Form Of Convolution Research Articles

Blur parameter locus curve and its applications

Conventionally, the point spread function (PSF) is understood as a characteristic function of any optical system. It captures the information about the amount of blur present along all the directions for a point in the scene. However, the dependence of blur on the PSF is in the form of convolution for any object other than a point source present in the scene and hence their relationship is less explicit. The authors propose a blur parameter locus curve (BPLC) as a system representation which has a one to one relationship with blur. BPLC simply is a chart of blur amounts in all directions of a given PSF with respect to the selected measurement function. They further characterise the PSF by decomposing the variation of BPLC across all directions based on the study performed for different possible forms of the blur kernels. Such decomposition provides powerful tools for various analysis. As PSF can be anisotropic, the computation of BPLC becomes an essential intermediate step to obtain the scale map as at the same scale, blur is different in different directions. Furthermore, they demonstrate the use of BPLC to obtain other system characteristics function such as PSF.

COMPUTING FUZZY INTEGRAL OF THE BASIS OF FUZZY MESURE

The fuzzy integral of a function with a fuzzy measure is a general estimate in the form of a nonlinear convolution of particular estimates of information elements, and the possibility of interconnection of information elements is not excluded. Here is an approach that allows the expert to best formalize his fuzzy ideas, transforming the language of words into a language of quantitative estimates.

DenseX-Net: An End-to-End Model for Lymphoma Segmentation in Whole-Body PET/CT Images

Automatic lymphoma detection and accurate lymphoma boundary delineation from whole body Positron Emission Tomography/Computed Tomography (PET/CT) scans are essential for surgical navigation and radiation therapy. Besides, labeling the data, which means contouring the lymphoma contour in images is time-consuming, operator intensive and subjective. Hence, this paper integrates the supervised learning and unsupervised learning to propose an end-to-end segmentation network, namely DenseX-Net, for both lymphoma detection and segmentation. There are two important flows in the proposed DenseX-Net. One is a reconstruction flow (based on the convolutional encoder-decoder form) that can be used for learning semantic representations of different lymphomas by minimizing the discrepancy between each input and its output in an unsupervised learning form. The other one is a segmentation flow (based on DenseU-Net) that performs the lymphoma segmentation task. Note that, the encoders in both flows are trained jointly with the same weights, which can facilitate DenseX-Net obtaining the accurate segmentation using a little labeled data. We evaluate our proposed DenseX-Net for lymphoma segmentation on 80 real PET/CT cases (from General Hospital of Northern Military Area) with a Dice coefficient of 72.84%. Experimentations and comparisons demonstrate the accuracy and robustness of DenseX-Net as well as its performance advantages as compared with related segmentation networks.

FORMATION OF AN INTEGRATED THREAT INDEX OF THE NATIONAL ECONOMY

The article considers the formation of an integrated threat index of the national economy. The purpose of the study is to form a methodological basis for determining the threat index of the national economy. It is determined that currently there is no perfect effective and high-quality approach to the methods of identifying threats to the country's economy, which causes an urgent need to develop an effective national methodology for ensuring the national economic security of the country. To assess the threat index of the national economy, a structural-logical mathematical model was built, which includes the appropriate sequence of certain stages of the study. First, an information base of input predictors for the period in the dynamics, such as the state budget deficit, total debt, the share of foreign capital in the authorized capital of banks, international reserves in the months of import, the level of dollarization, the share of foreign currency in the money supply, control corruption, political stability and absence of violence / terrorism, rule of law, inflation rate, unemployment rate, GINI index, shadow economy level. The following are the indicators of the input information base of the study to a comparable form by conducting nonlinear normalization. The next step is to select the relevant indicators for estimating the threat index of the national economy on the basis of a combination of Pareto methods and scatter plot; the theoretical aspects of application of the specified methods to filtering of relevant predictors of input information base of research are considered. The final stage was the assessment of the integrated threat index of the national economy using the Kernel function and the multiplicative form of convolution. The visualization of both the general trend of the behavior of the integral index of time threats and variations within the minimum and maximum possible levels is carried out. The practical application of the proposed methodology will allow timely and prompt support of the necessary organizational, institutional, regulatory conditions that provide the ability of the national economy to withstand external and internal threats and burdens, further quality adaptation to problems and destabilizing factors, rapid recovery from adverse factors.

