Harmonic Moments Research Articles

Specificity of manifestation of nonlinearities for angular oscillations of the reservoir with liquid.

Theproblemabouttransient modes of motion of acylindricalreservoirwiththeliquidwithafreesurfaceon a pendulum suspension under short-time moment pulse applies to reservoir walls is under consideration. The problem is considered in nonlinear combined statement. It was ascertained that manifestation of internal mechanisms of nonlinear interaction between normal modes of oscillations of a liquid differs considerably from the case of harmonic moment disturbance on the resonant frequency. For advanced studying the nature of these differences we study problems about harmonic disturbance of oscillations for the system under the moment with a frequency, which is not resonant and immediately resonant disturbance.

Distribution reconstruction and reliability assessment of complex LSFs via an adaptive Non-parametric Density Estimation Method

Complex limit state functions (LSFs), often characterized by strong nonlinearity, non-smoothness, or discontinuity, pose challenges for structural reliability analysis in engineering practices. Conventional methods for uncertainty propagation and reliability assessment may struggle to handle these issues effectively. This paper introduces a novel approach to adaptively reconstruct the unknown distributions of complex LSFs. The Non-parametric Density Estimation Method based on Harmonic Transform (NDEM-HT) is employed as the tool for this purpose. An adaptive strategy is then proposed to determine the number of harmonic moments required in NDEM-HT for achieving high accuracy. Specifically, the Adaptive Kernel Density Estimation (AKDE) method is also adopted to provide an initial estimation of the rough distribution. Subsequently, the optimal number of harmonic moments is determined by minimizing the relative entropy between the distributions obtained by AKDE and NDEM-HT. The efficacy of the proposed method is demonstrated through five numerical examples, considering various types of complex LSFs. Comparative results are also provided employing MCS along with both conventional and state-of-the-art methods.

Harmonic Moments for Supercritical Multi-type Galton–Watson Processes

Harmonic Moments for Supercritical Multi-type Galton–Watson Processes

From Simple to Complex Scenes: Learning Robust Feature Representations for Accurate Human Parsing.

Human parsing has attracted considerable research interest due to its broad potential applications in the computer vision community. In this paper, we explore several useful properties, including high-resolution representation, auxiliary guidance, and model robustness, which collectively contribute to a novel method for accurate human parsing in both simple and complex scenes. Starting from simple scenes: we propose the boundary-aware hybrid resolution network (BHRN), an advanced human parsing network. BHRN utilizes deconvolutional layers and multi-scale supervision to generate rich high-resolution representations. Additionally, it includes an edge perceiving branch designed to enhance the fineness of part boundaries. Building on BHRN, we construct a dual-task mutual learning (DTML) framework. It not only provides implicit guidance to assist the parser by incorporating boundary features, but also explicitly maintains the high-order consistency between the parsing prediction and the ground truth. Toward complex scenes: we develop a domain transform method to enhance the model robustness. By transforming the input space from the spatial domain to the polar harmonic Fourier moment domain, the mapping relationship to the output semantic space is highly stable. This transformation yields robust representations for both clean and corrupted data. When evaluated on standard benchmark datasets, our method achieves superior performance compared to state-of-the-art human parsing methods. Furthermore, our domain transform strategy significantly improves the robustness of DTML dramatically in most complex scenes.

Quaternion fast and accurate polar harmonic Fourier moments for color image analysis and object recognition

Image moments, as a kind of global feature descriptor of images, have become a valuable tool for pattern recognition and image analysis. However, traditional methods are mainly used to deal with grayscale images. In this paper, we apply quaternions to fast and accurate polar harmonic Fourier moments, proposing a kind of quaternion fast and accurate polar harmonic Fourier moment (QFAPHFM) capable of handling color images. Furthermore, this paper provides a detailed analysis of the invariance of QFAPHFMs under rotation, scaling, and translation transformations. The experimental results show that QFAPHFMs exhibit excellent performance in both image reconstruction and object recognition tasks. QFAPHFMs achieve accurate image reconstruction under noiseless and noisy conditions, and demonstrate excellent recognition performance in the color-based object recognition tasks.

Limit Theorems for a Supercritical Branching Process with Immigration at Zero in a Random Environment

Let Z be a supercritical branching process with immigration at zero in a random environment, where the immigration is allowed entering a generation iff the previous generation is empty. The limit theorems for the naturally normalized population size Wn shall be investigated, under both the annealed law and quenched law. In addition, in the linear fractional case, the harmonic moments of W and the convergence rate of the transition probabilities p(n) l;j of Z are studied.

