REFLECTIVE FUNCTION AND PERIODIC SOLUTION OF DIFFERENTIAL SYSTEMS

This article deals with the reflective function of the mth-order nonlinear differential systems.The results are applied to discussing the stability property of periodic solutions of these systems.

The Reflective Function of Differential System

This article deals with the reflective function of the differential systems. The results are applied to discussion of the existence and stability of the periodic solutions of these systems.

Three-Component Model for Bidirectional Reflection Distribution Function of Thermal Coating Surfaces

We present a bidirectional reflection distribution function （BRDF） model for thermal coating surfaces based on a three-component reflection assumption, in which the specular reflection is given according to the microfacet theory and Snell＇s law, the multiple reflection is considered Nth cosine distributed, and the volume scattering is uniformly distributed in reflection angles according to the experimental results. This model describes the reflection characteristics of thermal coating surfaces more completely and reasonably. Simulation and measurement results of two thermal coating samples SR107 and S781 are given to validate that this three-component model significantly improves the modeling accuracy for thermal coating surfaces compared with the existing BRDF models.

Model of bidirectional reflectance distribution function for metallic materials

Based on the three-component assumption that the reflection is divided into specular reflection,directional diffuse reflection,and ideal diffuse reflection,a bidirectional reflectance distribution function（BRDF） model of metallic materials is presented.Compared with the two-component assumption that the reflection is composed of specular reflection and diffuse reflection,the three-component assumption divides the diffuse reflection into directional diffuse and ideal diffuse reflection.This model effectively resolves the problem that constant diffuse reflection leads to considerable error for metallic materials.Simulation and measurement results validate that this three-component BRDF model can improve the modeling accuracy significantly and describe the reflection properties in the hemisphere space precisely for the metallic materials.

Bidirectional reflectance one-dimensional rough distribution function modeling of surface in the microwave band

In this study, the bidirectional reflectance distribution function （BRDF） of a one-dimensional conducting rough surface and a dielectric rough surface are calculated with different frequencies and roughness values in the microwave band by using the method of moments, and the relationship between the bistatic scattering coefficient and the BRDF of a rough surface is expressed. From the theory of the parameters of the rough surface BRDF, the parameters of the BRDF are obtained using a genetic algorithm. The BRDF of a rough surface is calculated using the obtained parameter values. Further, the fitting values and theoretical calculations of the BRDF are compared, and the optimization results are in agreement with the theoretical calculation results. Finally, a reference for BRDF modeling of a Gaussian rough surface in the microwave band is provided by the proposed method.

STABILITY OF DIFFERENTIAL SYSTEMS

This article deals with the reflecting function of the differential systems. The results are applied to discuss the stability of these differential systems.

A Synergic Algorithm for Retrieval of Aerosol Optical Depth over Land

In this paper, a novel algorithm for aerosol optical depth（AOD） retrieval with a 1 km spatial resolution over land is presented using the Advanced Along Track Scanning Radiometer （AATSR） dual-view capability at 0.55, 0.66 and 0.87μm, in combination with the Bi-directional Reflectance Distribution Function （BRDF） model, a product of the Moderate Resolution Imaging Spectroradiometer （MODIS）. The BRDF characteristics of the land surface, i.e. prior input parameters for this algorithm, are computed by extracting the geometrical information from AATSR and reducing the kernels from the MODIS BRDF/Albedo Model Parameters Product. Finally, AOD, with a i km resolution at 0.55, 0.66 and 0.87 μm for the forward and nadir views of AATSR, can be simultaneously obtained. Extensive validations of AOD derived from AATSR during the period from August 2005 to July 2006 in Beijing and its surrounding area, against in-situ AErosol RObotic NETwork （AERONET） measurements, were performed. The AOD difference between the retrievals from the forward and nadir views of AATSR was less than 5.72%, 1.9% and 13.7%, respectively. Meanwhile, it was found that the AATSR retrievals using the synergic algorithm developed in this paper are more favorable than those by assuming a Lambert surface, for the coefficient of determination between AATSR derived AOD and AERONET mearured AOD, decreased by 15.5% and 18.5%, compared to those derived by the synergic algorithm. This further suggests that the synergic algorithm can be potentially used in climate change and air quality monitoring.

