Foreign object debris (FOD) on airport runways can cause serious accidents and huge economic losses. FOD detection systems based on millimeter-wave (MMW) radar sensors have the advantages of higher range resolution and lower power consumption. However, it is difficult for traditional FOD detection methods to detect and distinguish weak signals of targets from strong ground clutter. To solve this problem, this paper proposes a new FOD detection approach based on optimized variational mode decomposition (VMD) and support vector data description (SVDD). This approach utilizes SVDD as a classifier to distinguish FOD signals from clutter signals. More importantly, the VMD optimized by whale optimization algorithm (WOA) is used to improve the accuracy and stability of the classifier. The results from both the simulation and field case show the excellent FOD detection performance of the proposed VMD-SVDD method. The foreign object debris (FOD)  on airpoHowever, the major challenge for radar systems is how to detect weak target signals from the strong ground clutter of airport runway background . The conTo solve this problem, some researchers have studied various FOD detection methods. Reference  proposedK. In .When In order to strengthen global search ability of WOA, whales also randomly search for the prey. If During each iteration, the prey position c and the radius Support vector data description (SVDD)  algorithfunction  and LagrBefore SVDD classification, it is necessary to extract two-dimensional features of the FOD and clutter as inputs of the classifier. The autocorrelation distribution of FOD signals is more concentrated while that of ground clutter is more dispersive on account of target echo signals have stronger correlation than clutter signal. The second-order center distance (F1) and fourth-order cumulant (F2) of normalized autocorrelation are chosen as two-dimensional features, which can increase the difference between FODs and clutter. F1 represents the distribution of normalized autocorrelation relative to the geometric center of mass. The more dispersed of the distribution is, the smaller F1 is. F2 can further solve the problems that cannot be solved by F1, such as Gaussian noise. The calculation is as follows:The normalized autocorrelation coefficient of Feature 1: the second order center distance of the normalized autocorrelation coefficientFeature 2: fourth-order cumulant of normalized autocorrelation coefficientThe operation and signal processing parameters of the radar system are provided in In the simulation, the ground clutter signal is the signal whose amplitude distribution satisfies Rayleigh distribution, and the target signal is linear frequency modulation signal. Suppose that there is a target at a distance of 40 m, which is marked with red star in the following figures. Without clutter signals, the target signal is obvious after frequency mixing and fast Fourier transform (FFT) processing that shown in K = 7.69 and α = 1497.10, and the integer formats of them are K = 7 and α = 1500, which are provided for the VMD.In the proposed method, firstly, quadratic penalty parameter Then, the signals in To select FOD mode component, set a selection threshold which is the average of cross-correlation coefficients of In addition, the following experiments have been conducted to illustrate the importance of setting appropriate VMD parameters and the cross-correlation threshold.K = 7. In K = 5. The inaccurate decomposition is caused by improper K = 7. The integrity of target signal is destroyed by the inappropriate α. In The simulation data in It can be seen from these selection results that, with the decrease of signal-to-clutter rate (SCR), the number of modes below the threshold decreases and the selected clutter modes decrease, regardless of single target or multiple targets. From the above simulation results, the number of clutter data used to train the classifier is sufficient, although some of clutter modes are selected as target modes. Moreover, if the number of targets increases further, more clutter modes can be obtained by increasing the decomposition layer of VMD. But this case of too many targets on airport runways is not common.After the mode components are divided into FOD modes and clutter modes by the cross-correlation threshold, the SVDD classifier is used to distinguish FOD signals from clutter signals.δ = 0.5 and C = 1, which are optimized by particle swarm optimization (PSO) [In the simulation, two important parameters of SVDD are set as follows: on (PSO) . AccordiWithout VMD processing, after the SVDD classifier is trained by clutter signals in the With VMD processing, the clutter modes in In order to test the classification performance of VMD-SVDD classifier, the proposed method is tested on a clutter data set without targets. In this case, the cross-correlation mode selection algorithm will mistakenly select some of the clutter modes as the target modes . However, sampling points of these false target modes are likely to be classified into the decision boundary by the trained classifier. As can be seen from For the training of VMD-SVDD classifier, the training set includes clutter modes selected by the cross-correlation threshold after VMD processing. While, the testing set includes target modes, and may also include other clutter modes. From above simulation and test results, it can be seen that using clutter modes as a test set results in an error probability of about To compare the detection performance of the proposed VMD-SVDD method, four methods are applied to detect a same target under different SCR. The cell-average CFAR (CA-CFAR) method is to obtain a detection threshold by averaging the clutter power around the target. If the amplitude of a signal exceeds the threshold, the signal is considered as a target. The principle of VMD-CACFAR method is to detect targets in FOD mode components by CA-CFAR method. In SVDD method and the proposed VMD-SVDD method, target sampling points are marked in advance, and the target is detected by confirming that sampling points outside the decision boundary are labeled.SCR > −10 dB. It can be seen from The numbers of simulation are 1000 in every case and the detection probability The VMD-SVDD method is more adaptable. There is no need to set VMD parameters, among which quadratic penalty parameter (2)The VMD-SVDD method can effectively suppress ground clutter signals and has the higher detection probability.The FOD detection method in the MMW radar sensor system is limited by the strong ground clutter on the airport runway. This work presents an improved VMD-SVDD method to detect FODs. In this method, the echo signal received by MMW radar system are is firstly decomposed into BLIMFs with the optimal VMD. Then the mode components divided into two parts: FOD mode components and clutter components. The selected clutter mode components are used to train the SVDD classifier, and then the FOD mode components are tested by the classifier. This method relies on the SVDD classifier to distinguish FOD signals from clutter signals, what’s more, the accuracy and stability of the classifier is improved by the optimal VMD. The proposed method has two significant advantages:After analytically describing the procedure, the effectiveness of the approach has been proven by simulation. Furthermore, the general validity of the method is evidenced with the measured data.


