption algorithm is a process of scrambling and diffusion simultaneously. This structure increases the security of the algorithm. We evaluate AEA-NCS in ESC-50, and the evaluation results show that AEA-NCS exhibits good performance, significantly reducing the correlation of audio information in adjacent times.
... At present, many image protection algorithms have been proposed. For example, image watermarking technology, image encryption technology, and image steganography technology [6][7][8][9][10]. Image encryption technology is one of the most widely used technologies. ...
Designing a chaotic system with a simple structure and complex dynamic behavior is one of the main tasks of chaotic cryptography. This paper designs a new 1D chaotic system called 1D two-parameters-sin-cos (1D-TPSC). Compared with high-dimensional chaotic systems, the 1D-TPSC has a simple structure and is easy to implement with software. The Lyapunov exponent analyzes the parameter space of the 1D-TPSC in a chaotic state. Furthermore, using sensitivity analysis, cobweb plot, and bifurcation diagram to verify that the sequence generated by 1D-TPSC has good performance. In addition, the 1D-TPSC has also been applied in chaotic image encryption. Arnold mapping is used to scramble the plaintext, and random XOR is used to diffuse the scrambled image. Simulation experiments show that the method can remarkably resist standard attack methods.
... Among them, encryption is one of the most common means of protecting information security. Compared with watermarking, hiding, steganography, etc. [5]- [8], encryption can better protect the content of information, especially for the protection of private information. ...
To ensure the safe and reliable transmission of images on public channels, this paper proposes a dual-domain image encryption algorithm based on hyperchaos and dynamic wavelet decomposition. The combination of dynamic wavelet decomposition and scrambling and diffusion operations is adopted in our algorithm to realize the combination of spatial and frequency domain encryption. This not only ensures the security of the encryption algorithm, but also ensures the robustness and operating efficiency of the encryption, and at the same time reduces the risk of being attacked. First, divide the original image into blocks, use a random number sequence to control the block scrambling process, and generate a scrambling matrix; Then by calculating the Hamming distance related to the plaintext, dynamically selecting the wavelet type, performing wavelet decomposition, and generating a wavelet coefficient matrix; Re-input the plaintext image to the SHA-512 algorithm to generate the initial value of the hyperchaos. The chaotic system generates the chaotic key matrix through iteration; Then the scrambling matrix is dynamically rotated, and then the Zigzag transform is used to generate the key matrix; Finally, the wavelet coefficient matrix, the chaotic key matrix, and the key matrix are subjected to bitwise XOR operation to realize the diffusion of pixel values and obtain the final encrypted image. Simulation experiments and performance analysis experiments can show that this algorithm can effectively encrypt and decrypt images, and has good encryption and decryption quality, and the ability to resist various attacks.
... The adjacent pixels of the image has a very strong correlation [13][14][15][16][17], and the traditional DES, AES and other algorithms [18] cannot eliminate this correlation, and the efficiency of these algorithms is very low. Currently, many image protection algorithms have been proposed, such as image watermarking technology, image encryption technology, and image steganography technology [19][20][21][22][23][24]. Among them, image encryption technology is one of the most widely used technologies [25,26]. ...
With the rise of technologies of VR technology, AR technology, and 3D printing, the application of 3D models has become more and more extensive. The data of the 3D model is the floating point and has a unique storage format, and the traditional 2D image encryption algorithms are unsuitable for 3D models. Therefore, based on 1D Sine-Map-Coupling-Logistic-Map (1D-SMCLM), a 3D model encryption algorithm is designed in this paper. The 1D-SMCLM is a new chaotic system with large parameter space and good chaotic characteristics. The keystream generated by the 1D-SMCLM has good randomness and is very suitable for cryptographic systems. In the new encryption algorithm (SMCLM-3ME), the vertices of the 3D models are divided into integer and decimal vertices. The integer part is encrypted by the strategy of simultaneous scrambling and diffusion. The 3D ciphertext model is obtained by combining the integer and fractional parts. Experimental results show that the SMCLM-IE exhibits excellent performance.
... For this reason, authors [21] proposed a new set of polar harmonic Fourier moments and invariant continuous orthogonal moments. Wang et al. [22] presented continuous orthogonal moments using Trinion Fractional-Order. Medical image protection without degrading the quality of original images is also a challenging task. ...
COVID-19 is the most transmissible disease, caused by the SARS-CoV-2 virus that severely infects the lungs and the upper respiratory tract of the human body. This virus badly affected the lives and wellness of millions of people worldwide and spread widely. Early diagnosis, timely treatment, and proper confinement of the infected patients are some possible ways to control the spreading of coronavirus. Computed tomography (CT) scanning has proven useful in diagnosing several respiratory lung problems, including COVID-19 infections. Automated detection of COVID-19 using chest CT-scan images may reduce the clinician’s load and save the lives of thousands of people. This study proposes a robust framework for the automated screening of COVID-19 using chest CT-scan images and deep learning-based techniques. In this work, a publically accessible CT-scan image dataset (contains the 1252 COVID-19 and 1230 non-COVID chest CT images), two pre-trained deep learning models (DLMs) namely, MobileNetV2 and DarkNet19, and a newly-designed lightweight DLM, are utilized for the automated screening of Covid-19. A repeated ten-fold holdout validation method is utilized for the training, validation, and testing of DLMs. The highest classification accuracy of 98.91% is achieved using transfer-learned DarkNet19. The proposed framework is ready to be tested with more CT images. The simulation results with the publicly available COVID-19 CT scan image dataset are included to show the effectiveness of the presented study.
... In general, chaotic systems can be divided into low-dimensional chaotic systems, high-dimensional chaotic systems, spatiotemporal chaotic systems, etc [21][22][23]. Combining these chaotic systems, some image encryption algorithms have been proposed [24][25][26]. For example, Wang et al uses the CML system and proposes a parallel diffusion encryption method, which reduce the complexity of the algorithm [27]. ...
In this paper, a new model of 2D absolute sine-cosine coupling (2D-ASCC) is proposed. In comparison with other 2D chaos map, the proposed system has higher complexity and better property of pseudo-random. It can effectively improve the security performance of encryption algorithm, if the proposed chaos map is applied in the design of image encryption algorithm based on chaos. Then, a new diffusion algorithm is designed based on the jumping diffusion. The plaintext is divided into two groups, and each group of plaintext is encrypted with a different formula. The pixel value of each ciphertext is composed of several non-adjacent pixels and the pseudo-random values generated by the proposed chaos map. In comparison with some existing encryption scheme, by using the design encryption scheme, the plaintext image can be completely encrypted in one iteration, it can significantly increase the security of algorithm and reduces the correlation between adjacent pixels. Finally, by using the numerical simulation and the security analysis, the effectiveness of the encryption algorithm is verified, and the comparison results show the higher security of the design encryption algorithm.