Blind watermarking algorithm with 2D-SCCM chaotic system encryption based on SURF and RHFMs

In this paper, a digital watermarking algorithm was proposed based on local feature regions and radial harmonic Fourier moments. It used a quantized modulation algorithm to embed the watermark information into the frequency domain information of the image. Compared with traditional watermarks directly embedded into the pixel values, the algorithm enhanced the invisibility of the watermark. Many existing digital watermarking algorithms neglected the security of the embedding process, because of more attention on the effect of post-embedding and extraction. To overcome this problem, we proposed a two-dimensional hyperchaotic system named 2D-SCCM chaotic system, which used classical sine mapping and cubic mapping for coupling. Before embedding, the correlation among the pixels of the watermarked image was disrupted, resulting in a full process security enhancement. Combining the clustering algorithm with feature point extraction, the obtained local feature region was more stable and suitable for watermark embedding. Results showed that the improved watermark embedding algorithm was more effective for resisting geometric attacks such as cropping attacks. Moreover, the PSNR values of the final watermark-embedded images were all greater than 50 dB, indicating a good balance between imperceptibility and robustness.

Specific elements of Cuban music, evolution

Although there is a substantial variety of educational materials that generally address jazz, improvised, harmonic moment, composition and orchestral arrangements, there is very little analysis of Cuban composers of music for Afro-Cuban jazz ensembles. The paper focuses on transcription, analysis of the background of the works selected by Chucho Valdes for the group Irakere, with emphasis on the selected passages for the rhythmic-harmonic section. Fundamental elements of Cuban music, including the executions of the clave formulas, the African rhythmic cells that subsequently influenced the bebop style, the Cuban vocabulary and dance music are addressed and provide the basis for analysis.

Robust multifunctional watermarking system based zero-watermarking and polar harmonic Fourier moments

The pseudo-randomness exhibited by chaotic systems has proven valuable not only in plaintext information encryption of images with varying dimensions but also as a key signal for protecting image copyright information. Image copyright protection is a crucial part of image information protection. Currently, digital watermarking technology is predominantly employed for copyright protection of digital images. However, most of the existing watermarking technologies primarily focus on the improvement of watermarking performance, neglecting the security of the watermarking system itself. Drawing inspiration from the Latin square rule, this paper proposes a novel hyperchaotic mapping modulation framework, which is employed to construct a new 3D hyperchaotic mapping and enhance the security of the fragile watermark and the zero-watermark generation process. Additionally, it is integrated into the classical image encryption framework of scrambling-diffusion to safeguard meaningful copyright information. Moreover, a functional watermarking system is designed based on the RSA asymmetric encryption algorithm, least significant bit (LSB), and polar harmonic Fourier moments (PHFMs). The proposed system enables identity verification, tampering location, and copyright authentication simultaneously. During the generation of zero watermarks, the binarization threshold of the PHFMs information matrix is determined by the method of maximum variance. The experimental results demonstrate that this scheme achieves a high level of security, better robustness to both conventional and geometric attacks, and precise localization for different types of tampering attacks.

Statistical Image Watermark Algorithm for FAPHFMs Domain Based on BKF–Rayleigh Distribution

In the field of image watermarking, imperceptibility, robustness, and watermarking capacity are key indicators for evaluating the performance of watermarking techniques. However, these three factors are often mutually constrained, posing a challenge in achieving a balance among them. To address this issue, this paper presents a novel image watermark detection algorithm based on local fast and accurate polar harmonic Fourier moments (FAPHFMs) and the BKF–Rayleigh distribution model. Firstly, the original image is chunked without overlapping, the entropy value is calculated, the high-entropy chunks are selected in descending order, and the local FAPHFM magnitudes are calculated. Secondly, the watermarking signals are embedded into the robust local FAPHFM magnitudes by the multiplication function, and then MMLE based on the RSS method is utilized to estimate the statistical parameters of the BKF–Rayleigh distribution model. Finally, a blind image watermarking detector is designed using BKF–Rayleigh distribution and LO decision criteria. In addition, we derive the closed expression of the watermark detector using the BKF–Rayleigh model. The experiments proved that the algorithm in this paper outperforms the existing methods in terms of performance, maintains robustness well under a large watermarking capacity, and has excellent imperceptibility at the same time. The algorithm maintains a well-balanced relationship between robustness, imperceptibility, and watermarking capacity.