This paper studies the social acceptability and feasibility of a focused protection strategy against coronavirus disease 2019 (COVID-19). We propose a control scheme to develop herd immunity while satisfying the following two basic requirements for a viable policy option. The first requirement is social acceptability: the overall deaths should be minimized for social acceptance. The second is feasibility: the healthcare system should not be overwhelmed to avoid various adverse effects. To exploit the fact that the disease severity increases considerably with age and comorbidities, we assume that some focused protection measures for those high-risk individuals are implemented and the disease does not spread within the high-risk population. Because the protected population has higher severity ratios than the unprotected population by definition, the protective measure can substantially reduce mortality in the whole population and also avoid the collapse of the healthcare system. Based on a simple susceptible-infected-recovered model, social acceptability and feasibility of the proposed strategy are summarized into two easily computable conditions. The proposed framework can be applied to various populations for studying the viability of herd immunity strategies against COVID-19. For Japan, herd immunity may be developed by the proposed scheme if  From the experiences of China, Italy, and the United States, it has been observed that COVID-19 can overwhelm healthcare capacities. Because of the absence of an effective antiviral drug or vaccine, many countries have adopted non-pharmaceutical interventions (NPIs), such as closing schools and workplaces and imposing rigorous social distancing measures, to reduce transmission of the virus. Initial efforts by governments worldwide have been concentrated on the short-run suppression of the first wave of the pandemic to avoid the collapse of the healthcare system. Suppression of an outbreak can, however, leave a large portion of the population uninfected and susceptible; therefore, resurgence of the outbreaks as severe as the initial one becomes a possibility4. Moreover, radical NPIs aimed at suppression are not sustainable, as they have already had devastating impacts on the global economy and personal lives of many. Long-run strategies that go beyond simple relaxation of the initial suppression-oriented responses are crucial, as we probably are at least one or two years away from substantial supply of a vaccine. Continued circulation of the virus in the global population for a prolonged period seems to be inevitable. A possible option might be the development of herd immunity by ensuring the presence of a sufficiently high proportion of immune individuals in the population; it may be achieved through a carefully managed, slow spread of infection, which could prevent the collapse of the healthcare system5.The coronavirus disease 2019 (COVID-19) pandemic has been a huge global health threat, with over 10 million cases and 500,000 deaths confirmed worldwide as of June 30, 20208, whereas the infection fatality ratio (IFR) is reported to be around 0.6 to 0.7%11. A crude estimate on the basis of these numbers is that the resulting mortality during the progress toward herd immunity can reach 400 per 100,000 population, that is, about 500,000 deaths in Japan and 1.3 million deaths in the United States. These figures would not be socially acceptable, given that the estimated deaths related to seasonal influenza in Japan and the United States were around 10,000 and 34,000 in the 2018–2019 season, respectively12. The basic premise of our research is that the “true” IFR for COVID-19 is lower than the reported value, as no herd immunity approaches can obtain social acceptance otherwise.Social acceptance is a significant issue for all types of herd immunity policies because it is associated with a considerably large number of infections and hence high mortality. For an infectious disease with a basic reproduction number acceptability  and feasibility . The proposed control strategy includes two components. The first component is a focused protection measure for high-risk individuals, e.g., the elderly and those with underlying health conditions), who are likely to die if they contract COVID-19. The second component is a dynamic control measure  among the unprotected to keep the daily number of infected individuals below the healthcare capacity, thereby avoiding the collapse of the healthcare system. Under the focused protection of high-risk individuals, the average disease severity ratios in the unprotected population becomes much smaller than those of the whole population including the vulnerable. Thus, the focused protection has two-fold implications. First, it contributes to social acceptance because it can substantially reduce mortality. Second, it contributes to feasibility because the society can accept a larger number of infections than it can without focused protection, as the proportion of severe cases goes down under the protective measure. With these effects and the imposed dynamic control measure, the number of infected individuals can increase without causing a collapse of the healthcare system. For COVID-19, age is a key factor associated with disease severity, with fatality increasing disproportionately with age. For instance, those aged 11. On the basis of this fact, our numerical examples consider an age-based definition of the protected group. Our analyses reveal that if several conditions are met with the basic reproduction number of the epidemic, We propose a long-run control strategy that aims at developing herd immunity and study its social 13. Further, as an idealization, our mathematical model assumes that the disease does not spread among the protected group at all, i.e., the group is isolated from the SIR epidemic dynamics during the outbreak. At the cost of the simplification, we can study the feasibility and social acceptability of herd immunity strategies semi-analytically with a limited number of input variables. The only required inputs are the age composition of the population, the healthcare system’s service capacity, and the age-specific severity rates for COVID-19; we acknowledge that uncertainties remain for the last parameter. For its simplicity, the proposed framework for investigating social acceptability and feasibility of focused protection policies is universally applicable to different populations without resorting to data-intensive and model-specific structural simulations and calibrations. For Japan, as an example, herd immunity can be developed if 9. Numerical results obtained by the proposed framework can be easily updated by incorporating the latest estimates for the input parameters.Rather than simulating highly structured models, we build on the basic susceptible-infected-recovered (SIR) modelConsider a population that faces a novel infectious disease with a basic reproduction number 14. Existing evidence consistently suggests that age is a key factor that affects the severity of COVID-19, with the fatality ratio substantially increasing among elderly individuals11. We assume that the entire population is partitioned into two groups: the protected and the active groups. The former group consists of high-risk individuals, such as elderly individuals and those with pre-existing medical conditions, who are likely to die if they contract COVID-19. The latter consists of low-risk individuals who have a high probability of recovering from the infection. The former group is safely isolated from the active group and protected from the disease during the outbreak. Individuals in the latter group can interact with others in the same group and thus are susceptible to infection. The size of the active group is normalized to unity. The size of the entire population, including both the protected and the active groups, is denoted by To minimize the fatality from an outbreak, some protective measures for high-risk individuals must be implementedI(t) be the number of infectious individuals in the active group at time t. To keep I(t) below the maximum level that the healthcare system can handle, the control scheme has a predetermined threshold