... Many image protection methods have been proposed, such as image hiding technology, image watermarking technology, and image encryption technology [7][8][9][10][11]. Among these image protection techniques, image encryption is the most direct way, which converts the original plaintext information into a noisy image. ...
In this paper, a novel image encryption algorithm is proposed based on hyperchaotic two-dimensional sin-fractional-cos-fractional (2D-SFCF), called sin-fractional-cos-fractional image-encryption (SFCF-IE). The 2D-SFCF is constructed from two one-dimensional cosine fractional (1-DCFs), and it has a more complex chaotic behavior with a larger parameter space than one-dimensional chaotic systems. Compared with the two-dimensional (2D) chaotic system, the 2D-SFCF has a simple structure, and the parameter space in the chaotic state is continuous, which is beneficial to generating the keystream in the cryptosystem. Therefore, in the novel image encryption algorithm, we use the 2D-SFCF to generate the keystream of the cryptosystem. The encryption algorithm is a process of scrambling and diffusion. Different from common diffusion methods, the diffusion starting position of the SFCF-IE is randomly generated, enhancing the algorithm’s security. Simulation experiments show that the image encrypted by this algorithm has better distribution characteristics and can resist common attack methods.
This paper provides an in-depth discussion on the application of quaternion orthogonal Fourier-Mellin Moments (QOFMM) in the field of digital image processing, and proposes a novel method of factorial operation aiming to optimize its computational efficiency and accuracy. In addition, this paper focuses on the importance of zero-watermark technology in the field of information security. QOFMM is an advanced feature mention technique, which is particularly applicable to the field of digital image processing and information security. In this technique, the factorial operation plays a key role. However, traditional factorial computation methods may encounter efficiency bottlenecks when dealing with large data, thus affecting the overall performance. To address this issue, this study proposes an innovative method for factorial operation, which performs factorial operation by improving the radial basis function computation strategy, aiming to reduce the computational complexity and enhance the computational accuracy. To verify the effectiveness of the proposed method, we compare it with existing methods of factorial computation. The experimental results show that the new method significantly improves both processing speed and computational capability. Overall, this paper provides a new QOFMM optimization strategy, which not only improves the computational efficiency and accuracy but also brings a new research direction to the field of digital image processing and zero-watermarking technology.
In open networks, the geometric deformation and common image processing are common image manipulation modes, which pose a great challenge in robust watermarking. To improve the robustness of GRHFM‐based watermarking, a watermarking algorithm based on the fast GRHFM calculation method and ant colony optimization (ACO) based fractional parameter selection method is proposed. With the similarity between the discrete Fourier transform and GRHFM moment calculation, the algorithm utilizes fast Fourier transform to improve the GRHFM calculation accuracy and speed. To select the optimal GRHFM fractional parameter for watermarking algorithm, ACO is introduced to the fractional parameter adaptive selection method. Here, the fast Fourier transform‐based calculation method is combined with the adaptive parameter selection method to maximize the invisibility and robustness of watermarking. The experimental results indicate that the algorithm achieves higher robustness with the same payload and invisibility compared with other existing watermarking methods.
In moment-based watermarking schemes, the accuracy of the moments is crucial for constructing robust watermarking schemes. The robustness of the watermarking scheme relies heavily on the proper representation of the moments. Despite the importance, current theoretical research on accuracy is very limited in watermarking techniques. To this end, we propose a novel robust image watermarking scheme based on accurate polar harmonic Fourier moments (PHFMs). Specifically, the accurate PHFMs computation based on polar pixel tiling with nearest neighbor interpolation (PPTN) is designed. This computation is general and used for embedder and extractor. This ingenious design eliminates geometric and numerical integration errors and also avoids the distortion interaction caused by watermarks. Also, an improved quantization strategy is applied to the embedding process, and satisfactory imperceptibility is obtained. The watermark is extracted without the host image. The experimental results show the excellent robustness of the proposed watermarking scheme to common image processing attacks, geometric attacks, and some kinds of compound attacks. The proposed scheme is superior to the state-of-the-art image watermarking schemes.
With the advent of quantum computing, numerous efforts have been made to standardize post-quantum cryptosystems with the intention of (eventually) replacing Elliptic Curve Cryptography (ECC) and Rivets-Shamir-Adelman (RSA). A modified version of the traditional N-Th Degree Truncated Polynomial Ring (NTRU) cryptosystem called NTRU Prime has been developed to reduce the attack surface. In this paper, the Signcryption scheme was proposed, and it is most efficient than others since it reduces the complexity and runs the time of the code execution, and at the same time, provides a better security degree since it ensures the integrity of the sent message, confidentiality of the data, forward secrecy when using refreshed parameters for each session. Unforgeability to prevent the man-in-the-middle attack from being active or passive, and non-repudiation when the sender can’t deny the recently sent message. This study aims to create a novel NTRU cryptography algorithm system that takes advantage of the security features of curve fitting operations and the valuable characteristics of chaotic systems. The proposed algorithm combines the (NTRU Prime) and Shamir's Secret Sharing (SSS) features to improve the security of the NTRU encryption and key generation stages that rely on robust polynomial generation. Based on experimental results and a comparison of the time required for crucial exchange between NTRU-SSS and the original NTRU, this study shows a rise in complexity with a decrease in execution time in the case when compared to the original NTRU. It’s encouraging to see signs that the suggested changes to the NTRU work to increase accuracy and efficiency.
By introducing parameters with local information, several types of orthogonal moments have recently been developed for the extraction of local features in an image. But with the existing orthogonal moments, local features cannot be well-controlled with these parameters. The reason lies in that zeros distribution of these moments’ basis function cannot be well-adjusted by the introduced parameters. To overcome this obstacle, a new framework,
transformed orthogonal moment
(TOM), is set up. Most existing continuous orthogonal moments such as Zernike moments,
fractional-order orthogonal moments
(FOOMs), etc. are all special cases of TOM. To control the basis function’s zeros distribution, a novel local constructor is designed, and
local orthogonal moment
(LOM) is proposed. Zeros distribution of LOM’s basis function can be adjusted with parameters introduced by the designed local constructor. Consequently, locations, where local features extracted from by LOM, are more accurate than those by FOOMs. In comparison with Krawtchouk moments and Hahn moments etc., the range, where local features are extracted from by LOM, is order insensitive. Experimental results demonstrate that LOM can be utilized to extract local features in an image.
An asynchronous updating Boolean network is employed to simulate and analyze the gene expression of a particular tissue or species, revealing the life activity process from a system perspective to reveal the disease mechanism and treat the disease. Therefore, to ensure the safe transmission of the asynchronous updating Boolean network in the network, we designed an asynchronous updating Boolean network encryption algorithm based on chaos (ABNEA). First, a novel 2D chaotic system (2D-FPSM) is designed. This system has better performance than the classical 2D chaotic system. It is very suitable for cryptographic systems to generate key streams. Second, an encoding rule is designed to convert the asynchronous updating Boolean network to a Boolean matrix and propagate it on the network as an image. The receiver and sender jointly save the encoding rule. Last, to protect the safe propagation of the Boolean network matrix on the network, the method of synchronous scrambling-diffusion is adapted to encrypt the Boolean network matrix based on the 2D-FPSM. Simulation experiments and security analysis show that the average correlation of adjacent pixels of ciphertext are 0.0010, -0.0010, -0.0020, and the average information entropy is 7.9984. The ABNEA can complete the encryption tasks of asynchronously updating Boolean networks and exhibits good security characteristics.