A Novel Method of Bearing Fault Diagnosis in Time-Frequency Graphs Using InceptionResnet and Deformable Convolution Networks

Bearing fault diagnosis has attracted increasing attention due to its importance in the health status of rotating machinery. The data-driven models based on deep learning (DL) have become more and more intelligent in the field of fault diagnosis, and among them convolutional neural network (CNN) has been widely used in recent researches. However, traditional CNN is not easy to capture right fault features due to their fixed geometric structures, especially under complex working conditions in fault diagnosis. To address these challenges, we propose a novel model by combining InceptionResnetV2 with Deformable Convolution Networks, named DeIN. We replace the basic form of convolution with deformable convolution in specific layers, and a main classifier and an auxiliary classifier are designed to output the classification result of our proposed model, to adapt to the non-rigid characters and larger receptive field in time-frequency graph (TFG). Experimentally, the one-dimensional signals are transformed into TFGs and as input of the proposed model, and this aims to find useful features during the training process. To verify the generalization ability of the proposed model, we apply a set of cross-over tests based on two popular datasets, and our model achieved 99.87% and 94.52% highest-precision fault classification results comparing with other state-of-the-art CNN models.

Shape Deviation Generator--A Convolution Framework for Learning and Predicting 3-D Printing Shape Accuracy

The 3-D shape accuracy is a critical performance measure for products built via additive manufacturing (AM). With advances in computing and increased accessibility of AM product data, machine learning for AM (ML4AM) has become a viable strategy for enhancing 3-D printing performance. A proper description of the 3-D shape formation through the layer-by-layer fabrication process is critical to ML4AM, such as feature selection and AM process modeling. The physics-based modeling and simulation approaches present voxel-level description of an object formation from points to lines, lines to surfaces, and surfaces to 3-D shapes. However, this computationally intensive modeling framework does not provide a clear structure for machine learning of AM data. Significant progress has been made to model and predict the shape accuracy of planar objects under data analytical frameworks. In order to predict, learn, and compensate for 3-D shape deviations using shape measurement data, we propose a shape deviation generator (SDG) under a novel convolution formulation to facilitate the learning and prediction of 3-D printing accuracy. The shape deviation representation, individual layer input function, and layer-to-layer transfer function for the convolution modeling framework are proposed and derived. A deconvolution problem for identifying the transfer function is formulated to capture the interlayer interaction and error accumulation effects in the layer-by-layer fabrication processes. Physics-informed sequential model estimation is developed to fully establish the SDG models. The Gaussian process regression is adopted to capture spatial correlations. The printed 2-D and 3-D shapes via a stereolithography (SLA) process are used to demonstrate the proposed modeling framework and derive new process insights for AM processes. Note to Practitioners —With advances in computing and increased availability of product data, machine learning for additive manufacturing (ML4AM) has become a viable strategy for enhancing 3-D printing accuracy. This work establishes the shape deviation generator (SDG) as a novel data analytical framework through a convolution formulation to model the 3-D shape formation in the AM process. This new engineering-informed machine-learning framework will facilitate the learning of AM data to establish models for geometric shape accuracy prediction and control.

Efficiency bounds for semiparametric models with singular score functions

This paper is concerned with asymptotic efficiency bounds for the estimation of the finite dimension parameter of semiparametric models that have singular score function for θ at the true value The resulting singularity of the matrix of Fisher information means that the standard bound for is not defined. We study the case of single rank deficiency of the score and focus on the case where the derivative of the root density in the direction of the last parameter component, θ2, is nil while the derivatives in the p – 1 other directions, θ1, are linearly independent. We then distinguish two cases: (i) The second derivative of the root density in the direction of θ2 and the first derivative in the direction of θ1 are linearly independent and (ii) The second derivative of the root density in the direction of θ2 is also nil but the third derivative in θ2 is linearly independent of the first derivative in the direction of θ1. We show that in both cases, efficiency bounds can be obtained for the estimation of with j = 2 and 3, respectively and argue that an estimator is efficient if reaches its bound. We provide the bounds in form of convolution and asymptotic minimax theorems. For case (i), we propose a transformation of the Gaussian variable that appears in our convolution theorem to account for the restricted set of values of This transformation effectively gives the efficiency bound for the estimation of in the model configuration (i). We apply these results to locally under-identified moment condition models and show that the generalized method of moments (GMM) estimator using as weighting matrix, where is the variance of the estimating function, is optimal even in these non standard settings. Examples of models are provided that fit the two configurations explored.