I(t) and aims to maintaint is set toI(t) reaches I(t) stays at the threshold level herd immunity threshold, or the threshold share of infected individuals for a population to develop herd immunity15. Thus, herd immunity for the active group  is developed at A.As the disease can spread within the active group, some dynamic control measures should be implemented in this group to avoid the collapse of the healthcare system. Figure mentclass2pt{minimmentclass2pt{minimmentclass2pt{minimA, should be sufficiently high to acquire herd immunity. The last two conditions may be called feasibility conditions. If the proposed strategy is both socially acceptable and feasible, herd immunity approaches of the proposed type would be viable policy options.There are three conditions under which the proposed control policy can be a viable policy option against a novel infectious disease such as COVID-19. First, for social acceptance, the overall mortality should not become too large. Second, the healthcare system should not be overwhelmed. Third, the final number of infected individuals, A is the final cumulative number of infections in the active group. The left-hand side of  acceptable if condition (The first component (a) of the control scheme aims at reducing mortality. Suppose that the society can accept only 9. The flip side of this is that we can substantially reduce the average mortality rate The condition  restrictrelaxing  without effective capacity of the healthcare system, which we denote by service capacity of the healthcare system. To avoid various adverse effects, including a surge in mortality, the service capacity must not be exceeded. Suppose that a given proportion, The second component (b) of the proposed control scheme aims at acquiring herd immunity with limited healthcare resources. The first feasibility requirement for this component is that the control threshold N because N. Furthermore, N because the per capita service capacity for the active group is The effective capacity A, must be sufficiently high to acquire herd immunity for the whole population. Specifically, A should satisfy the following condition for herd immunity as the whole population to be acquired:The last condition requires that the final number of infected individuals in the active group, A is an increasing function of A must be sufficiently high, there is a minimum value N, as the right-hand side of ,,6), the n. The other constants are the per capita healthcare service capacity The variables that appear in our framework are as follows. The policy variables that characterize the proposed control scheme are the size of the active group 9 and the latest estimate for the population composition of the country16.Considering Japan as an example, this section illustrates how we can assess the social acceptability and feasibility of the proposed control scheme. We can define the protected group arbitrarily up to availability of group-specific disease severity data. With age being a key factor for the severity of COVID-19, a pragmatic method of defining the active group would be selecting a threshold age n, Table We observe that the proposed approach, or herd immunity strategies in general, would not be socially acceptable for Japan if the reported estimate of IFR for COVID-19 is not an overestimation. Table ondition  requiresentclass1pt{minimaany form of herd immunity strategies would not be socially acceptable for the country. However, the adopted baseline estimate of the IFR is a pessimistic bound. For instance, various reports suggest that there is a large number of asymptomatic infections19, which can imply 20. This result could be an overestimation, with all its limitations, including the specificity of the employed test kit and selection bias. However, these studies consistently suggest that true IFR can be much smaller than the previous estimates owing to asymptomatic or mild infections.That said, if the reported IFR is true, 9. Based on the assumption that the true IFR of COVID-19 is at least 1/10 times smaller than the reported value, the resulting mortality owing to the proposed strategy becomes the order of 10,000 for Japan (Case 3), which is akin to the average annual influenza-related mortality in the country.Below, as a thought experiment, we assume that the IFR 21. The effective capacity is then given by9 to ensure consistency with the corresponding assumption on Next, we evaluated feasibility by considering Case 3  minimize the resulting mortality and (ii) prevent the collapse of the healthcare system by reducing the proportion of severe cases during the outbreak. The thought experiment with Japanese parameters suggests that the proposed strategy can be an acceptable and feasible option if the “true” severity of the disease  lasts or whether we can develop sufficient immunity against SARS-CoV-2 in the first place remains unknown. If sufficient immunity against the virus cannot be developed, herd immunity strategies, in general, would fail. Because of unanswered questions regarding the pathogen, including the ones mentioned above, extreme care should be taken before adopting any form of herd immunity policies. Should a herd immunity policy be adopted despite the expected risks, some protective measures for high-risk individuals are promising methods to achieve both social acceptability and feasibility.Supplementary material 1


The simplest elasticity model of the foundation underlying a slender beam under flexure was conceived by Winkler, requiring local proportionality between soil reactions and beam deflection. Such an approach leads to well-posed elastostatic and elastodynamic problems, but as highlighted by Wieghardt, it provides elastic responses that are not technically significant for a wide variety of engineering applications. Thus, Winkler’s model was replaced by Wieghardt himself by assuming that the beam deflection is the convolution integral between soil reaction field and an averaging kernel. Due to conflict between constitutive and kinematic compatibility requirements, the corresponding elastic problem of an inflected beam resting on a Wieghardt foundation is ill-posed. Modifications of the original Wieghardt model were proposed by introducing fictitious boundary concentrated forces of constitutive type, which are physically questionable, being significantly influenced on prescribed kinematic boundary conditions. Inherent difficulties and issues are overcome in the present research using a displacement-driven nonlocal integral strategy obtained by swapping the input and output fields involved in Wieghardt’s original formulation. That is, nonlocal soil reaction fields are the output of integral convolutions of beam deflection fields with an averaging kernel. Equipping the displacement-driven nonlocal integral law with the bi-exponential averaging kernel, an equivalent nonlocal differential problem, supplemented with non-standard constitutive boundary conditions involving nonlocal soil reactions, is established. As a key implication, the integrodifferential equations governing the elastostatic problem of an inflected elastic slender beam resting on a displacement-driven nonlocal integral foundation are replaced with much simpler differential equations supplemented with kinematic, static, and new constitutive boundary conditions. The proposed nonlocal approach is illustrated by examining and analytically solving exemplar problems of structural engineering. Benchmark solutions for numerical analyses are also detected. Structural models of beams on an elastic foundation have been widely exploited by the scientific community to describe engineering problems with numerous applications in geotechnics, road, railroad, marine engineering, and biomechanics; see e.g., .The problem of a beam subjected to transverse distributed loading proportional to its deflection was considered by E. Winkler in the framework of the local theory of elasticity . It was However, E. Wieghardt  remarkedIn 1922, Wieghardt proposed a model in which the deflection at each point of the surface of the foundation depends on the response of the entire contact region beam-soil through an integral of soil reactions weighted by a suitable kernel