An image encryption algorithm is proposed by combining chaotic system with semi-tensor product theory. First, the four-way diffusion is performed on the plaintext image with a random interpolation. To further destroy or eliminate the image structure features, the image pixels are split into the octal plane and confused by Josephs scrambling with a variable step. Finally, the ciphertext image is obtained by performing a semi-tensor product operation on an encryption matrix. In this algorithm, the selection of the positions in the chaotic sequence is highly correlated with the plaintext image, which ensures the security of the algorithm without affecting the encryption efficiency.
Although image encryption is developing rapidly, it lacks the pertinence of specific scenarios. This paper proposes a complementary embedding encryption strategy. The strategy firstly identifies the airport area, then replaces the optimal similar area and embeds the airport image into a random position through the complementary embedding algorithm. In the encryption stage, to generate a better key stream, we propose an improved sine cross coupled mapping lattice (ISCCML). Comprehensive performance analysis shows that ISCCML has a larger parameter space and better chaotic cryptographic properties. Furthermore, a fractal disordered matrix (FDM) with iterative and out-of-order properties is presented for the simultaneous scrambling diffusion of images. In particular, the encryption algorithm has generalization and is also suitable for ordinary image encryption. Our results indicate that the proposed scheme can avoid repeated encryption on the premise of ensuring the security of important information; at the same time, the security analysis shows that our algorithm has security, practicality and scalability.
In the modern block cipher, the substitution box (S-box) is a nonlinear constituent that plays a substantial role to create the confusion in ciphertext. S-boxes with low value of differential uniformity and high value of nonlinearity are considered more secure against cryptanalysis attacks. For the construction of 8×8 S-boxes, an efficient and novel scheme is presented in this paper. This scheme based on polynomial mapped and finite field which work only for even integers without multiple of 4 in the range (2-254). Firstly, we take a quadratic polynomial mapped for the construction of S-box from the newly designed map. To keep the S-box bijective, swap each missing entries with repeating entries after that we acquire the initial box. Secondly, to increase the randomness of initial S-box special permutations of symmetric group S
<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">256</sub>
used and generated the proposed S-box. Lastly, to examine the validity of the suggested S-box we used various tests such as nonlinearity (NL), bit independence criteria (BIC), strict avalanche criteria (SAC), differential uniformity (DU) and linear approximation probability (LAP) which all certify algebraic properties of S-box. Moreover, the features of newly constructed S-box compared with recent S-boxes from literature which show superior performance against intruders’ attacks. Further, S-box is utilized in image encryption scheme and apply MLC (majority logic criterion) and histogram analysis to examined the encryption quality. Our results shows that proposed S-box based encryption scheme is very good as compared to other encryption methods.
An effective error prediction algorithm is the key to improving the embedding performance of reversible data hiding schemes. In this paper, high-performance ridge regression predictor-based reversible data hiding (RDH) is proposed. The ridge regression predictor is an adaptive predictor that adds L2 regularisation to minimise the residual sum of squares between the prediction pixels and the target pixels. The L2 norm as a penalty function decreases the weights for the prediction coefficients of unimportant pixels. In other words, the ridge regression predictor limits prediction coefficients that have negative or no influence on predicting the target pixels (abnormal samples). The ridge regression predictor allows the prediction coefficients to be small, which avoids the overfitting problem and enhances tamper-resistance and generalisation ability. In addition, to increase the prediction accuracy of the ridge regression predictor, the proposed method employs small samples to obtain more accurate prediction values. The neighbouring pixels closest to the target pixels are selected as the training sets and supported sets during the prediction process. In summary, the ridge regression predictor can generate an error plane that is more suitable for embedding, thereby improving the embedding performance of RDH. Extensive experimental results also show that the proposed method is superior to the state-of-the-art RDH schemes in terms of prediction accuracy and embedding performance.
Here, a new set of fractional‐order moments, named fractional‐order generalized Laguerre moments (FGLM), is introduced. These proposed moments are defined on the Cartesian coordinate system and their basis functions are represented by the fractional‐order generalized Laguerre polynomials. Contrary to the classical Chebyshev, Legendre and Gegenbauer moments, which provide only global feature, our proposed FGLM have the ability to extract both global and local features. Moreover, a new set of rotation, scale and translation invariants of the FGLM, is derived and introduced for image classification and invariant pattern recognition. Just as important, we have presented a systematic parameter selection method for finding the optimal fractional parameter values with respect to pattern recognition applications. Finally, several recursive methods for reducing the computation time of our proposed invariants are also provided in this study. Therefore, to demonstrate the performance of the introduced fractional‐order moments and moment invariants, a number of experimental analysis are performed in terms of global and local features extraction, robustness to noise, invariance to geometric deformations, object recognition and computational speed. The presented theoretical and experimental results clearly show that the proposed fractional‐order moments and their corresponding invariants could be extremely useful in the field of image analysis.
Color face recognition has more attention recently since it considered one of the most popular biometric pattern recognitions. With a considerable development in multimedia technologies, finding a suitable color information extraction from color images becomes a hard problem. Several color face recognition methods have been developed. However, these methods still suffer from some limitations, such as increasing the number of extracted features, which leads to an increase in computational time. Besides, among those features some of them are redundant and irrelevant that will influence the quality of the recognition. Therefore, this paper presents a novel color face recognition method that depends on a new family of fractional-order orthogonal functions, which is called orthogonal fractional-order exponent functions. Then, using these functions as the basis functions of novel multi-channel orthogonal fractional-order exponent moments (FrMEMs), these novel descriptors are defined in polar coordinates over the unit circle and have many characteristics. A set of experimental series are performed using a set of well-known color face recognition and compared with other CFR techniques. Besides, a group of feature selection methods with different classifiers used to evaluate the number of extracted features is suitable or needs to be enhanced. Experimental results illustrate that the proposed method based on FrMEMs outperforms other CFR methods. As well as, the recognition rate doesn't influence by reducing the number of features using different FS methods.
Exponential moments (EMs) are important radial orthogonal moments, which have good image description ability and have less information redundancy compared with other orthogonal moments. Therefore, it has been used in various fields of image processing in recent years. However, EMs can only take integer order, which limits their reconstruction and antinoising attack performances. The promotion of fractional-order exponential moments (FrEMs) effectively alleviates the numerical instability problem of EMs; however, the numerical integration errors generated by the traditional calculation methods of FrEMs still affect the accuracy of FrEMs. Therefore, the Gaussian numerical integration (GNI) is used in this paper to propose an accurate calculation method of FrEMs, which effectively alleviates the numerical integration error. Extensive experiments are carried out in this paper to prove that the GNI method can significantly improve the performance of FrEMs in many aspects.