A Depthwise Separable Network for Action Recognition

Action recognition is one important but challenging tasks in computer vision. The 3D convolutional neural network is one mainstream method for action recognition because it can extract temporal and spatial information in the video simultaneously. However, 3D convolutional neural network has a serious drawback which is that its parameter quantity is too large. Depthwise convolution is a form of group convolution, which can effectively reduce the parameter of convolution kernel, and has been widely applied in 2D convolutional neural network. Therefore, we propose to introduce depthwise convolution into the 3D convolutional neural network. We choose 3D resnet as our basic model, and construct our model by replacing the 3D convolution kernel in the baseline with the depthwise convolution, we named our proposed model as depthwise separable network (DSN). We conducted experiments on UCF101 and HMDB51 dataset. The experimental results show that by introducing the depthwise convolution, our DSN network can not only reduce the parameters of the baseline, but also can moderately improve the accuracy.

TasselNetv2: in-field counting of wheat spikes with context-augmented local regression networks

BackgroundGrain yield of wheat is greatly associated with the population of wheat spikes, i.e., spike~number~text {m}^{-2}. To obtain this index in a reliable and efficient way, it is necessary to count wheat spikes accurately and automatically. Currently computer vision technologies have shown great potential to automate this task effectively in a low-end manner. In particular, counting wheat spikes is a typical visual counting problem, which is substantially studied under the name of object counting in Computer Vision. TasselNet, which represents one of the state-of-the-art counting approaches, is a convolutional neural network-based local regression model, and currently benchmarks the best record on counting maize tassels. However, when applying TasselNet to wheat spikes, it cannot predict accurate counts when spikes partially present.ResultsIn this paper, we make an important observation that the counting performance of local regression networks can be significantly improved via adding visual context to the local patches. Meanwhile, such context can be treated as part of the receptive field without increasing the model capacity. We thus propose a simple yet effective contextual extension of TasselNet—TasselNetv2. If implementing TasselNetv2 in a fully convolutional form, both training and inference can be greatly sped up by reducing redundant computations. In particular, we collected and labeled a large-scale wheat spikes counting (WSC) dataset, with 1764 high-resolution images and 675,322 manually-annotated instances. Extensive experiments show that, TasselNetv2 not only achieves state-of-the-art performance on the WSC dataset (91.01% counting accuracy) but also is more than an order of magnitude faster than TasselNet (13.82 fps on 912times 1216 images). The generality of TasselNetv2 is further demonstrated by advancing the state of the art on both the Maize Tassels Counting and ShanghaiTech Crowd Counting datasets.ConclusionsThis paper describes TasselNetv2 for counting wheat spikes, which simultaneously addresses two important use cases in plant counting: improving the counting accuracy without increasing model capacity, and improving efficiency without sacrificing accuracy. It is promising to be deployed in a real-time system with high-throughput demand. In particular, TasselNetv2 can achieve sufficiently accurate results when training from scratch with small networks, and adopting larger pre-trained networks can further boost accuracy. In practice, one can trade off the performance and efficiency according to certain application scenarios. Code and models are made available at: https://tinyurl.com/TasselNetv2.

The Scattering of Electromagnetic Fields from Anisotropic Objects Embedded in Anisotropic Multilayers

This article presents an efficient method for calculating the scattered electromagnetic (EM) fields from anisotropic objects embedded in general anisotropic multilayers, both with arbitrary anisotropy. The electric field integral equation (EFIE) is derived based on the electric dyadic Green’s functions for general anisotropic multilayers. The volume integral equation (VIE) involves a convolution form between the dyadic Green’s function and equivalent sources. To accelerate the integral computation, the fast Fourier transform technique (FFT) is adopted which reduces the computational cost from $O(N^{2})$ to $O (N \log N)$ . The biconjugate gradient stabilized method (BiCGSTAB) is then applied to solve the EFIE efficiently to calculate the total electric fields in the computational domain. In order to validate the algorithm, several examples are modeled for anisotropic objects embedded in both isotropic and anisotropic multilayers. The modeled scattered fields are compared with the finite-element method (FEM) results. The good agreement between the two results shows the algorithm works properly.

Field equations and corresponding memory responses for a fiber-reinforced functionally graded medium due to heat source

Fractional derivative is a widely accepted theory to describe the physical phenomena and the processes with memory effects which is defined in the form of convolution having kernels as power functions. Due to the shortcomings of power-law distributions, some other forms of derivatives with few other kernel functions are proposed. This present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena in a fiber-reinforced functionally graded unbounded medium due to the presence of periodically varying heat source in the context of three-phase-lag model of generalized thermoelasticity, which is defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent heat transfer. Employing Laplace and Fourier transforms as tools, the problem has been solved analytically in the transformed domain. The inversion of the Fourier transform is carried out using residual calculus, and the numerical inversion of the Laplace transform has been executed using a method on Fourier series expansion. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed. Excellent predictive capability is demonstrated due to the presence of memory dependent derivative, reinforcement, and non-homogeneity also. Communicated by S. Velinsky