function. The mathematical model thus depends on a stiffness parameter and on an additional parameter entering the averaging kernel. Later on, this problem was tackled by W. Prager  for two-Subsequently, in the framework of the local theory of elasticity, two different soil models characterized by two material parameters were introduced. The former was proposed by M. Filonenko-Borodich  assumingL laying on an elastic foundation. The x-coordinate is taken along the beam length, the y-coordinate is along the thickness (height), and the z-coordinate is along the beam width originating at the cross-sectional elastic centre C. The pair Let us consider a straight beam, with a cross section b the width of the beam cross section in contact with the surface of the elastic soil, the related stiffness is given by The classical Winkler theory of a continuous medium supporting a beam  consiv of the beam coincides with the transverse displacement of the surface of the foundation. According to the classical  Winkler elastic model provided by Equation  integral convolution lawThe refinement originally proposed by Wieghardt , afterwaThe smoothing kernel e, e.g., ,29:(3)ϕ formulation of the Wieghardt elastic foundation Equation  can be eProof of the result above is analogous to the one in  regardinIt is then apparent that ill-posedness of a Bernoulli–Euler beam on an RD model of Wieghardt elastic foundation is related to the incompatibility between kinematic boundary conditions and RDFBCs. In fact, Equation  forces tv of the surface of the elastic foundation in terms of the reaction r and of two fictitious forces In order to by-pass the ill-posedness of the elastostatic problem of a beam on Wieghardt elastic foundation, two fictitious reactive forces exerted by the soil were introduced at the beam end points . AccordiThe elastic equilibrium problem of a beam on the modified Wieghardt elastic foundation is reported for completeness in The motivation of the present paper consists in formulating a well-posed nonlocal integral model of elastic foundation such that no fictitious forces are postulated at the end points of Bernoulli–Euler beams in order to solve the relevant structural problem. Specifically, the nonlocal model of elastic foundation is cast in the framework of Eringen theory ,32,33 reIt is worth recalling that, as acknowledged by the scientific community, Eringen’s strain-driven nonlocal model of internal elasticity is inapplicable to structural problems of applicative interest due to incompatibility between equilibrium and constitutive requirements ,35. On tHowever, the corresponding equations of elastic equilibrium are described by complicated integrodifferential laws , the solIn this paper, the integrodifferential elastic problem of a beam resting on a displacement-driven nonlocal foundation is shown to be equivalent to a much simpler differential problem that can be analytically solved without any additional complication with respect to classical Winkler equations. The key idea consists in proving that the convolution integral describing the nonlocal model of an elastic foundation is equivalent to an ordinary second-order differential equation equipped with nonstandard constitutive boundary conditions. The new approach is exploited to investigate the bending behavior of Bernoulli–Eulerelastic beams on displacement-driven nonlocal foundation for a variety of boundary kinematic constraints of technical interest. The effects of nonlocal parameters and the stiffness coefficient of the Winkler elastic soil on structural transverse displacements, reactions, bending, and shear forces are analytically evaluated and compared with outcomes in literature.x- and y-coordinates and are given byv is the transverse displacement of the cross section and the symbol x.In a Bernoulli–Euler beam, applied loads and geometry are such that the displacements The rotation M isz axis of the distribution of Young’s moduli The stress resultant moment T shear force and The differential equilibrium equation of a beam subject to a distributed transverse load Using the differential condition of equilibrium, the definition of bending curvature Equation , we obtaA well-posed nonlocal model of a beam lying on elastic foundation see  is preser are linked to the transverse displacement v of the surface of the foundation in correspondence to the beam interval Let us assume that reactions r on the characteristic length For simplicity, in the sequel, explicit dependence of The bi-exponential kernel Equation  fulfils x have the same influence on the reactions r at x. Moreover, the characteristic parameter v at a point t decreases with the distance from the considered point x. Denoting by x inside the structural interval, the impulsivity conditionThe symmetry condition Equation  yields rondition3limLc→0+The elastostatic structural problem of a beam resting on nonlocal DD elastic foundation can be formulated by considering the beam elastic equilibrium Equation , with clBox 1A noteworthy result shows that the nonlocal integral Equation (14c) can be replaced with an equivalent differential problem and foundation boundary conditions according to the next proposition proved in Proposition 1The reactions r of the integral equation Equation (14c) with the special kernel Equation  provideswith  elastic foundation). Accordingly, the DD convolution law Equation (14c) can be replaced with the differential equation in Equation  and the v, obtained from Equation .The sixth-order differential equation of the elastic problem Equation  can be sv in the beam interval rThe transverse displacement Equation  in termsFurther, bending moment and shear force fields of the beam are given byIt is worth noting that the elastostatic structural problem of a beam on nonlocal DD elastic foundation is solved without postulating the existence of any fictitious reactive force at the beam end points as it must be done in the modified Wieghardt model.r is the solution of the elastostatic structural problem of the beam on the nonlocal DD elastic foundation. The parameters If the elastic foundation extends outside the beam interval Since the continuity of the displacement field at Equation , the twoHence, the transverse displacement fields Equation  of the sRemark 1.The transverse displacement fields Equation  to obtaiThe solution of the differential Equation  providesEnforcing continuity of the displacement field at Equation , it resuso that the transverse displacement fields of the surface of the elastic foundation Equation  into EquEquation . The traEquation  are thusRemark 2.The transverse displacement fields of the surface of the elastic foundation pertaining to the MRD nonlocal model ing form :The two fictitious forces with Equation , the traIt is worth noting that Equation  turn outWe provide some numerical results of technical interest to illustrate the effectiveness of the proposed methodology for the analysis of Bernoulli–Euler beams on a nonlocal foundation. The free-beam M* nonlocal integral approach. The nonlocal equations governing the relevant structural problem were formulated by conveniently replacing the DD convolution integral characterizing the soil elasticity model with an equivalent nonlocal differential relation and constitutive boundary conditions. No concentrated forces at beam boundary (on model  and its on model ,25, wher