Degree of polarization based on the three-component pBRDF model for metallic materials

An expression of degree of polarization（DOP） for metallic material is presented based on the three-component polarized bidirectional reflectance distribution function（p BRDF） model with considering specular reflection, directional diffuse reflection and ideal diffuse reflection. The three-component p BRDF model with a detailed reflection assumption is validated by comparing simulations with measurements. The DOP expression presented in this paper is related to surface roughness, which makes it more reasonable in physics. Test results for two metallic samples show that the DOP based on the three-component p BRDF model accords well with the measurement and the error of existing DOP expression is significantly reduced by introducing the diffuse reflection. It indicates that our DOP expression describes the polarized reflection properties of metallic surfaces more accurately.

Modeling of radiative properties of metallic microscale rough surface

The radiative properties of a gold surface with one-dimensional Gaussian random roughness distribution were obtained with the finite-difference time-domain （FDTD） method and the recursive convolution treatment of the Drude Model. The bi-directional reflection distribution function （BRDF） for both TM mode and TE mode were obtained and compared with the highly accurate experimental data from the earlier work. The incident wavelength varies from 1.152 μm to 3.392 μm and incident angle is at 300-70°, respectively. The results show that, the predicted values and experimental results are in good agreement. The highly specular peak in the BRDF is reproduced in the numerical simulations, and the increase of the TM mode BRDF is found to be attributed to the effect of a variation in the optical constant at the incident wavelength period.

Error Detection and Pattern Prediction Through Phase II Process Monitoring

The continuous monitoring of the machine is beneficial in improving its process reliability through reflected power function distribution.It is substantial for identifying and removing errors at the early stages of production that ultimately benefit the firms in cost-saving and quality improvement.The current study introduces control charts that help the manufacturing concerns to keep the production process in control.It presents an exponentially weighted moving average and extended exponentially weighted moving average and then compared their performance.The percentiles estimator and the modified maximum likelihood estimator are used to constructing the control charts.The findings suggest that an extended exponentially weighted moving average control chart based on the percentiles estimator performs better than exponentially weightedmoving average control charts based on the percentiles estimator and modified maximum likelihood estimator.Further,these results will help the firms in the early detection of errors that enhance the process reliability of the telecommunications and financing industry.

Shape recovery using high dynamic range images

An effective method for object shape recovery using HDRIs （high dynamic range images） is proposed. The radiance values of each point on the reference sphere and target object are firstly calculated, thus the set of candidate normals of each target point are found by comparing its radiance to that of each reference sphere point. In single-image shape recovery, a smoothness operation is applied to the target normals to obtain a stable and reasonable result; while in photometric stereo, radiance vectors of reference and target objects formed due to illuminations under different fight source directions are directly compared to get the most suitable target normals. Finally, the height values can be recovered from the resulting normal field. Because diffuse and specular reflection are handled in an unified framework with radiance, our approach eliminates the limitation presented in most recovery strategies, i.e., only Lambertian model can be used. The experiment results from the real and synthesized images show the performance of our approach.

Comparative Study on Polarization Spectral Parameters of Fruit in Southern Xinjiang Based on Roujean Model

Based on the study of phase angle and wavelength in pBRDF (Polarized bidirectional reflectance distribution function), roujean model was proposed to describe Orient (Polarization phase angle) quantitatively. The Roujean model was used to quantitatively describe different fruits intensity components (F00) and polarization phase angle (Orient), and the simulation results were analyzed and compared using statistical analysis and comparison methods to realize the prediction from the regular model to the outdoor fruit tree canopy to the canopy of outdoor fruit tree canopy random distribution. The experimental results showed that: 1) when the phase angle of jujube was 52.19°, 66.51° and 88.26°, the R2 and average errors of F00 parameters described by Roujean model are 0.9982, 0.9963, 0.9912 and 3.80%, 4.17%, 6.40%, respectively; and the R2 and average error of Orient parameters described by Roujean model are 0.9056, 0.9223, 0.9260 and 6.23%, 3.32%, 8.05%, respectively;It can be seen that roujean model can quantitatively describe the Orient parameter of jujube;2) When the phase angle of apricot was 70.99°, 71.28° and 67.91°, the R2 and average errors of F00 parameters described by Roujean model is 0.9862, 0.9823, 0.9792 and 3.40%, 4.82%, 5.19%, respectively; And the R2 and average error of Orient parameters described by Roujean model are 0.9382, 0.8947, 0.8849 and 7.19%, 9.28%, 9.47%, respectively. Roujean model can also quantitatively describe the Orient parameter of white apricot. In summary, the Roujean model can provide a good quantitative description of f00 and a good quantitative description of Orient, which in turn can predict the pBRDF parameter for more fruits with different incidence and detection directions. It can correct the influence of angle factor in the nondestructive testing of outdoor fruits.

