High-order perturbed corrections with scaling transformation

The performance of the so-called superconvergent quantum perturbation theory （Wenhua Hal et al2000 Phys. Rev. A 61 052105） is investigated for the case of the ground-state energy of the helium-like ions. The scaling transformation τ → τ/Z applied to the Hamiltonian of a two-electron atomic ion with a nuclear charge Z （in atomic units）. Using the improved Rayleigh-SchrSdinger perturbation theory based on the integral equation to helium-like ions in the ground states and treating the electron correlations as perturbations, we have performed a third-order perturbation calculation and obtained the second-order corrected wavefunctions consisting of a few terms and third-order energy corrections. We find that third-order and higher-order energy corrections are improved with decreasing nuclear charge. This result means that the former is quadratically integrable and the latter is physically meaningful. The improved quantum perturbation theory fits the higher-order perturbation case. This work shows that it is a development on the quantum perturbation problem of helium-like systems.

SIMPLIFIED SCALING TRANSFORMATION FOR THE NUMERICAL SIMULATION OF MEMS DEVICES WITH THIN FILM STRUCTURES

Thin film is a widely used structure in the present microelectromechanical systems （MEMS） and plays a vital role in many functional devices. However, the great size difference between the film＇s thickness and its planar dimensions makes it difficult to study the thin film performance numerically. In this work, a scaling transformation was presented to make the different dimensional sizes equivalent, and thereby, to improve the grid quality considerably. Two numerical experiments were studied to validate the present scaling transformation method. The numerical results indicated that the largest grid size difference can be decreased to one to two orders of magnitude by using the present scaling transformation, and the memory required by the numerical simulation, i.e., the total grid number, could be reduced by about two to three orders of magnitude, while the numerical accuracies with and without this scaling transformation were nearly the same.

In the Atmosphere and Oceanic Fluids:Scaling Transformations,Bilinear Forms,Bäcklund Transformations and Solitons for A Generalized Variable-Coefficient Korteweg-de Vries-Modified Korteweg-de Vries Equation

The atmosphere is an evolutionary agent essential to the shaping of a planet,while in oceanic science and daily life,liquids are commonly seen.In this paper,we investigate a generalized variable-coefficient Korteweg-de Vriesmodified Korteweg-de Vries equation for the atmosphere,oceanic fluids and plasmas.With symbolic computation,beginning with a presumption,we work out certain scaling transformations,bilinear forms through the binary Bell polynomials and our scaling transformations,N solitons(with N being a positive integer)via the aforementioned bilinear forms and bilinear auto-Bäcklund transformations through the Hirota method with some solitons.In addition,Painlevé-type auto-Bäcklund transformations with some solitons are symbolically computed out.Respective dependences and constraints on the variable/constant coefficients are discussed,while those coefficients correspond to the quadratic-nonlinear,cubic-nonlinear,dispersive,dissipative and line-damping effects in the atmosphere,oceanic fluids and plasmas.

A graph autoencoder network to measure the geometric similarity of drainage networks in scaling transformation

Similarity measurement has been a prevailing research topic geographic information science.Geometric similarity measurement inin scaling transformation(GSM_ST)is critical to ensure spatial data quality while balancing detailed information with distinctive features.However,GSM_ST is an uncertain problem due to subjective spatial cognition,global and local concerns,and geometric complexity.Traditional rule-based methods considering multiple consistent conditions require subjective adjustments to characteristics and weights,leading to poor robustness in addressing GSM_ST.This study proposes an unsupervised representation learning framework for automated GSM_ST,using a Graph Autoencoder Network(GAE)and drainage networks as an example.The framework involves constructing a drainage graph,designing the GAE architecture for GSM_ST,and using Cosine similarity to measure similarity based on the GAE-derived drainage embeddings in different scales.We perform extensive experiments and compare methods across 71 drainage networks duringfive scaling transformations.The results show that the proposed GAE method outperforms other methods with a satisfaction ratio of around 88%and has strong robustness.Moreover,our proposed method also can be applied to other scenarios,such as measuring similarity between geographical entities at different times and data from different datasets.

The Application of Continuous Spatial Scaling Model of NDVI in Validation and Its Sensibility Analysis to Various Image Characteristics

Based on the fractal theory, this study establishes a Continuous Spatial Scaling Model （CSSM） of the Normalized Difference Vegetation Index （NDVI） to address issues arising with spatial up-scaling in quantitative remote sensing. This model is able to quantitatively describe transformation relationships of the NDVI on continuous scales. Then the following experiments are accomplished： （1） the validation of ETM＋ NDVI imagery is implemented based on the GEOEYE-1 image and its NDVI CSSM, and the following conclusion is obtained： because of bad stripes in the ETM＋ image and the limited effect of destriping, the ETM＋ NDVI image had a rather large error, and the error for the entire experimental imagery is about 25%, so the ETM＋ NDVI product is not suitable for direct practical application; （2） Shatian Byland （Beihai City, China） is taken as the experimental area, and four images （two ETM＋ images with wider and smaller coverage, respectively, a GEOEYE-1 image, and an HJ-1B CCD1 image） are studied. The most suitable scale levels are computed and compared for the four images, and a better understanding is obtained of the impact of various image characteristics （area of coverage, spatial resolution, and imaging quality） on determining the scale level for the NDVI CSSM.