Blind/no-reference image quality assessment is performed to accurately evaluate the perceptual quality of a distorted image without prior information from a reference image. In this paper, an effective blind image quality assessment approach based on entropy differences in the discrete cosine transform domain for natural images is proposed. Information entropy is an effective measure of the amount of information in an image. We find the discrete cosine transform coefficient distribution of distorted natural images shows a pulse-shape phenomenon, which directly affects the differences of entropy. Then, a Weibull model is used to fit the distributions of natural and distorted images. This is because the Weibull model sufficiently approximates the pulse-shape phenomenon as well as the sharp-peak and heavy-tail phenomena of natural scene statistics rules. Four features that are related to entropy differences and human visual system are extracted from the Weibull model for three scaling images. Image quality is assessed by the support vector regression method based on the extracted features. This blind Weibull statistics algorithm is thoroughly evaluated using three widely used databases: LIVE, TID2008, and CSIQ. The experimental results show that the performance of the proposed blind Weibull statistics method is highly consistent with that of human visual perception and greater than that of the state-of-the-art blind and full-reference image quality assessment methods in most cases. The human visual system (HVS) is important for perceiving the world. As an important medium of information transmission and communication, images play an increasingly vital role in human life. Since distortions can be introduced during image acquisition, compression, transmission and storage, the image quality assessment (IQA) method is widely studied for evaluating the influence of various distortions on perceived image quality ,2.In principal, subjective assessment is the most reliable way to evaluate the visual quality of images. However, this method is time-consuming, expensive, and impossible to implement in real-world systems. Therefore, objective assessment of image quality has gained growing attention in recent years. Depending on to what extent a reference image is used for quality assessment, existing objective IQA methods can be classified into three categories: full-reference (FR), reduced-reference (RR) and no-reference/blind (NR/B) methods. Accessing all or part of the reference image information is unrealistic in many circumstances ,5,6,7,8,Many NR IQA metrics focus on assessing a specific type of visual artifact, such as blockiness artifacts , blur diAccording to the dependency on human opinion scores, the generic NR approaches can be roughly divided into two categories : distancLearning-based methods have attracted increasing attention with the development of artificial intelligence. The basic strategy is to learn a regression model that maps the image features directly to a quality score. Various regression methods, including support vector regression (SVR) , neural NSS model-based methods have achieved promising results. The NSS model assumes that natural images share certain statistical regularities and various distortions may change these statistics. Therefore, the NSS model is capable of fitting statistics of natural and distorted images. The GGD model is a typical NSS model that is widely studied and applied. The GGD model in the DCT domain is able to follow the heavy-tail and sharp-peak characteristics of natural images. By using the GGD features, the distorted image quality can be estimated. However, the GGD model has some shortcomings in fitting the statistics of distorted images because the distribution of DCT coefficients shows a pulse-shape phenomenon for distorted images, which is described as the rapid increase of discontinuity. The discontinuity is derived from the differences between the high- and low-frequency coefficients of distorted images. Thus, the pulse-shape phenomenon cannot be fitted by the GGD model, which leads to inaccurate quality assessments.In this paper, an effective blind IQA approach of natural scenes related to entropy differences is developed in the DCT domain. The differences of entropy can be described by probability distribution in distorted images. We find the DCT coefficients’ distribution of distorted images shows a pulse-shape phenomenon in addition to the heavy-tail and sharp-peak phenomena. Since the pulse-shape phenomenon is often neglected in NSS model, image structure cannot be fully presented by image entropy. Therefore, the performance of the IQA methods based on such NSS model can be affected to some extent. To this end, the Weibull model is proposed in this paper to overcome the under-fit caused by the pulse shape phenomenon of traditional GGD model. Furthermore, we prove that the Weibull model correlates well with the human visual perception. Based on the Weibull model, corresponding features are extracted in different scales and the prediction model is derived using the SVR method. Experimental results show that the Weibull statistics (BWS) method consistently outperforms the state-of-the-art NR and FR IQA methods over different image databases. Moreover, the BWS method is a generic image quality algorithm, which is applicable to multiple distortion types.The novelty of our work lies in that we find the pulse-shape phenomenon when using existing GGD model to characterize image distortions. Then, we propose a useful Weibull model to overcome under-fit the pulse-shape phenomenon and extract features related to visual perception from the Weibull model to evaluated image quality. Furthermore, the proposed method has the advantage of high prediction accuracy and high generalization ability.The rest of the paper is organized as follows. Information entropy indicates the amount of information contained within an image and the changes of entropy are highly sensitive to the degrees and types of image distortions. Our method utilizes distribution difference of DCT coefficients that directly affects entropy changes to assess image quality. As reported in the literature ,36, natuThe GGD model, as a typical NSS model, is widely used to fit distribution of AC coefficients in the DCT domain for natural images , and it Weibull Distribution Modela and m are the shape parameter and the scale parameter. The family of Weibull distributions includes the Exponential distribution x approaches zero. The characteristic can be used to describe the pulse-shape phenomenon for the distribution of AC coefficients. m is fixed and a is less than 1, a larger shape parameter a corresponds to a slower change of a is fixed, a larger scale parameter m corresponds to a faster change of To well fit the distribution of AC coefficients for a distorted image, the Weibull distribution model is employed, which is given by :(1)fX(x)We also develop a Weibull model that fits five representative distortion types in the LIVE database: JP2K compression (JP2K), JPEG compression (JPEG), white noise (WN), Gaussian blur (GB), and fast-fading (FF) channel distortions . Figure In this section, we describe the proposed BWS method in detail. The framework is illustrated in One advantage of this approach is that we consider only the change of luminance information in the BWS algorithm because neuroscience research shows that the HVS is highly sensitive to changes in image luminance information . In addiIQA modeling must be able to satisfy human perceptual requirements, which are closely related to HVS. Designing an HVS-based model for directly predicting image quality is infeasible because of the complexity. Therefore, in this paper, the features related to the HVS are extracted from the Weibull model and used to predict perceptual image quality scores by a learning method.The visual perception system has been shown to be highly hierarchical . Visual m and shape parameter a in the Weibull distribution are strongly correlated with brain responses. The experiments on brain responses showed that a and m explain up to 71 % of variance of the early electroencephalogram signal [a and m. In other words, the response of the brain to external image signals is highly correlated with the parameters a and m of the Weibull distribution. Thus, we defined the shape-scale parameter feature a and a and m, considering only the influence of a while ignoring the effect of m on the Weibull distribution does not produce accurate results. Therefore, we chose Before extracting features, we divide the image into m signal . These pm signal . In addiEquation . The EquEquation  is the dThe efficiency of the features is verified in the LIVE database. We extracted the average value of the highest 10% and 100%  of the shape-scale parameter features  regions ,48,49. Te scores . TherefoNatural images are known to be highly correlated ,37. The Therefore, we define the coefficient of variation feature We calculated the average value of the highest 10% of Natural images are highly structured