A Note on the Solution of Water Wave Scattering Problem Involving Small Deformation on a Porous Channel-Bed

The solution of water wave scattering problem involving small deformation on a porous bed in a channel, where the upper surface is bounded above by an infinitely extent rigid horizontal surface, is studied here within the framework of linearized water wave theory. In such a situation, there exists only one mode of waves propagating on the porous surface. A simplified perturbation analysis, involving a small parameter ε （≤1） , which measures the smallness of the deformation, is employed to reduce the governing Boundary Value Problem （BVP） to a simpler BVP for the first-order correction of the potential function. The first-order potential function and, hence, the first-order reflection and transmission coefficients are obtained by the method based on Fourier transform technique as well as Green＇s integral theorem with the introduction of appropriate Green＇s function. Two special examples of bottom deformation： the exponentially damped deformation and the sinusoidal ripple bed, are considered to validate the results. For the particular example of a patch of sinusoidal ripples, the resonant interaction between the bed and the upper surface of the fluid is attained in the neighborhood of a singularity, when the ripples wavenumbers of the bottom deformation become approximately twice the components of the incident field wavenumber along the positive x -direction. Also, the main advantage of the present study is that the results for the values of reflection and transmission coefficients are found to satisfy the energy-balance relation almost accurately.

Vector Radiative Transfer in a Vertically Inhomogeneous Scattering and Emitting Atmosphere. Part Ⅱ: Coupling with Azimuthally Asymmetric Polarized Bidirectional Reflection over Oceans

The reflection of ocean surface is often assumed azimuthally symmetric in the previous vector discrete ordinate radiative transfer(VDISORT)and many other radiative transfer solvers.This assumption can lead to obvious errors in the simulated radiances.In this study,the vector radiative transfer equation is solved with a polarized bidirectional reflection distribution function(pBRDF)for computing the surface-leaving radiation from the lower boundary.An azimuthally asymmetric pBRDF model at visible and infrared bands over oceans is fully coupled with the updated VDISORT model.The radiance at the ocean surface is combined with the contributions of atmospheric scattering and surface properties.It is shown that the radiance at the ocean surface also exhibits a strong angular dependence in the Stokes vector and the magnitudes of I.Q.and V increase for a larger azimuthal dependence of pBRDF.In addition,the solar position affects the peaks of sun glitter pattern,thus modulating the signal magnitudes and the angular distributions.As ocean wind increases,the reflection weakens with reduced magnitudes of Stokes parameters and lessvarying angular distributions.

Visible characteristics of space-based targets based on bidirectional reflection distribution function

A precise modeling method of visible characteristics of the space-based target was presented based on bidirectional reflection distribution function (BRDF). The background characteristics of the space-based target were represented to build models of direct solar radiation and reflected radiation of the Earth based on blackbody radiation theory. The geometry characteristics of the target were analyzed to establish a surface equation of each surface based on its body coordinate system. The material characteristics of the target surface were described by introducing a BRDF model which considers the character of surface Gauss statistics and self-shadow and is obtained by measurement and modeling in advance. The relative positions of the space-based target, the background radiation sources and the observation platform were determined based on coordinate con- version to judge contributing surface of the target to observation system. Then a mathematical model on visible characteristics of the space target for the given optical system was built by summing reflection components of all the surfaces. Simulation of visible characteristics of the space-based target in orbit was achieved according to its given geometrical dimensions, physical parameters and orbital parameters. The results show that the method is effective for analysis on visible characteristics of the space-based target when single reflection is considered and its surface is regularly described in a surface equation, which provides a way to real-time calculation of visible characteristics of the space-based target.

Kostka functions associated to complex reflection groups and a conjecture of Finkelberg-Ionov

Kostka functions K_(λ,μ)~±(t), indexed by r-partitions λ and μ of n, are a generalization of Kostka polynomials K_(λ,μ)(t) indexed by partitions λ,μ of n. It is known that Kostka polynomials have an interpretation in terms of Lusztig's partition function. Finkelberg and Ionov(2016) defined alternate functions K_(λ,μ)(t) by using an analogue of Lusztig's partition function, and showed that K_(λ,μ)(t) ∈Z≥0[t] for generic μ by making use of a coherent realization. They conjectured that K_(λ,μ)(t) coincide with K_(λ,μ)^-(t). In this paper, we show that their conjecture holds. We also discuss the multi-variable version, namely, r-variable Kostka functions K_(λ,μ)~±(t_1,…,t_r).

THE DIFFERENTIAL SYSTEMS WITH THE SAME REFLECTING FUNCTION

Using reflecting function of Mironenko we construct some difFerential sy-stems which are equivalent to the given differential system.