In this paper, a chaotic image encryption algorithm based on the matrix semi-tensor product (STP) with a compound secret key is designed. First, a new scrambling method is designed. The pixels of the initial plaintext image are randomly divided into four blocks. The pixels in each block are then subjected to different numbers of rounds of Arnold transformation, and the four blocks are combined to generate a scrambled image. Then, a compound secret key is designed. A set of pseudosecret keys is given and filtered through a synchronously updating Boolean network to generate the real secret key. This secret key is used as the initial value of the mixed linear-nonlinear coupled map lattice (MLNCML) system to generate a chaotic sequence. Finally, the STP operation is applied to the chaotic sequences and the scrambled image to generate an encrypted image. Compared with other encryption algorithms, the algorithm proposed in this paper is more secure and effective, and it is also suitable for color image encryption.
This article presents a new series of invariant moments, called Fractional-order Generalized Laguerre Moment Invariants (FGLMI), based on Fractional-order Generalized Laguerre polynomials (FGLPs). To begin, we provide the relations and the properties necessary to define the fractional-order generalized Laguerre moments. Then, we present the theoretical framework to derive invariants from fractional-order moments with respect to the change in orientation, size and position based on the algebraic relationships between FGLM and fractional-order geometric moments. In addition, a fast and precise algorithm has been proposed for the calculation of FGLM in order to speed up the calculation time and ensure the numerical stability of the invariant moments. Numerical experiments are carried out to demonstrate the efficiency of FGLM and their proposed invariants compared to existing methods, with regard to the reconstruction of 2D and 3D images, the computation time, the global entity extraction capacity and image localization, invariability property and 2D / 3D image classification performance on different 2D and 3D image databases. The theoretical and experimental results presented clearly show the efficiency of the descriptors proposed for the representation and classification of 2D and 3D images by other types of orthogonal moments.
Orthogonal moments are used to represent digital images with minimum redundancy. Orthogonal moments with fractional-orders show better capabilities in digital image analysis than integer-order moments. In this work, the authors present new fractional-order shifted Gegenbauer polynomials. These new polynomials are used to defined a novel set of orthogonal fractional-order shifted Gegenbauer moments (FrSGMs). The proposed method is applied in gray-scale image analysis and recognition. The invariances to rotation, scaling and translation (RST), are achieved using invariant fractional-order geometric moments. Experiments are conducted to evaluate the proposed FrSGMs and compare with the classical orthogonal integer-order Gegenbauer moments (GMs) and the existing orthogonal fractional-order moments. The new FrSGMs outperformed GMs and the existing orthogonal fractional-order moments in terms of image recognition and reconstruction, RST invariance, and robustness to noise.
The classical radial harmonic Fourier moments (RHFMs) and the quaternion radial harmonic Fourier moments (QRHFMs) are gray-scale and color image descriptors. The radial harmonic functions with integer orders are not able to extract fine features from the input images. In this paper, the authors derived novel fractional-order radial harmonic functions in polar coordinates. The obtained functions are used to defined novel multi-channel fractional-order radialharmonicmoments(FrMRHFMs)forcolorimagedescriptionandanalysis.Theinvariantsto geometric transformations for these new moments are derived. A theoretical comparison between FrMRHFMs and QRHFMs is performed from the aspects of kernel function and the spectrum analysis. Numerical simulation is carried out to test these new moments in terms of image reconstruction capabilities, invariance to the similarity transformations, color image recognition and the CPU computational times. yellowThe obtained theoretical and numerical results clearly show that the proposed FrMRHFMs is superior to the QRHFMs and the existing fractional-order orthogonal moments.
This paper studies chaotic image encryption technology and an application of matrix semi-tensor product theory, and a Boolean network encryption algorithm for a synchronous update process is proposed. A 2D-LASM chaotic system is used to generate a random key stream. First, a Boolean network is coded, and a Boolean matrix is generated. If necessary, the Boolean network matrix is diffused in one round so that the Boolean matrix can be saved in the form of an image. Then, three random position scramblings are used to scramble the plaintext image. Finally, using a matrix semi-tensor product technique to generate an encrypted image in a second round of diffusion, a new Boolean network can be generated by encoding the encrypted image. In secure communications, users can choose to implement an image encryption transmission or a Boolean network encryption transmission according to their own needs. Compared with other algorithms, this algorithm exhibits good security characteristics.
Orthogonal moments are the projections of image functions onto particular kernel functions. They play vital role in digital image feature extraction being rotation, scaling, translation invariant, robust to image noise and contain minimal information redundancy. These moments are derived from statistically independent orthogonal polynomials which can be continuous or discrete. Most of the modern researches have explored integer-order orthogonal moments, but fractional-order moments are in fact superclass of integer order and more efficient but underrated. This paper proposes fractional-order Zernike moments (FZM) along with SVM to recognize grape leaf diseases. Comparative analysis with integer-order Zernike moments along with other feature selection methods has been explored. FZM–SVM-based technique outperforms other state-of-art techniques yielding \(97.34\%\) at order 30.
In this paper, fractional Zernike moments (FrZMs) for complex signals are generalized to fractional quaternion Zernike moments (FrQZMs) for quaternion signal processing in a holistic manner by the quaternion algebra. We first present the definition of FrQZMs and an efficient implementation algorithm for speeding up the computation of FrQZMs through FrZMs of each component of the quaternion signal. The performance of the proposed FrQZMs is evaluated by considering robust color image copymove forgery detection. The proposed robust copy-move forgery detection algorithm considers the FrQZMs as a feature and a modified PatchMatch algorithm as a feature matching algorithm. Experimental results on two publicly available datasets (FAU and GRIP dataset) have demonstrated that the proposed FrQZMsbased algorithm can achieve an overall better performance than the state-of-the-art algorithms, especially in additional operation case.
Motion-compensated frame-interpolation (MCFI), a frame interpolation technique to increase the motion continuity of low frame-rate video, can be utilized by counterfeiters for faking high bitrate video or splicing videos with different frame-rates. For existing MCFI detectors, their performances are degraded under real-world scenarios such as H.264/AVC compression, noise or blur. To address this issue, a robust MCFI detector is proposed to locate interpolated frames. By analyzing the distribution of residual energies within interpolated frames, we observe that there exist strong correlations between artifact regions and high residual energies. Thus, an artifact indicated map (AIM) is introduced to select candidate artifact regions. Then, Tchebichef moments (TMs) are exploited to characterize the blurring effects or deformed structures among these regions. Specifically, the mean value of absolute high-order TMs of selected regions is used to model these temporal inconsistencies. Finally, a sliding window is adopted to locate interpolated frames, which are further refined by three post-processing operations. Chrominance information is also integrated with luminance information for robust identification of interpolated frames. Extensive experimental results show that compared with the state-of-the-art MCFI detectors, the proposed approach is more robust for compressed videos under various real-world scenarios.