in the frequency domain. Image distortions often modify the local spectral properties of an image so that these properties are dissimilar to those of in natural images . For JP2f. According to the method in [f.To measure this difference, we defined the frequency sub-band feature ethod in , we diviEquation  in the tf, and the average value of 100% of f in all blocks across the image in the LIVE database. In The feature was pooled by calculating the average value of the highest 10% of The HVS also has different sensitivities to sub-bands in different directions . Image dTherefore, this inconsistency can be described by the orientation sub-band feature Equation , in threThe average values of the highest 10% and 100% of Previous research has demonstrated that the incorporation of multi-scale information can enhance the prediction accuracy . The staAfter extracting features in three scales, we learned the relationship between image features and subjective scores. In the literature, SVR is widely adopted as the mapping function for learning this relationship ,52. Cons package  to imple(1)The LIVE database includes 29 reference images and 779 distorted images corrupted by five types of distortions: JP2K, JPEG, WN, GB and FF. Subjective quality scores are provided in the form of DMOS ranging from 0 to 100. Each of the distorted images is associated with a DMOS, representing the subjective quality of this image.(2)The TID2008 database covers 17 distortion types, each of which consists of 100 distorted versions from 25 reference images. Subjective quality scores are provided for each image in the form of MOS, ranging from 0 to 9. Note that there is one artificial image and its distortion images in the TID2008 database. We discarded these images when evaluating the performance of the BWS method because the proposed method was designed to evaluate the quality of natural scenes. In addition, we mainly considered the subsets with JP2K, JPEG, WN and GB distortion types that appear in LIVE database. These four distortion types are also the most commonly encountered distortions in practical applications.(3)The CSIQ database consists of 30 reference images and 866 distorted images corrupted by six types of distortions: JPEG, JP2K, WN, GB, pink Gaussian noise and global contrast decrements. Each distorted image has five different distortion levels. Subjective quality scores are provided in the form of DMOS ranging from 0 to 1. Similarly, we mainly considered the same four distortion types as included the LIVE database.The performance of the blind IQA algorithms was validated using subjective image quality databases, where each image is associated with a human score  Mean Opinion Scores (DMOS/MOS)). The performance describes how well the objective metric is correlated with human ratings. Several subjective image quality evaluation databases have been established. We employed three widely used databases, namely, the LIVE database , the TIDTo evaluate the performance of the BWS algorithm, two correlation coefficients, the Pearson Linear Correlation Coefficient (PLCC) and the SROCC, are used as the criteria. The PLCC measures the prediction accuracy, whereas the SROCC represents the prediction monotonicity. Before calculating the PLCC, the algorithm scores are mapped using a logistic non-linearity as described in . Both thFirst, we evaluated the overall performance of the BWS method and other competing IQA methods, namely, BLIINDS-II , DIIVINEBecause the BWS approach is based on SVR, we randomly divided each image database into two sets: a training set and a testing set. The training set is used to train the prediction model and the testing set is used to test the prediction results. In our experimental setup, 80% of the distorted images for each database are used as the training set and the remaining 20% of the images are used as the testing set. Content does not overlap between these two sets. We repeat the training–testing procedure 1000 times, and the median value of the obtained SROCCs and PLCCs is reported as the final performance of the proposed metric. Meanwhile, we adapted the same experimental setup for comparison algorithms. Although the FR IQA approaches PSNR and SSIM do not require training on a database, for a fair comparison, we also conducted the experiments on the randomly partitioned testing set and recorded the median value of the PLCC and SROCC.Moreover, we present weighted-average SROCC and PLCC results of competing IQA methods on all three databases in To determine whether the superiority of the BWS method over its counterparts is statistical significance, we conducted statistical analysis to validate their differences in performance. The hypothesis testing, which was based on the t-test , was preIn this section, we tested the performances of the proposed BWS method and other competing IQA methods on individual distortion type over the LIVE, TID2008 and CSIQ databases. For NR IQA, we trained on 80% of the distorted images with various distortion types randomly and tested on the remaining 20% of the distorted images with a specific distortion type. The SROCC and PLCC comparisons on each database are illustrated in We observed the advantages of the individual distortion type of the BWS algorithm on each database. For the LIVE database, we clearly found that the proposed metric outperforms other NR metrics in FF. In particular, compared with the BLIINDS-II method, implemented in the same DCT domain, BWS performs better on the JP2K, WN, GB and FF distortion types. For FR metrics, although these methods require the complete information of the reference images, our algorithm still outperforms PSNR on all distortion types and outperforms SSIM on WN and GB distortions. For the TID2008 database, the performance of our method is superior on JP2K distortions relative to other NR metrics. Similarly, the performances on JP2K, WN, and GB distortion are better than those of the BLIINDS-II method. Compared with the FR metric, the performance of the BWS algorithm on the JP2K distortion type is better than those of PSNR and SSIM. For the CSIQ database, our method outperforms the remaining NR metrics on WN and GB distortions. Compared with the BLIINDS-II algorithm, the BWS method consistently performs better. Compared with the FR metric, the performances of BWS on the JPEG and GB types are better than those of PSNR, and on GB and WN the distortion is better than with SSIM. Therefore, we found that the performance of the BWS algorithm is superior on some specific distortion types in each database.To facilitate a comparison of the effects between BWS method and the other IQA methods, 13 groups of distorted images were considered in the three databases. The best two results of the SROCC and PLCC are highlighted in boldface for the NR IQA methods. We calculated the number of times that each method was ranked in the top two in terms of the SROCC values and PLCC values for each distortion type. For the 13 groups of distorted images in the three databases, the BWS algorithm was ranked in the top two the most times, with 10 times for the SROCC and 11 times for the PLCC. We also report the weighted means and standard deviations (STDs) of competing IQA methods across all distortion groups in To visually show the correlation of the BWS method between the predicted quality scores and the subjective scores, we present scatter plots  of the predicted scores and the subjective scores in In our previous experiments, the training samples and test samples were selected from the same database. It is expected that an IQA model that has learned on one image quality database should be able to accurately assess the quality of images in other databases. Therefore, to demonstrate the generality and robustness of the proposed BWS method, the following experiments were conducted. We trained all distorted images from one database to obtain a prediction model and used this model to test the scores of distorted images from other databases. With the three databases, six combinations of training and testing database pairs were created. We compared our proposed BWS algorithm and BLIINDS-II method on the same DCT domain. The SROCC results of the