An attention-embedded GAN for SVBRDF recovery from a single image

Learning-based approaches have made substantial progress in capturing spatially-varying bidirectional reflectance distribution functions(SVBRDFs)from a single image with unknown lighting and geometry.However,most existing networks only consider per-pixel losses which limit their capability to recover local features such as smooth glossy regions.A few generative adversarial networks use multiple discriminators for different parameter maps,increasing network complexity.We present a novel end-to-end generative adversarial network(GAN)to recover appearance from a single picture of a nearly-flat surface lit by flash.We use a single unified adversarial framework for each parameter map.An attention module guides the network to focus on details of the maps.Furthermore,the SVBRDF map loss is combined to prevent paying excess attention to specular highlights.We demonstrate and evaluate our method on both public datasets and real data.Quantitative analysis and visual comparisons indicate that our method achieves better results than the state-of-the-art in most cases.

First Look of Surface Vegetation from the Advanced Geostationary Radiation Imager(AGRI) onboard Fengyun-4B

For many years, the status of surface vegetation has been monitored by using polar-orbiting satellite imagers such as Moderate Resolution Imaging Spectroradiometer(MODIS). However, limited availability of clear-sky samples makes the derived vegetation index dependent on multiple days of observations. High-frequency observations from the geostationary Fengyun(FY) satellites can significantly reduce the influence of clouds on the synthesis of terrestrial normalized difference vegetation index(NDVI). In this study, we derived the land surface vegetation index based on observational data from the Advanced Geostationary Radiation Imager(AGRI) onboard the FY-4B geostationary satellite. First, the AGRI reflectance of visible band and near-infrared band is corrected to the land surface reflectance by the 6S radiative transfer model. The bidirectional reflectance distribution function(BRDF) model is then used to normalize the AGRI surface reflectance at different observation angles and solar geometries, and an angle-independent reflectance is derived. The AGRI surface reflectance is further corrected to the MODIS levels according to the AGRI spectral response function(SRF). Finally, the daily AGRI data are used to synthesize the surface vegetation index. It is shown that the spatial distribution of NDVI images retrieved by single-day AGRI is consistent with that of 16-day MODIS data. At the same time, the dynamic range of the revised NDVI is closer to that of MODIS.

Innovative Analysis Ready Data(ARD)product and process requirements,software system design,algorithms and implementation at the midstream as necessary-but-notsuffcient precondition of the downstream in a new notion of Space Economy 4.0-Part 1:Problem background in Artificial General Intelligence(AGI)

Aiming at the convergence between Earth observation(EO)Big Data and Artificial General Intelligence(AGI),this two-part paper identifies an innovative,but realistic EO optical sensory imagederived semantics-enriched Analysis Ready Data(ARD)productpair and process gold standard as linchpin for success of a new notion of Space Economy 4.0.To be implemented in operational mode at the space segment and/or midstream segment by both public and private EO big data providers,it is regarded as necessarybut-not-sufficient“horizontal”(enabling)precondition for:(I)Transforming existing EO big raster-based data cubes at the midstream segment,typically affected by the so-called data-rich information-poor syndrome,into a new generation of semanticsenabled EO big raster-based numerical data and vector-based categorical(symbolic,semi-symbolic or subsymbolic)information cube management systems,eligible for semantic content-based image retrieval and semantics-enabled information/knowledge discovery.(II)Boosting the downstream segment in the development of an ever-increasing ensemble of“vertical”(deep and narrow,user-specific and domain-dependent)value–adding information products and services,suitable for a potentially huge worldwide market of institutional and private end-users of space technology.For the sake of readability,this paper consists of two parts.In the present Part 1,first,background notions in the remote sensing metascience domain are critically revised for harmonization across the multidisciplinary domain of cognitive science.In short,keyword“information”is disambiguated into the two complementary notions of quantitative/unequivocal information-as-thing and qualitative/equivocal/inherently ill-posed information-as-data-interpretation.Moreover,buzzword“artificial intelligence”is disambiguated into the two better-constrained notions of Artificial Narrow Intelligence as part-without-inheritance-of AGI.Second,based on a betterdefined and better-understood vocabulary of multidisciplinary terms,existing EO optical sensory image-derived Level 2/ARD products and processes are investigated at the Marr five levels of understanding of an information processing system.To overcome their drawbacks,an innovative,but realistic EO optical sensory image-derived semantics-enriched ARD product-pair and process gold standard is proposed in the subsequent Part 2.