Invariant harmonic transforms based on the fractional Fourier transform are proposed in this paper. The so-called fractional polar harmonic transforms (FrPHTs) with the order parameter α are first defined, which are generalizations of the PHTs. Second, a watermarking scheme is presented and discussed in detail associated with the newly defined FrPHTs. Finally, the simulations are clearly performed to verify the well capabilities of the transforms on image watermarking, which show that the proposed transforms with suitable parameters outperform the traditional PHTs. In addition, the experimental results also demonstrate that the order parameter α has an effect on the performance of FrPHTs in the image watermarking robustness and can improve the watermarking safety.
Blur is a key determinant in the perception of image quality. Generally, blur causes spread of edges, which leads to shape changes in images. Discrete orthogonal moments have been widely studied as effective shape descriptors. Intuitively, blur can be represented using discrete moments since noticeable blur affects the magnitudes of moments of an image. With this consideration, this paper presents a blind image blur evaluation algorithm based on discrete Tchebichef moments. The gradient of a blurred image is first computed to account for the shape, which is more effective for blur representation. Then the gradient image is divided into equal-size blocks and the Tchebichef moments are calculated to characterize image shape. The energy of a block is computed as the sum of squared non-DC moment values. Finally, the proposed image blur score is defined as the variance-normalized moment energy, which is computed with the guidance of a visual saliency model to adapt to the characteristic of human visual system. The performance of the proposed method is evaluated on four public image quality databases. The experimental results demonstrate that our method can produce blur scores highly consistent with subjective evaluations. It also outperforms the state-of-the-art image blur metrics and several general-purpose no-reference quality metrics.
loss, and redundancy.2 From the uniqueness theorem of moments, an image is uniquely determined by its geometrical moments of all orders. Low-order moments contain less information about image detail. High-order moments are vulner- able to noise. Interesting questions are how a finite number of moments can work well to describe an im- age for a particular application and what is gained by inclusion of higher-order moments. The answers to these questions can be found with the use of the or- thogonal moments.3 Teh and Chin recently evaluated various types of image moments, including geometrical moments, Legendre moments, Zernike moments, Pseudo- Zernike moments, Fourier-Mellin moments, and complex moments, in terms of noise sensitivity, information redun- dancy, and capability of image description. They found that Zernike moments have the best overall performance.4 Zernike moments (ZM's) play a fundamental role in the theories of optical aberration and diffraction. Teague proposed ZM's for generating the moment invariants. 5 ZM's are orthogonal and rotation invariant. But, when they are used for scale-invariant pattern recognition, ZM's have difficulty in describing images of small size, as we show in this paper. Bhatia and Wolf pointed out that there exist an infinite number of complete sets of polynomials that are rotation invariant in form and arc orthogonal for the interior of the unit circle.6 In this paper we introduce orthogonal Fourier-Mellin moments (OFMM's), based on a new set of radial polynomials. The new moments belong to general- ized ZM's and to orthogonalized complex moments. We show that OFMM's have better performance than ZM's in terms of image description and noise sensitivity. In Section 2 we introduce OFMM's and show their relations to ZM's and to complex moments. In Section 3 we com- pare the performance of OFMM's and ZM's. In Section 4 we present an experiment of rotation, scale, intensity, and shift-invariant pattern recognition, using OFMM's.
Robust and discriminative image representation is a long-lasting battle in the computer vision and pattern recognition. Moment-based image representation model is effective in satisfying the core conditions of semantic description, due to its geometric invariance and independence. However, moment-based descriptors suffer from a contradiction between the robustness and discriminability, which limits the further improvement of description quality. In this paper, a set of generic moments along with a novel representation framework are proposed to mitigate this troublesome contradiction. We first define a new set of orthogonal moments, named Fractional-order Jacobi-Fourier Moments (FJFM), which is characterized by the generic nature and time-frequency analysis capability. We then develop a new framework to improve both the robustness and discriminability of image representation, called Mixed Low-order Moment Feature (MLMF), by fully exploiting the time-frequency property of FJFM. Extensive experimental results and a real-world application are provided to demonstrate the superior performance of our FJFM-based MLMF, with respect to robustness and discriminability.
Due to their strong image description ability, in recent years, quaternion exponential moments (QEMs) have attracted wide attention from relevant researchers. However, there is a numerical instability problem with QEMs because they can only take integer orders, and this problem restricts the performance of QEMs in image reconstruction and noise resistance. In this paper, the concept of fractional order is introduced and incorporated into exponential moments (EMs) and fractional-order exponential moments (FrEMs) are proposed; then the FrEMs are extended to fractional-order quaternion exponential moments (FrQEMs) that are suitable for color images and have better performance than QEMs in noise resistance and image reconstruction; subsequently, it is proved that FrQEMs are invariant to rotation; and finally, the properties of FrQEMs are experimentally analyzed and FrQEMs are used for object recognition. The experimental results show that FrQEMs have very excellent performance in color image reconstruction, high noise resistance, good rotation invariance and object recognition in color images.
This article creatively proposes a class of sorting matrices with fractal characteristics, named the fractal sorting matrix (FSM), and introduces its iterative calculation method. The FSM is irregular, self-similar and infinitely iterative. Notably, scrambling images or information based on this new cluster of matrices can effectively improve encryption algorithm security. Then, the article presents a new method of global pixel diffusion with two chaotic sequences, which offers good security and high encryption efficiency. Based on the FSM and global chaotic pixel diffusion, this paper constructs a more efficient and secure chaotic image encryption algorithm than other approaches. According to experimental comparison, the proposed algorithm is faster and has a higher pass rate associated with the local Shannon entropy. The data in the antidifferential attack test are closer to the theoretical values and smaller in data fluctuation, and the images obtained from the cropping and noise attacks are clearer. Therefore, the proposed algorithm shows better security and resistance to various attacks.
There are two main issues in RGB-D salient object detection: (1) how to effectively integrate the complementarity from the cross-modal RGB-D data; (2) how to prevent the contamination effect from the unreliable depth map. In fact, these two problems are linked and intertwined, but the previous methods tend to focus only on the first problem and ignore the consideration of depth map quality, which may yield the model fall into the sub-optimal state. In this paper, we address these two issues in a holistic model synergistically, and propose a novel network named DPANet to explicitly model the potentiality of the depth map and effectively integrate the cross-modal complementarity. By introducing the depth potentiality perception, the network can perceive the potentiality of depth information in a learning-based manner, and guide the fusion process of two modal data to prevent the contamination occurred. The gated multi-modality attention module in the fusion process exploits the attention mechanism with a gate controller to capture long-range dependencies from a cross-modal perspective. Experimental results compared with 16 state-of-the-art methods on 8 datasets demonstrate the validity of the proposed approach both quantitatively and qualitatively.