cross-database validation are tabulated in In In the BWS method, we selected sessment ,61,62. TPooling strategy has been studied recently as an important factor to the accuracy of objective quality metrics. In our method, we calculated the average value of the highest 10% of features and that of 100% of features. The highest 10% and the 100% features of all blocks in image describe image distortion of the worst 10% regions and the overall image regions. The averaging of features in all the local regions is one of the widely used methods in image quality metrics. It describes the global distortion of the image. However, when only a small region in an image is corrupted with extremely annoying artifacts, human subjects tend to pay more attention to the low-quality region. Thus, we also considered the image distortion of the worst 10% regions because the human eye is more annoyed by the local distortion of the image and the subjects are likely to focus their quality opinions on the worst 10% of the whole image .We extracted three feature sets: the average values of the highest 10% features, the average values of the 100% features and the combination of the first two feature sets in three scales from the LIVE database. The feature extraction method and the experimental setup were the same as those reported in A multi-scale segmentation method has been developed and implemented for IQA. We proposed multi-scale features for predicting image quality because the perceptibility of image details depends on the viewing conditions. The subjective evaluation of a given image varies with these factors. Therefore, a multi-scale method is an effective method of incorporating image details at different resolutions.We conducted an experiment to determine the impact of scale on IQA. In our method, we selected three scale images for extracting features because no significant gain in performance is obtained beyond the third scale of feature extraction. The methods of scale image segmentation, feature extraction and experiment setup were the same as the previous operation. We report the correlations of different scales between the predicted scores and the subjective scores on the LIVE database in In many practical applications, the prediction accuracy and the algorithm complexity need to be considered comprehensively. Therefore, we evaluated the computational complexity of all competing methods in Since there exists a strong relationship between the changes of entropy and distribution of images, existing NR IQA models typically use the GGD model to fit the distribution of a natural image in the DCT domain and extract features from this model to learn a quality prediction model. However, the difference between the distribution of the distorted image and that of its natural image, which includes the pulse-shape phenomenon, is neglected. In this paper, we propose the BWS method, which is a new NR IQA method based on the Weibull model in the DCT domain. The most important pulse-shape phenomenon is first considered in the distorted image distribution. The proposed Weibull model not only overcomes the disadvantages of the GGD model but also reflects HVS perception. Our research findings suggest that the Weibull model plays an important role in quality assessment tasks. Extensive experimental results on three public databases have demonstrated that the proposed BWS method is highly correlated with human visual perception and competitive with the state-of-the-art NR and FR IQA methods in terms of prediction accuracy and database independence.


Aim: The aim of this study was to evaluate and compare two different techniques for the treatment of plaque-induced gingivitis, demonstrating whether the causal therapy supported by diode laser can allow a resolution of the edema caused by gingivitis in less time compared to the single traditional causal therapy. Materials and methods: Twenty-five patients between 20 and 60 years of age with a specific diagnosis of gingivitis were evaluated at the CLID-HSR oral hygiene department. Once the clinical parameters  were recorded, each of them was subjected to a professional oral hygiene session and instructed in correct home hygiene procedures. Through a split-mouth protocol for each individual patient, hemi-arches were treated by simple randomization to be treated with causal therapy supported by the action of the diode laser  and which with traditional causal therapy (control therapy). A first intraoral scan was performed before therapy (T0), which was repeated 20 min after rinsing with CHX. The intraoral scans were repeated at a control 7 (T1) and 14 days (T2) after the session. For each intraoral scan, a volumetric value was calculated, proportional to the edema of the gingival tissues, using special digital software. The operator who carried out the volumetric measurements on the software was not aware of the therapy implemented on each half-arch. The operator who carried out the statistical analysis was not aware of the therapy applied to each group. The collected data were statistically compared in order to detect any differences between the volumetric variations between the two therapy groups and within the therapy groups over time. After evaluating the distribution of data by means of the Kolmogorov-Smirnov statistical test, the appropriate nonparametric tests were chosen to carry out the statistical comparisons. Results: Based on the analysis of the gingival-periodontal health parameters and the volumetric value of the treated areas, no statistically significant differences were detected between the areas treated with the adjuvant action of the diode laser compared to those treated with causal therapy alone. Conclusions: With the limitations of this study, in accordance with the statistical results obtained, diode laser therapy does not allow a faster resolution of gingival edema compared to traditional therapy; the two treatment techniques for plaque-induced gingivitis, therefore, have the same efficacy. Gingivitis is an inflammatory process caused by the presence of bacteria, which, starting from the gingival margin, can also spread to the rest of the gum ,2,3. EveThe present pilot study was conducted on a sample of 25 patients, aged between twenty and sixty years. All patients were recruited from the CLID oral hygiene department within the Scientific Hospitalization and Care Institute, San Raffaele Hospital. The sample was made up of specially selected individuals with a specific diagnosis of gingivitis.The study protocol was approved by the Local Ethics Committee, Milan, no. PR246 and written informed consent was obtained from all study participants in accordance with the Helsinki Declaration.In order to participate in the study, patients in good health, free of oral and periodontal systemic diseases, were selected. Left-handed patients were excluded. The whole sample must have completed any drug therapy with antibiotics and anti-inflammatories at least two weeks before participating in the study.Inflammation caused by systemic factors; a typical example is represented by pregnancy or by hormonal upheavals such as puberty or menstruation.Phlogistic-hyperplastic alterations in conjunction with the intake of antiepileptics, calcium channel blockers, and cyclosporine.Gingivitis caused by the use of oral contraceptives.Gingivitis modified by systemic diseases.Gingivitis affecting patients with diabetes mellitus.Gingivitis associated with disorders of the blood picture .Plaque gingivitis modified by malnutrition, such as chronic deficiency of vitamins A, C, and D .Patients with a specific diagnosis of nonplaque-induced gingivitis were also excluded :The participants were informed about the methods of the experimental study and about the objectives and purposes of the latter. Subsequently, before proceeding, patients had to sign the Informed Consent, in which the protocol was accurately described. Clinical parameters  were initially evaluated and recorded in all patients. The standard parameters of plaque index, bleeding index, etc. were evaluated to exclude that the patient could have periodontal disease through the PSR Periodontal Screening and Recording), which consists of a simplified