Comment on 'The scale-transformation of electromagnetic theory and its applications','Distribution characteristic of scattering field for an ellipsoidal target irradiated by an electromagnetic wave from an arbitrary direction' and 'Electric fields inside a

It is shown that the ’scale-transformation’ method proposed by Li Ying-Le et al.is not applicable to the Maxwell theory.

Scale effect removal and range migration correction for hypersonic target coherent detection

The detection of hypersonic targets usually confronts range migration(RM)issue before coherent integration(CI).The traditional methods aiming at correcting RM to obtain CI mainly considers the narrow-band radar condition.However,with the increasing requirement of far-range detection,the time bandwidth product,which is corresponding to radar’s mean power,should be promoted in actual application.Thus,the echo signal generates the scale effect(SE)at large time bandwidth product situation,influencing the intra and inter pulse integration performance.To eliminate SE and correct RM,this paper proposes an effective algorithm,i.e.,scaled location rotation transform(ScLRT).The ScLRT can remove SE to obtain the matching pulse compression(PC)as well as correct RM to complete CI via the location rotation transform,being implemented by seeking the actual rotation angle.Compared to the traditional coherent detection algorithms,Sc LRT can address the SE problem to achieve better detection/estimation capabilities.At last,this paper gives several simulations to assess the viability of ScLRT.

A Novel Dynamic Stretching Solution to Eliminate Saturation Effect in NDVI and Its Application in Drought Monitoring

The normalized difference vegetation index(NDVI) is one of the key input variables for developing drought indices.However,the NDVI quickly saturates in high vegetation surfaces,and thus,the generalization of a drought index over different ecosystems becomes a challenge.This paper presents a novel,dynamic stretching algorithm to overcome the saturation effect in NDVI.A scaling transformation function to eliminate saturation effects when the vegetation fraction(VF) is large is proposed.Dynamic range adjustment is conducted using three coefficients,namely,the normalization factor(a),the stretching range controlling factor(m),and the stretching size controlling factor(e).The results show that the stretched NDVI(S-NDVI) is more sensitive to vegetation fraction than NDVI when the VF is large,ranging from 0.75 to 1.00.Moreover,the saturation effect in NDVI is effectively removed by using the S-NDVI.Further analysis suggests that there is a good linear correlation between the S-NDVI and the leaf area index(LAI).At the same time,the proposed S-NDVI significantly reduces or even eliminates the saturation effect over high biomass.A comparative analysis is performed between drought indices derived from NDVI and S-NDVI,respectively.In the experiment,reflectance data from the moderate resolution imaging spectroradiometer(MODIS) products and in-situ observation data from the meteorological sites at a regional scale are used.In this study,the coefficient of determination(R2) of the stretched drought index(S-DI) is above 0.5,indicating the reliability of the proposed algorithm with surface soil moisture content.Thus,the S-DI is suggested to be used as a drought index in extended regions,thus regional heterogeneity should be taken into account when applying stretching method.

Enhanced Detection of Rolling Element Bearing Fault Based on Stochastic Resonance

Early bearing faults can generate a series of weak impacts. All the influence factors in measurement may degrade the vibration signal. Currently, bearing fault enhanced detection method based on stochastic resonance（SR） is implemented by expensive computation and demands high sampling rate, which requires high quality software and hardware for fault diagnosis. In order to extract bearing characteristic frequencies component, SR normalized scale transform procedures are presented and a circuit module is designed based on parameter-tuning bistable SR. In the simulation test, discrete and analog sinusoidal signals under heavy noise are enhanced by SR normalized scale transform and circuit module respectively. Two bearing fault enhanced detection strategies are proposed. One is realized by pure computation with normalized scale transform for sampled vibration signal, and the other is carried out by designed SR hardware with circuit module for analog vibration signal directly. The first strategy is flexible for discrete signal processing, and the second strategy demands much lower sampling frequency and less computational cost. The application results of the two strategies on bearing inner race fault detection of a test rig show that the local signal to noise ratio of the characteristic components obtained by the proposed methods are enhanced by about 50% compared with the band pass envelope analysis for the bearing with weaker fault. In addition, helicopter transmission bearing fault detection validates the effectiveness of the enhanced detection strategy with hardware. The combination of SR normalized scale transform and circuit module can meet the need of different application fields or conditions, thus providing a practical scheme for enhanced detection of bearing fault.