In order to improve the performance of the Meixner moments, we suggest in this article a new set of Fractional Discrete Meixner Polynomials (FrDMPs), a sort of a generalization of the traditional whole order. Firstly, we introduce the necessary algebraic derivatives of FrDMPs using the spectral decomposition of Discrete Meixner Polynomials (DMPs) for any order without numerical fluctuation and always preserving the property of orthogonality thanks to the algorithm of the Gram-Schmidt process. Then, we determine the eigenvalues and the corresponding multiplicity of the Meixner transform matrix. An image encryption and decryption method was proposed based on jigsaw transform and generation of Fractional Discrete Meixner Moments (FrDMMs), in which the image is broken up into bit planes. Each bit plane undergoes a jigsaw transform is divided into blocks and encrypted. The transformed bit planes are combined together and then encrypted using random phase masks and fractional discrete Meixner moments. In addition, we introduce a new encryption and decryption scheme based on the proposed FrDMMs. This scheme has a good encryption effect because the fractional parameters used as key to the encrypted data. Experimental results show that the encryption scheme is sensitive to keys, it is resist a variety of attacks, and decrypted images are almost non-distored, which indicate excellent encryption effect, sufficient security and robustness of the method.
Although zero-watermarking can provide an effective and distortion-free scheme for image copyright protection, its robustness and discriminability do not meet expectations in existing methods. Some cannot resist effectively geometric attacks, others do not consider the discriminability and equalization. For that reason, this paper proposes a robust and distinguishable color image zero-watermarking algorithm based on polar harmonic transforms (PHTs) and compound chaotic map. In the proposed algorithm, firstly three PHTs moments of an image are computed simultaneously and accurate moments are selected for the robustness. Then, content-based binary feature sequence is acquired by judging the relation between magnitudes of adjacent moments for the discriminability. Finally, compound chaotic map is employed to encrypt copyright logo for ensuring security and scramble binary feature sequence for improving the equalization. Experimental results show that the proposed zero-watermarking algorithm has good equalization and discriminability, and an advantage in robustness compared with other zero-watermarking and traditional watermarking.
Orthogonal moments enable computer-based systems to discriminate between similar objects. Mathematicians proved that the orthogonal polynomials of fractional-orders outperformed their corresponding counterparts in representing the fine details of a given function. In this work, novel orthogonal fractional-order Legendre-Fourier moments are proposed for pattern recognition applications. The basis functions of these moments are defined and the essential mathematical equations for the recurrence relations, orthogonality and the similarity transformations (rotation and scaling) are derived. The proposed new fractional-order moments are tested where their performance is compared with the existing orthogonal quaternion, multi-channel and fractional moments. New descriptors were found to be superior to the existing ones in terms of accuracy, stability, noise resistance, invariance to similarity transformations, recognition rates and computational times.
Orthogonal moments were successfully used to extract features from gray-scale and color images. Recently, scientists show that orthogonal moments of fractional-orders have better capabilities to extract the fine features. In this work, novel orthogonal generic fractional-order Jacobi-Fourier moments are proposed for image processing, pattern recognition and computer vision applications. Novel orthogonal Jacobi-Fourier polynomials of fractional-order were derived and defined in polar coordinates. The mathematical equation for orthogonality was formulated and a three-term recurrence relation was derived for easier computation of these polynomials. The proposed orthogonal fractional-order Jacobi-Fourier moments are generic where other orthogonal fractional-order moments are derived as special cases by choosing different values of the controlling parameters. The invariance to geometric transformations, rotation, scaling and translations, is proved where the required mathematical formulae for these invariances are presented. The proposed new fractional-order moments were tested using different datasets of gray-scale and color images in terms of image reconstruction, invariance to geometric transformations, robustness to noise, image recognition, and computational times where their performance were compared with the recent existing orthogonal integer- and fractional-order moments. The proposed generic fractional-order Jacobi-Fourier moments outperformed all existing orthogonal moments.
A novel set of fractional orthogonal polar harmonic transforms for gray-scale and color image analysis are presented in this paper. These transforms are divided into two groups. The first group contains fractional polar complex exponential transforms (FrPCETs), fractional polar cosine transforms (FrPCTs), and fractional polar sine transforms (FrPSTs) for gray-scale images. The second group contains the fractional quaternion polar complex exponential transforms (FrQPCETs), fractional quaternion polar cosine transforms (FrQPCTs), and fractional quaternion polar sine transforms (FrQPSTs) for color images. All mathematical formulae for the basis functions, orthogonality relations and reconstruction forms are derived and their validity are proved. The required mathematical forms for invariance to rotation, scaling and translation (RST) are derived. A series of experiments is performed to test the validity of the proposed fractional polar harmonic transforms (FrPHTs) and the fractional quaternion polar harmonic transforms (FrQPHTs). The performances of the proposed FrPHTs and FrQPHTs are outperformed the classical polar harmonic transforms, the quaternion polar harmonic transforms and the existing fractional orthogonal transforms in terms of accuracy and numerical stability, digital image reconstruction, RST invariances, robustness to noise and computational efficiency.
Discrete Tchebyshev moments (DTMs), as a kind of typical discrete orthogonal moments, have been widely used in image analysis. However, the order of DTMs is restricted to an integer, and the fractional versions of DTMs have not been investigated. A novel framework for deriving fractional order DTMs (FrDTMs) by the eigen-decomposition of kernel matrices is proposed in this paper, and some properties of the proposed FrDTMs are analyzed. Two applications, i.e., image encryption and image watermarking, are investigated to validate the superiorities of the proposed FrDTMs.
Depth information has been demonstrated to be useful for saliency detection. However, the existing methods for RGBD saliency detection mainly focus on designing straightforward and comprehensive models, while ignoring the transferable ability of the existing RGB saliency detection models. In this article, we propose a novel depth-guided transformation model (DTM) going from RGB saliency to RGBD saliency. The proposed model includes three components, that is: 1) multilevel RGBD saliency initialization; 2) depth-guided saliency refinement; and 3) saliency optimization with depth constraints. The explicit depth feature is first utilized in the multilevel RGBD saliency model to initialize the RGBD saliency by combining the global compactness saliency cue and local geodesic saliency cue. The depth-guided saliency refinement is used to further highlight the salient objects and suppress the background regions by introducing the prior depth domain knowledge and prior refined depth shape. Benefiting from the consistency of the entire object in the depth map, we formulate an optimization model to attain more consistent and accurate saliency results via an energy function, which integrates the unary data term, color smooth term, and depth consistency term. Experiments on three public RGBD saliency detection benchmarks demonstrate the effectiveness and performance improvement of the proposed DTM from RGB to RGBD saliency.