Asymptotics of the distribution and harmonic moments for a supercritical branching process in a random environment

Asymptotics of the distribution and harmonic moments for a supercritical branching process in a random environment

UDTCWT-PHFMs Domain Statistical Image Watermarking Using Vector BW-Type R Distribution

For any image watermarking algorithm, how to achieve the trade-off among robustness, imperceptibility, and watermark capacity is a challenging problem because of their mutually constrained relationship. In this paper, we design a statistical-based image watermarking system to solve the trade-off problem. In embedding process, consider the imperceptibility and the robustness, we inventively combine the undecimated dual tree complex Wavelet transform (UDTCWT) and the polar harmonic Fourier moments (PHFMs) to obtain the UDTCWT-PHFMs magnitudes as the watermark carriers, and we embed watermark signals in multiplicative manner. In modeling phase, by analyzing the statistical property and the multiple correlations of the UDTCWT-PHFMs magnitudes, we bound the magnitudes of different directions into the vector groups, and then we model them with the vector Roy type bivariate Weibull (BW-Type R) distribution so that we can capture accurately the marginal characteristics, the inter-scale dependencies, and the inter-orientation dependencies at the same time. Moreover, we obtain the model parameters with the double looped maximum likelihood estimation (double-looped MLE). Benefit from the reliable modeling result, we finally derive a novel specific image watermark decoder to blindly extract the hidden watermarks. Extensive experiment results declare the designed statistical image watermarking system achieves the better balance among imperceptibility, robustness, and payload.

Fast object imaging and classification based on circular harmonic Fourier moment detection.

Limited by the number of illumination fields and the speed of a spatial light modulator, single-pixel imaging (SPI) cannot realize real-time imaging and fast classification of an object. In this paper, we proposed the circular harmonic Fourier single-pixel imaging (CHF-SPI) for the first time to realize fast imaging and classification of objects. The light field distribution satisfies the circular harmonic Fourier formula, and the light intensity values of the single-pixel detector are equivalent to the circular harmonic Fourier moments. Then the target can be reconstructed under low sampling ratio by inverse transformation. Through simulation and experimental verification, clear imaging can be performed at a sampling ratio of 0.9%. In addition, circular harmonic Fourier moments are used to construct multi-distortion invariant to classify objects with rotation and scale change. The scale change multiples of objects can be calculated and the objects can be classified by using 10 light fields. It is of great significance to classify objects quickly without imaging.

Fast and accurate computation of polar harmonic Fourier moments for image description.

Continuous orthogonal moments are widely used in various image techniques due to their simplicity and good rotational invariance and stability. In recent years, numerous excellent continuous orthogonal moments have been developed, among which polar harmonic Fourier moments (PHFMs) exhibit strong image description capabilities. However, the numerical integration error is large in the calculation, which seriously affects the calculation accuracy, especially in higher-order calculation. In this paper, a continuous orthogonal moments-fast and accurate PHFM (FAPHFM) is proposed. It utilizes the polar pixel tiling technique to reduce numerical errors in the computation; this method particularly improves the accuracy of higher-order moments of traditional PHFMs. However, as accuracy increases, calculation complexity also increases. To address this issue, an eight-way symmetric/anti-symmetric calculation of the angular and radial functions was performed using the symmetry and anti-symmetry of traditional PHFMs, and clustering of pixels was performed as a way to improve the computational speed. The experimental results show that FAPHFMs perform better in image reconstruction (including noise), with higher computational accuracy, lower time complexity, and better image description ability.

Harmonic Moments and Large Deviations for the Markov Branching Process with Immigration

Harmonic Moments and Large Deviations for the Markov Branching Process with Immigration

Adaptive multiple zero-watermarking based on local fast quaternion radial harmonic Fourier moments for color medical images

The copyright protection of medical images is receiving increasing attention. Zero-watermarking schemes are a critical technology for copyright protection of medical images and show better imperceptibility performance than embedded watermarking schemes. However, existing zero-watermarking schemes still have some limitations that prevent them from fully exploiting their potential, including failure against complex desynchronization attacks and high computational complexity. To this end, we propose a novel zero-watermarking scheme based on fast quaternion radial harmonic Fourier moments (FQRHFMs) that is resistant to desynchronization attacks. Specifically, this article formulates multiple local feature regions (LFRs) based on a speeded-up robust feature (SURF) operator and provides a fast computation method for QRHFMs by using fast Fourier transform (FFT). The magnitudes of FQRHFMs are computed in each incomplete overlapping LFR for generating multiple zero-watermarks to resist desynchronization attacks. Experimental results show that the proposed scheme achieves state-of-the-art robustness against various desynchronization attacks (e.g., translation, cropping, and length-width ratio changing), and outperforms existing local zero-watermarking frameworks with regard to accuracy and efficiency.