Semi-analytical recursive convolution finite-element time-domain method for electromagnetic analysis of dispersive media

Based on the idea of semi-analytical convolution in digital signal processing (DSP), a new technique of finite-element time-domain (FETD) for dealing with dispersive media is presented. By comparison with semi-analytical convolution in DSP, a unified recursive formulation of semi-analytical convolution for three kinds of dispersive media models i.e. Drude model, Debye model and Lorentz model is described. This formulation includes electric field E and complex polarization vector ψ. On the other hand, the weak form solution of the FETD equation on account of the idea of DSP and the iteration equation including E and ψ are obtained. Then the achievement of semi-analytical recursive convolution finite-element time-domain (SARC-FETD) method is developed by combining the above two equations. Finally, the feasibility of this algorithm is validated with three-dimension numerical examples.

Transient heating within skin tissue due to time-dependent thermal therapy in the context of memory dependent heat transport law

In the present analysis, the bio-heat equation has been studied in the context of memory responses which is defined in the form of convolution having kernels as power functions. The heat transport equation for this problem involving the memory dependent derivative on a slipping interval in the context of Lord-Shulman (LS) model is formulated. The thermal damage within the skin tissue during the thermal therapy is also reported in the literature. Laplace transform technique is implemented to solve the governing equations. The influences of the memory-dependent derivative and time-dependent moving heat source velocity on the temperature of skin tissues and the thermal injuries are precisely investigated. The thermal injuries to the tissue are assessed by the denatured protein range using the current formulation in which the numerical inversion of the Laplace transform is carried out using Zakian methods. The numerical outcomes of thermal injuries and temperatures have been represented graphically. Excellent predictive capability is demonstrated for identification of appropriate procedure to select different kernel functions to reach effective heating in hyperthermia treatment. Significant effect of the thermal therapy is reported due to the effect of delay time also.

The Optimal Detector of Distributed MIMO Radar Under Swerling-Chi Scattering Models

In this letter, the optimal detector of distributed multiple-input multiple-output (MIMO) radar based on the Swerling-chi scattering model with $2k$ degrees of freedom is investigated. An optimal detector with a closed-form expression involving the confluent hypergeometric function is derived when the transmitting waveforms are orthogonal. When $2k=2$ or $2k=4$ , the derived expression will be reduced to the optimal detector of the Swerling I/II model or the Swerling III/IV model, respectively. When $2k$ is not an integer, the approximate expression of the optimal detector is proposed. Moreover, the probability density functions of the proposed approximate expressions under both null and alternative hypotheses are derived in the form of convolutions of transcendental functions.

Accelerating the discrete dipole approximation via circulant preconditioning

The discrete dipole approximation (DDA) is a popular numerical method for electromagnetic scattering calculations. The standard DDA formulation involves the uniform discretization of the underlying volume integral equation, leading to a linear system of convolution form. This permits a matrix-vector product to be performed with O(nlogn) complexity via the fast-Fourier transform (FFT). Thus, in principle, the system can be solved rapidly using an iterative method. However, it is well known that the convergence of iterative methods becomes increasing slow as the optical size and refractive index of the scattering obstacle are increased. In this paper, we present a preconditioning strategy based on the multi-level circulant preconditioner of Chan and Olkin [Numer. Algorithms 6, 89 (1994)] and assess its performance for improving this rate of convergence. In particular, we approximate the system matrix by a circulant matrix which can be inverted efficiently using the FFT. We present numerical experiments for scattering by highly oblate non-absorbing hexagonal plates, demonstrating that this approach serves as an effective preconditioning strategy, reducing simulation times by orders of magnitude in many cases. A Matlab implementation of this work is freely available online.

Fractional convolution, correlation theorem and its application in filter design

In this paper, fractional convolution and correlation structures are proposed. The corresponding theorems for fractional Fourier transform (FRFT) are derived, which state that fractional convolution in the time domain is equivalent to a simple multiplication operation for FRFT and FT domain; this feature is more instrumental for the multiplicative filter model in FRFT domain. Moreover, the fractional convolution operation proposed in this paper can be expressed as ordinary convolution form in FT domain; such expression is particularly useful and easy to implement in filter design in time domain. Classical convolution and correlation theorems for Fourier transform (FT) are shown to be special case of our achieved result. The potential application of the derived result in filter design is also discussed, and the proposed method has lower computational complexity and can be easily implemented in FRFT domain.