Current blind image quality assessment (BIQA) algorithms are mainly designed for natural images. Unfortunately, cartoon and cartoon-like images are quite different from natural images. Hence, recent BIQA methods are not very robust to cartoon images. In this paper, we propose a specific BIQA algorithm designed for cartoon images, which consists of the following terms. First, a cartoon image is divided into edge areas and nonedge areas via a Tchebichef moment (TM)-based process. Second, a multiorder sharpness statistic term is used to measure the quality of the edges, and a sharpness statistic prior model of high-quality (HQ) cartoon images is built. Third, a local encoding statistic term is adopted to describe the textural complexity in the nonedge areas, and a texture statistic prior model is also established. Experimental results on cartoon image datasets demonstrate that the proposed method can accurately evaluate the visual quality of cartoon images and is more suitable for cartoon scenarios than some traditional BIQA algorithms.
To ensure security, image encryption algorithms generally include two stages: permutation and diffusion. The traditional image permutation algorithms include the sort-based permutation algorithm, Arnold-based permutation algorithm, Baker-based permutation algorithm and the cyclic shift permutation algorithm, etc. However, these algorithms have the disadvantages of either high time complexity or poor permutation performance. Therefore, in combination with cyclic shift and sorting, this paper proposes a permutation algorithm that can not only guarantees good permutation performance but also guarantee low time and space complexity. Most importantly, this paper proposes a parallel diffusion method. This method ensures the parallelism of diffusion to the utmost extent and achieves a qualitative improvement in efficiency over traditional streaming diffusion methods. Finally, combined with the proposed permutation and diffusion, the paper proposes a computational model for parallel image encryption algorithms.
With the increasingly widespread use of medical images in medical institutions and networks, the copyright protection of medical images has become increasingly urgent. Since traditional embedded watermarking technology degrades the quality of the original images, it is not suitable for medical images. In addition, most medical watermarking algorithms are aimed at grayscale images; therefore, a smaller number of color medical image watermarking algorithms are available. In this paper, we propose a lossless watermarking scheme for color medical image copyright protection based on a chaotic system and quaternion polar harmonic transforms (QPHTs), which is a quaternion orthogonal moment method. In watermark embedding, we compute the QPHTs for the original color medical image and select accurate coefficients to construct a zero-watermark image. Then, the zero-watermark image is stored in the intellectual property right (IPR) database. Experimental results show that the proposed scheme is robust to geometric attacks and common attacks and that it has better performance than similar lossless watermarking schemes. In addition, this paper details the selection of accurate coefficients for QPHTs and compares stability with different choices of unit pure quaternions.
In this paper, we present a new set of fractional-order orthogonal moments, named Fractional-order Chebyshev Moments (FCM). We initially introduce the necessary relations and properties to define the FCM in the Cartesian coordinates. Then, we provide the theoretical framework to construct the Fractional-order Chebyshev Moment Invariants (FCMI), which are invariants with respect to rotation, scaling and translation transforms. In addition, we devoted a substantial attention to enhance their computational time and numerical accuracy. Consequently, the numerical experiments are carried out to demonstrate the validity of the introduced fractional-order moments and moment invariants in comparison with the classical methods, with regard to image representation capability and object recognition accuracy on several publicly available databases. The presented theoretical and experimental results demonstrate the efficiency and the superiority of the proposed method.
In this paper, a novel forensics scheme for color image is proposed in color quaternion wavelet transform (CQWT) domain. Compared to discrete wavelet transform (DWT), contourlet wavelet transform (CWT) and local binary patterns (LBP), CQWT processes a color image as a unit and so it can provide more forensics information to identify the photograph (PG) and computer generated (CG) images by considering the quaternion magnitude and phase measures. Meanwhile, two novel quaternion central moments for color images, i.e. quaternion skewness and kurtosis are proposed to extract forensics features. In the condition of the same statistical model as Farid’s, the CQWT can boost the performance of existing identification models. Compared with Farid’s model and Li’s model in 7500 PG and 7500 CG, the quaternion statistical features show a better classification performance. Results in the comparative experiments show that the classification accuracy of the CQWT improves by 19% more than Farid’s, and the quaternion features approximately improve by 2% more than the traditional.
With the development and popularization of computer network technology, the copyright protection of stereo images is a serious problem to be solved. Based on ternary number theory and radial harmonic Fourier moments (RHFM), ternary radial harmonic Fourier moments (TRHFM) is proposed to deal with stereo images in a holistic manner, and based on this moment, this paper proposes a robust stereo image zero-watermarking algorithm. We first compute the TRHFM of the original stereo image, and we randomly select TRHFMs using logistic mapping; then, we obtain a binary feature image using the magnitudes of the selected TRHFMs, and finally, we apply a bitwise exclusive-or operation on permuted logo image and binary feature image to obtain the zero-watermark image. Experimental results indicate that the proposed stereo image zero-watermarking algorithm is strongly robust to various asymmetric and symmetric attacks and has superiority compared with other zero-watermarking algorithms.
This paper proposes quaternion polar harmonic Fourier moments (QPHFM) for color image processing and analyzes the properties of QPHFM. After extending Chebyshev-Fourier moments (CHFM) to quaternion Chebyshev-Fourier moments (QCHFM), comparison experiments, including image reconstruction and color image object recognition, on the performance of QPHFM and quaternion Zernike moments (QZM), quaternion pseudo-Zernike moments (QPZM), quaternion orthogonal Fourier-Mellin moments (QOFMM), QCHFM, and quaternion radial harmonic Fourier moments (QRHFM) are carried out. Experimental results show QPHFM can achieve an ideal performance in image reconstruction and invariant object recognition in noise-free and noisy conditions. In addition, this paper discusses the importance of phase information of quaternion orthogonal moments in image reconstruction.
This paper proposes a novel fractional transform, denoted as the fractional Krawtchouk transform (FrKT), a generalization of the Krawtchouk transform. The derivation of the FrKT uses the eigenvalue decomposition method. We determine the eigenvalues and the corresponding multiplicity of the Krawtchouk transform matrix. Moreover, the orthonormal eigenvectors of the transform matrix are derived. For validation purpose only and as a first illustration of the interest of FrKT, a watermarking example was chosen. Experimental results show that better watermark robustness and imperceptibility are achieved by adjusting the fractional orders in the FrKT.
Orthogonal moments play an important role in image analysis and other similar applications. However, existing orthogonal moments are restricted to integer order, and little investigation of non-integer order orthogonal moments has been conducted to date. In this paper, a general framework of real-order orthogonal moments, also known as fractional-order orthogonal moments, is proposed. In this general framework, fractional-order orthogonal moments can be defined in Cartesian and polar coordinate systems. Shifted Legendre polynomials are implemented in this paper to investigate the properties of fractional-order orthogonal moments. A series of experiments are performed, which demonstrate that fractional-order orthogonal moments are not only capable of region-of-interest (ROI) feature extraction but also have potential for image reconstruction and face recognition and have high noise robustness in invariant image recognition.