Electric fields inside and outside an anisotropic dielectric sphere

Analytical expressions of electric fields inside and outside an anisotropic dielectric sphere are presented by transforming an anisotropic medium into an isotropic one based on the multi-scale transformation of electromagnetic theory. The theoretical expressions are consistent with those in the literature. The inside electric field, the outside electric field and the angle between their directions are derived in detail. Numerical simulations show that the direction of the outside field influences the magnitude of the inside field, while the dielectric constant tensor greatly affects its direction.

Target classification using SIFT sequence scale invariants

On the basis of scale invariant feature transform（SIFT） descriptors,a novel kind of local invariants based on SIFT sequence scale（SIFT-SS） is proposed and applied to target classification.First of all,the merits of using an SIFT algorithm for target classification are discussed.Secondly,the scales of SIFT descriptors are sorted by descending as SIFT-SS,which is sent to a support vector machine（SVM） with radial based function（RBF） kernel in order to train SVM classifier,which will be used for achieving target classification.Experimental results indicate that the SIFT-SS algorithm is efficient for target classification and can obtain a higher recognition rate than affine moment invariants（AMI） and multi-scale auto-convolution（MSA） in some complex situations,such as the situation with the existence of noises and occlusions.Moreover,the computational time of SIFT-SS is shorter than MSA and longer than AMI.

Color Correction for Multi-view Video Using Energy Minimization of View Networks

Systems using numerous cameras are emerging in many fields due to their ease of production and reduced cost, and one of the fields where they are expected to be used more actively in the near future is in image-based rendering （IBR）. Color correction between views is necessary to use multi-view systems in IBR to make audiences feel comfortable when views are switched or when a free viewpoint video is displayed. Color correction usually involves two steps： the first is to adjust camera parameters such as gain, brightness, and aperture before capture, and the second is to modify captured videos through image processing. This paper deals with the latter, which does not need a color pattern board. The proposed method uses scale invariant feature transform （SIFT） to detect correspondences, treats RGB channels independently, calculates lookup tables with an energy-minimization approach, and corrects captured video with these tables. The experimental results reveal that this approach works well.

Modified SIFT descriptor and key-point matching for fast and robust image mosaic

To improve the performance of the scale invariant feature transform （ SIFT）, a modified SIFT （M-SIFT） descriptor is proposed to realize fast and robust key-point extraction and matching. In descriptor generation, 3 rotation-invariant concentric-ring grids around the key-point location are used instead of 16 square grids used in the original SIFT. Then, 10 orientations are accumulated for each grid, which results in a 30-dimension descriptor. In descriptor matching, rough rejection mismatches is proposed based on the difference of grey information between matching points. The per- formance of the proposed method is tested for image mosaic on simulated and real-worid images. Experimental results show that the M-SIFT descriptor inherits the SIFT＇ s ability of being invariant to image scale and rotation, illumination change and affine distortion. Besides the time cost of feature extraction is reduced by 50% compared with the original SIFT. And the rough rejection mismatches can reject at least 70% of mismatches. The results also demonstrate that the performance of the pro- posed M-SIFT method is superior to other improved SIFT methods in speed and robustness.

Image matching algorithm based on SIFT using color and exposure information

Image matching based on scale invariant feature transform（SIFT） is one of the most popular image matching algorithms, which exhibits high robustness and accuracy. Grayscale images rather than color images are generally used to get SIFT descriptors in order to reduce the complexity. The regions which have a similar grayscale level but different hues tend to produce wrong matching results in this case. Therefore, the loss of color information may result in decreasing of matching ratio. An image matching algorithm based on SIFT is proposed, which adds a color offset and an exposure offset when converting color images to grayscale images in order to enhance the matching ratio. Experimental results show that the proposed algorithm can effectively differentiate the regions with different colors but the similar grayscale level, and increase the matching ratio of image matching based on SIFT. Furthermore, it does not introduce much complexity than the traditional SIFT.

Scale transform algorithm used in FMCW SAR data processing

The frequency-modulated continuous-wave （FMCW） synthetic aperture radar （SAR） is a light-weight, cost-effective, high-resolution imaging radar, which is suitable for a small flight platform. The signal model is derived for FMCW SAR used in unmanned aerial vehicles （UAV） reconnaissance and remote sensing. An appropriate algorithm is proposed. The algorithm performs the range cell migration correction （RCMC） for continuous nonchirped raw data using the energy invariance of the scaling of a signal in the scale domain. The azimuth processing is based on step transform without geometric resampling operation. The complete derivation of the algorithm is presented. The algorithm performance is shown by simulation results.