Sedenion polar harmonic Fourier moments and their application in multi-view color image watermarking

In recent years, the research on image moments has made significant progress, transitioning from gray image moments to color image moments and from gray stereo image moments to color stereo image moments. However, the application of stereo image moments is limited to binocular stereo images with two views, and cannot handle images with more than two views. Multi-view images are more promising but are difficult to handle due to their intricate structure. Based on the sedenion theory and polar harmonic Fourier moments (PHFMs), this paper proposes the sedenion polar harmonic Fourier moments (SPHFMs) for processing multi-view color images. The imaginary part of sedenion encodes all views of multi-view color images, thus allowing all views to be processed as a single unit and internal correlations between all views to be maintained. The results of the stability experiment and image reconstruction experiment demonstrate that good stability and high image reconstruction performance are achieved when the SPHFMs are applied to processing multi-view color images. Since existing multi-view color image watermarking methods are not resistant to geometric attacks, we use SPHFMs for multi-view color image watermarking, which exhibits good imperceptibility and robustness.

Geometrical attacks resilient statistical watermark decoder using polar harmonic Fourier moments

This paper presents a new robust multiplicative watermark detector. Due to the strong robustness against various attacks, polar harmonic Fourier moment (PHFM) magnitudes are used as the employed watermark carrier. The distribution of PHFM magnitudes is highly non-Gaussian and can be properly modeled by a heavy-tailed probability density function (PDF). In this paper, we proved that Weibull distribution can suitably fit the distribution of PHFM magnitudes, and based on this, we presented a statistics-based watermark decoder by using the Weibull as a prior for the PHFM magnitudes. In watermark embedding, a multiplicative manner was used to embed watermark information in PHFM magnitudes of the highest entropy blocks to achieve better robustness and imperceptibility. In watermark detection, we developed a Weibull distribution-based statistical watermark decoder, which uses the maximum likelihood (ML) decision rule. Compared with Bessel K form (BKF), Cauchy, and generalized Gaussian (GG)-based decoders, the Weibull-based decoder demonstrates stronger robustness. In addition, the proposed watermark decoder is more robust against geometrical and common image processing attacks than existing statistical watermark decoders.

Image watermarking using DNST-PHFMs magnitude domain vector AGGM-HMT

Invisibility, robustness and payload are three indispensable and contradictory properties for any image watermarking systems. Therefore, in this paper a novel statistical image watermark decoder based on robust discrete nonseparable Shearlet transform (DNST)-polar harmonic Fourier moments (PHFMs) magnitude and effective vector anisotropic generalized Gaussian mixtures (AGGM)-hidden Markov tree (HMT). We begin with a detailed study on the robustness and statistical characteristics of local DNST- PHFMs magnitudes of natural images. This study reveals the excellent robustness, highly non-Gaussian marginal statistics and strong dependencies of local DNST-PHFMs magnitudes. We also find that conditioned on their generalized neighborhoods, the local DNST-PHFMs magnitudes can be approximately modeled as anisotropic generalized Gaussian variables. Based on these findings, we model local DNST-PHFMs magnitudes using a vector AGGM-HMT that can capture all interscale, interdirection, and interlocation dependencies. Meanwhile, model parameters can be estimated effectively by using localization clues guided expectation–maximization (LCGEM) approach. Finally, we develop a new statistical image watermark decoder using the vector AGGM-HMT and maximum likelihood (ML) decision rule. Extensive experimental results show the superiority of the proposed watermark decoder over several state-of-the-art statistical watermarking methods and some approaches based on convolutional neural networks.

Robust and blind watermarking algorithm for chaotic system encryption based on discrete cosine transform-singular value decomposition

Through comparison with most frequency-domain digital watermarking approaches, the spread transform dither modulation (STDM) method exhibits a good embedding effect and is capable of meeting the requirements of blind extraction. However, the rotating attack is difficult to counter, and the cropping attack is seriously impacted by location factors. In addition, there exist numerous algorithms concentrate solely on the watermarking process, ignoring the image’s security. In these views, our work proposes a two-dimensional hyperchaotic system, the so-named Chebyshev ICMIC cascade map with the Knuth–Durstenfeld method, aiming to enhance the security of digital watermarking systems. The scrambled pixels improve the anticropping attack effect through breaking the location correlation of watermark information. For the purpose of magnifying resistance to rotation attack impact, the radial harmonic Fourier moments subtraction coefficient matrix distribution expectation is appropriately adapted to carry out the rotation correction. The performed experiments reveal that the suggested improved STDM watermarking algorithm demonstrates better robustness and invisibility, resisting more attacks than the existing methodologies. Finally, the feasibility of the proposed methods is proved based on the simulation results.