In this paper, we generalize the orthogonal Fourier-Mellin moments (OFMMs) to the fractional orthogonal Fourier-Mellin moments (FOFMMs), which are based on the fractional radial polynomials. We propose a new method to construct FOFMMs by using a continuous parameter \( t \) \( \left( {t > 0} \right) \). The fractional radial polynomials of FOFMMs have the same number of zeros as OFMMs with the same degree. But the zeros of FOFMMs polynomial are more uniformly distributed than which of OFMMs and the first zero is closer to the origin. A recursive method is also given to reduce computation time and improve numerical stability. Experimental results show that the proposed FOFMMs have better performance.
In order to protect the copyright of stereoscopic images in the condition of the image quality, a zero-watermarking stereoscopic image algorithm is presented based on hyperchaotic system. In the proposed algorithm, disparity zero-watermark is constructed according to the stability of disparity between low frequency bands of wavelet decomposition of the left and the right views and direct coefficients of discrete cosine transform; in the process of zero-watermark construction, the zero-watermark position mapping according to the features of the sensitivity of hyperchaotic discrete system initial value, ampleness of parameter key space and complexity of dynamic behavior, enhances the security of algorithm. The relationship between security and watermark capacity is also analyzed. Experimental results show that the proposed algorithm is strong robust to noise, filtering, compression, and the shearing of asymmetrical and symmetrical attacks.
In order to protect the copyright of stereoscopic images in the condition of the image quality, a zero-watermarking stereoscopic image algorithm is presented based on hyperchaotic system. In the proposed algorithm, disparity zero-watermark is constructed according to the stability of disparity between low frequency bands of wavelet decomposition of the left and the right views and direct coefficients of discrete cosine transform; in the process of zero-watermark construction, the zero-watermark position mapping according to the features of the sensitivity of hyperchaotic discrete system initial value, ampleness of parameter key space and complexity of dynamic behavior, enhances the security of algorithm. The relationship between security and watermark capacity is also analyzed. Experimental results show that the proposed algorithm is strong robust to noise, filtering, compression, and the shearing of asymmetrical and symmetrical attacks.
In this paper, a robust watermarking scheme based on orthogonal Fourier-Mellin moments and chaotic map is introduced, which achieves copyright authentication for double images simultaneously. The proposed scheme consists of an ownership registration phase and a verification phase. Compared to the congeneric schemes, the new scheme achieves a high level security and saves storage space. Firstly, two images are combined into a single-channel architecture, then the feature invariants derived from orthogonal Fourier-Mellin moments are computed and utilized to construct a binary feature image. Together with the watermark, they are scrambled by chaotic map and subsequently used for generating the verification image. Experimental results demonstrate the validity and security of the proposed scheme as well as its robustness against different attacks.
Fourier transforms are a fundamental tool in signal and image processing, yet, until recently, there was no definition of a Fourier transform applicable to color images in a holistic manner. In this paper, hypercomplex numbers, specifically quaternions, are used to define a Fourier transform applicable to color images. The properties of the transform are developed, and it is shown that the transform may be computed using two standard complex fast Fourier transforms. The resulting spectrum is explained in terms of familiar phase and modulus concepts, and a new concept of hypercomplex axis. A method for visualizing the spectrum using color graphics is also presented. Finally, a convolution operational formula in the spectral domain is discussed
Orthogonal multi-distorted invariant Complex Exponent Moments (CEMs) are proposed. A fast and accurate 2-D Fast Fourier Transform (FFT) algorithm is used to calculate CEMs. Theoretical analysis is presented to demonstrate the multi-distorted invariant property of CEMs. The proposed method is applied in the pattern recognition of human faces, English letters and Chinese characters. Experimental results show that CEMs have higher quality and lower computational complexity than RHFMs in image reconstruction and pattern recognition.
In this paper, we propose a new set of orthogonal moments based on Exponent functions, named Exponent-Fourier moments (EFMs), which are suitable for image analysis and rotation invariant pattern recognition. Compared with Zernike polynomials of the same degree, the new radial functions have more zeros, and these zeros are evenly distributed, this property make EFMs have strong ability in describing image. Unlike Zernike moments, the kernel of computation of EFMs is extremely simple. Theoretical and experimental results show that Exponent-Fourier moments perform very well in terms of image reconstruction capability and invariant recognition accuracy in noise-free, noisy and smooth distortion conditions. The Exponent-Fourier moments can be thought of as generalized orthogonal complex moments.
Moments extraction from high resolution images in real time may require a large amount of hardware resources. Using a direct method may involve a critically high operating frequency. This paper presents two improved digital-filter based moment accelerators, as exemplified by a Tchebichef moments computation engine, to introduce features that contribute to an area-efficient and timing-efficient accelerator design. The design of the accelerators invariably consists of two on-chip units: the digital filter and the matrix multiplication units. Among the features introduced are: a data-shifting means, a filter load distribution method, a reduced set of column filters, sectioned left shifters, a double-line buffer, time-multiplexed and pipelined matrix multiplication sections, and multichip amenable features. A total of 98 frames of test data from high definition videos, real and synthetic images are used in the functional tests. The single-chip field-programmable gate array implementation results show the successful realizations of accelerators capable of moment computations of (31, 31) orders, at 50 frames of 1920 $\,\times\,$1080 8-bit pixels per second, and (63, 63) orders, at 30 frames of 512$\,\times\,$512 pixels per second. These performances have exceeded that of existing multichip and multiplatform designs.
Previous optical implementations of the two-dimensional fractional Fourier transform have assumed identical transform orders in both dimensions. We let the orders in the two orthogonal dimensions to be different and present general design formulae for optically implementing such transforms. This design formulae allows us to specify the two orders and the input, output scale parameters simultaneously.
Invariant combinations of moments of arbitrary order are defined. Application to a vehicle image shows that a reconstructed image having <10% error may be obtained by using invariants formed from moments uop to order eight.
Two-dimensional image moments with respect to Zernike polynomials are defined, and it is shown how to construct an arbitrarily large number of independent, algebraic combinations of Zernike moments that are invariant to image translation, orientation, and size. This approach is contrasted with the usual method of moments. The general problem of two-dimensional pattern recognition and three-dimensional object recognition is discussed within this framework. A unique reconstruction of an image in either real space or Fourier space is given in terms of a finite number of moments. Examples of applications of the method are given. A coding scheme for image storage and retrieval is discussed.
Stereo correspondence methods rely on matching costs for computing the similarity of image locations. In this pa- per we evaluate the insensitivity of different matching costs with respect to radiometric variations of the input images. We consider both pixel-based and window-based variants and measure their performance in the presence of global intensity changes (e.g., due to gain and exposure differ- ences), local intensity changes (e.g., due to vignetting, non- Lambertian surfaces, and varying lighting), and noise. Us- ing existing stereo datasets with ground-truth disparities as well as six new datasets taken under controlled changes of exposure and lighting, we evaluate the different costs with a local, a semi-global, and a global stereo method.