Shear strength criteria for rock,rock joints,rockfill and rock masses:Problems and some solutions

Although many intact rock types can be very strong,a critical confining pressure can eventually be reached in triaxial testing,such that the Mohr shear strength envelope becomes horizontal.This critical state has recently been better defined,and correct curvature or correct deviation from linear Mohr-Coulomb（MC） has finally been found.Standard shear testing procedures for rock joints,using multiple testing of the same sample,in case of insufficient samples,can be shown to exaggerate apparent cohesion.Even rough joints do not have any cohesion,but instead have very high friction angles at low stress,due to strong dilation.Rock masses,implying problems of large-scale interaction with engineering structures,may have both cohesive and frictional strength components.However,it is not correct to add these,following linear M-C or nonlinear Hoek-Brown（H-B） standard routines.Cohesion is broken at small strain,while friction is mobilized at larger strain and remains to the end of the shear deformation.The criterion ＇c then σn tan φ＇ should replace ＇c plus σn tan φ＇ for improved fit to reality.Transformation of principal stresses to a shear plane seems to ignore mobilized dilation,and caused great experimental difficulties until understood.There seems to be plenty of room for continued research,so that errors of judgement of the last 50 years can be corrected.

Rotational parameters estimation of maneuvering target in ISAR imaging

The rotational parameters estimation of maneuvering target is the key of cross-range scaling of ISAR （inverse synthetic aperture radar）, which can be used in the target feature extraction. The cross-range signal model of rotating target with fixed acceleration is presented and the weighted linear least squares estimation of rotational parameters with fixed velocity or acceleration is proposed via the relationship of cross-range FM （frequency modulation） parameter, scatterers coordinates and rotational parameters. The FM parameter is calculated via RWT （Radon-Wigner transform）. The ISAR imaging and cross-range scaling based on scaled RWT imaging method are implemented after obtaining rotational parameters. The rotational parameters estimation and cross-range scaling are validated by the ISAR processing of experimental radar data, and the method presents good application foreground to the ISAR imaging and scaling of maneuvering target.

Effects of slip condition on MHD stagnation-point flow over a power-law stretching sheet

The steady two-dimensional magnetohydrodynamic stagnation flow towards a nonlinear stretching surface is studied. The no-slip condition on the solid boundary is replaced with a partial slip condition. A scaling group transformation is used to get the invariants. Using the invariants, a third-order ordinary differential equation corresponding to the momentum is obtained. An analytical solution is obtained in a series form using a homotopy analysis method. Reliability and efficiency of series solutions are shown by the good agreement with numerical results presented in the literature. The effects of the slip parameter, the magnetic field parameter, the velocity ratio parameter, the suction velocity parameter, and the power law exponent on the flow are investigated. The results show that the velocity and shear stress profiles are greatly influenced by these parameters.

An Approach to Parallelization of SIFT Algorithm on GPUs for Real-Time Applications

Scale Invariant Feature Transform (SIFT) algorithm is a widely used computer vision algorithm that detects and extracts local feature descriptors from images. SIFT is computationally intensive, making it infeasible for single threaded im-plementation to extract local feature descriptors for high-resolution images in real time. In this paper, an approach to parallelization of the SIFT algorithm is demonstrated using NVIDIA’s Graphics Processing Unit (GPU). The parallel-ization design for SIFT on GPUs is divided into two stages, a) Algorithm de-sign-generic design strategies which focuses on data and b) Implementation de-sign-architecture specific design strategies which focuses on optimally using GPU resources for maximum occupancy. Increasing memory latency hiding, eliminating branches and data blocking achieve a significant decrease in aver-age computational time. Furthermore, it is observed via Paraver tools that our approach to parallelization while optimizing for maximum occupancy allows GPU to execute memory bound SIFT algorithm at optimal levels.

Research on will-dimension SIFT algorithms for multi-attitude face recognition

The results of face recognition are often inaccurate due to factors such as illumination,noise intensity,and affine/projection transformation.In response to these problems,the scale invariant feature transformation(SIFT) is proposed,but its computational complexity and complication seriously affect the efficiency of the algorithm.In order to solve this problem,SIFT algorithm is proposed based on principal component analysis(PCA) dimensionality reduction.The algorithm first uses PCA algorithm,which has the function of screening feature points,to filter the feature points extracted in advance by the SIFT algorithm;then the high-dimensional data is projected into the low-dimensional space to remove the redundant feature points,thereby changing the way of generating feature descriptors and finally achieving the effect of dimensionality reduction.In this paper,through experiments on the public ORL face database,the dimension of SIFT is reduced to 20 dimensions,which improves the efficiency of face extraction;the comparison of several experimental results is completed and analyzed to verify the superiority of the improved algorithm.