registration of clinical findings. With the PSR, in fact, all the sites of all the dental elements are explored with a periodontal probe, after completing the anamnestic surveys. A first intraoral scan prior to therapy was then performed, which consists of a reference scan; this was repeated at twenty minutes, after having made the patient rinse with 0.2% CHX (T0). Each of them was subjected to the professional oral hygiene session, and through a split-mouth protocol, for each individual patient, they were chosen by simple randomization which hemi-arches to treat with causal therapy assisted by the action of the diode laser  and which with traditional causal therapy (control therapy). At the end of the session, each individual patient was instructed on correct home oral hygiene procedures. Subsequently, a control scan was performed 7 days after the session (T1) and 14 days (T2), during which the clinical indexes were resumed. For the clinical application of tissue biostimulation, the Raphael Laser , a medic2, capable of emitting a collimated Gaussian beam with very low divergence. The instrument has been positioned at 12−mm perpendicular to the site, thus reducing reflection bias. The movement is defined as “lawn mowing” in the apico-coronal direction. The application time of 80 s for each site and output power set to 2−3.5 W, average fluency of 10 J/cm2 and average power density (at the target) was 0.125 W/cm2 with a cumulative density dose of 20 J per site for each treatment (max n. of treatment 4 × 20 J = 80 J).The diode laser protocol has been the subject of study at our university center, Vita Salute San Raffaele; the study protocol concerns the Raphael diode laser . The laser works continuously with a 3003−3020 μm optical fiber connected to a probe with an output surface of 0.5 cmFor each intraoral scan, the CS 3600 intraoral scanner from Carestream Dental was used by the dentist.mandiblemaxillabuccal occlusal registrationCS 3600 has been designed to acquire 3D still images in the following ways:Partial scan of the arch: several teeth in the preparation area on the mandible and maxilla, and a buccal occlusal registration.Complete scan of the arch: maxilla, mandible and buccal occlusal registration.The CS 3600 system adopts the following software: Imaging software (CS orthodontic imaging) and CS 3600 acquisition interface. The CS 3600 acquisition interface has made it possible to acquire images in two ways:The collected data were processed in double-blind since the operator who carried out the static and volumetric analyzes was not aware of the group belonging to the data deriving from the patients. These data were then statistically compared in order to detect any differences between the volumetric variations and through the analysis of the gingival-periodontal health parameters between the two therapy groups and within the therapy groups over time.The normality of the distribution was tested by Shapiro–Wilk test, and given the non-normality of the data distribution, nonparametric methods were applied. The statistical analyzes were then performed by comparing the two therapy groups with the Mann–Whitney test and the effectiveness of the therapy between T0 and T2 using Friedman’s test.Once the scans were collected, they were selected to carry out the analysis, the pre-treatment scan (T1), and the scan performed after two weeks (T2).First, all the detected scans that were presented in STL format were imported into the data management software.The STL files were imported into a scanning software: Optical Revenge Dental 5.0.Once imported, both scans obtained simultaneously from the same mouth in half-arches were divided , creatinIn this way, the operator obtained four hemi-arches from each individual scan. Once these sections are obtained, the sectoral alignment by hemi-arch is followed so as to be able to proceed with the volumetric analysis. This operation allowed the alignment of two sections of the same subject which takes place automatically  by the sIn this second phase, hard tissues were used as reference points.Once superimposed, the images were associated with the same two different colors  to perfoAfter the alignment procedure, cleaning operations were carried out (mesh cleaning) to delimit the area to be analyzed.In order to create a solid for each individual impression and perform an evaluation as detailed as possible, the Exocad Model Creator program was used. It allowed to use a fixed surface  as the bThis step was made for the sections of both scans so that the two sections presented the exact same distance at the highest point. In this way, the STL files that were previously open have been closed .This procedure was necessary to make the two sections completely superimposable in order to continue with the volumetric analysis.Finally, the files were imported  into theIn conclusion, a colorimetric evaluation was performed through a special analysis tool that made it possible to evaluate the volume using the colorimetric scale. This analysis tool used the micron as the reference unit of measurement and made it possible to evaluate the volume of an area or of the whole section through the colorimetric scale  which inTo perform all these evaluations, however, it was necessary that the files were as similar as possible. For this purpose, sections of the scans obtained have been created.The collected data were statistically compared in order to detect any differences between the volumetric variations between the two therapy groups and within the therapy groups over time. Statistical comparisons regarding the analysis of PI and BoP parameters are illustrated in After evaluating the distribution of data through the Kolmogorov–Smirnov statistical test, the appropriate nonparametric tests were chosen to carry out the statistical comparisons. Given certain values for each patient, no significant differences were found in the comparison between the two therapy groups. On the basis of the analysis of the gingival–periodontal health parameters and the volumetric value of the treated areas, no statistically significant differences were detected between the areas treated with the adjuvant action of the diode laser compared to those treated with causal therapy alone.The periodontium includes the following tissues: gingiva, periodontal ligament, root cement, alveolar bone  . The ginGingivitis is an inflammatory process caused by the presence of bacteria, which starting from the gingival margin, can also spread to the rest of the gum ,2,3. TheThe task of the dentist and dental hygienist is to monitor the patient so as to avoid progression or any recurrence of these pathologies, restoring a state of health of the tooth support tissues and allowing the success of implant-prosthetic rehabilitations over time ,48,49,50The intensity of clinical signs and symptoms of gingival inflammation can vary both between different individuals and between sites in the same mouth ,32. NormThe diode laser is a semiconductor. The wavelengths of diode lasers most commonly used in dentistry range from 610 to 980 nanometers. It can work in both continuous and intermittent wave (PW) modes. When interacting with the surface of the fabric, the laser light can be refracted, diffused, absorbed, or transmitted. The laser energy absorbed by the tissues can cause heating, coagulation, or vaporization effects depending on the wavelength, power, and optical properties of the tissue . As partIn reality, compared to what has been shown by the studies mentioned above, the literature is controversial: as reported by several authors, the diode laser, associated with the traditional method, does not provide statistically significant results in microbiological terms and the reduction of clinical signs of gingival inflammation ,49,50. IWith the limitations of this study, such as the possible inter-individual variability in terms of compliance, in accordance with the statistical results obtained, diode laser therapy does not allow a faster resolution of gingival edema compared to traditional therapy; the two treatment techniques for plaque-induced gingivitis, therefore, have the same efficacy. Further studies are needed to confirm the results obtained.