Memory response on thermal wave propagation in an elastic solid with voids due to influence of magnetic field

Fractional derivative is a widely accepted theory to describe the physical phenomena and the processes with memory responses which are defined in the form of convolution having kernels as power functions. Due to the shortcomings of power-law distributions, some other forms of derivatives with few other kernel functions are proposed. This present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for an infinite solid with void under the action of an induced magnetic field due to the presence of a prescribed plane heat source. The heat transport equation for this problem is involving the memory-dependent derivative on a slipping interval in the context of Lord Shulman model of generalized thermoelasticity. Employing the Laplace transform as a tool, the analytical results for the distributions of the change in volume fraction field, temperature and deformations are obtained on solving the vector-matrix differential equation using eigenvalue approach. The numerical inversion of the Laplace transform is performed using the Zakian method. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative and presence of a magnetic field also.

Memory response on thermal wave propagation in an elastic solid with voids

Fractional derivative is a widely accepted theory to describe the physical phenomena and the processes with memory responses which is defined in the form of convolution having kernels as power functions. Due to the shortcomings of power law distributions, some other forms of derivatives with few other kernel functions are proposed. This present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for an infinite porous material subjected to the presence of distributed time-dependent heat source acting over the plane area. The heat transport equation for this problem is involving the memory dependent derivative on a slipping interval in the context of three-phase-lag (3PL) model of generalized thermoelasticity. Employing the Laplace transform as a tool, the analytical results for the distributions of the change in volume fraction field, temperature, stress, and displacement are obtained on solving the vector-matrix differential equation using eigenvalue approach. The numerical inversion of the Laplace transform is performed using the Zakian method. Excellent predictive capability is demonstrated due to the presence of memory dependent derivative and delay time also.Communicated by Nickolay Banichuk.

A discontinuous Galerkin method for wave propagation in orthotropic poroelastic media with memory terms

Poroelastic materials play an important role in biomechanical and geophysical research. In this paper, we investigate wave propagation in orthotropic poroelastic media by studying the time-domain poroelastic wave equations. Both the low frequency Biot's (LF-Biot) equations and the Biot-Johnson-Koplik-Dashen (Biot-JKD) model are considered. In LF-Biot equations, the dissipation terms are proportional to the relative velocity between the fluid and the solid by a constant. Contrast to this, the dissipation terms in the Biot-JKD model are in the form of time convolution (memory) as a result of the frequency-dependence of fluid-solid interaction at the underlying microscopic scale in the frequency domain. The dynamic tortuosity and permeability described by Darcy's law are two crucial factors in this problem, and highly linked to the viscous force. In the Biot model, the key difficulty is to handle the viscous term when the pore fluid is viscous. In the Biot-JKD model, the convolution operator involves order 1/2 shifted fractional derivatives in the time domain, which is challenging to discretize.In this work, a new method of the multipoint Padé (or Rational) approximation for Stieltjes function is applied to approximate the JKD dynamic tortuosity and then an augmented system of Biot-JKD model is obtained, where the kernel of the memory term is replaced by the finite auxiliary variables satisfying a local system of ordinary differential equations. The Runge-Kutta discontinuous Galerkin (RKDG) method with the un-splitting method is used to compute the numerical solution, and numerical examples are presented to demonstrate the high order accuracy and stability of the method. Compared with the existing approaches for solving the Biot-JKD equations, the augmented system presented here require neither the storage of solution history nor the computation of the flux of the auxiliary variables.

Self-gravitational Force Calculation of High-order Accuracy for Infinitesimally Thin Gaseous Disks

Abstract Self-gravitational force calculation for infinitesimally thin disks is important for studies on the evolution of galactic and protoplanetary disks. Although high-order methods have been developed for hydrodynamic and magnetohydrodynamic equations, high-order improvement is desirable for solving self-gravitational forces for thin disks. In this work, we present a new numerical algorithm that is of linear complexity and of high-order accuracy. This approach is fast since the force calculation is associated with a convolution form, and the fast calculation can be achieved using Fast Fourier Transform. The nice properties, such as the finite supports and smoothness, of basis spline functions are exploited to stably interpolate a surface density and to achieve a high-order accuracy in forces. Moreover, if the mass distribution of interest is exclusively confined within a calculation domain, the method does not require artificial boundary values to be specified before the force calculation. To validate the proposed algorithm, a series of numerical tests, ranging from first- to third-order implementations, are performed, and the results are compared with analytic expressions derived for third- and fourth-order generalized Maclaurin disks. We conclude that the improvement on the numerical accuracy is significant with the order of the method, with only little increase of the complexity of the method.