Interpolation Kernel Research Articles

Optimization of the 2P fifth degree convolution kernel in the spectral domain

The first part of the paper describes a two-parameter (2P) fifth-order interpolation kernel, r. After that, from the 2P kernel, the kernel components were created. By applying the Fourier transformation to each kernel component, the spectral components of the 2P kernel were obtained. The spectral characteristic of the 2P kernel, H, was created from the spectral components. After that, the algorithm, that optimizes the parameters of the 2P kernel so as to eliminate the ripple of the spectral characteristics, is described. The optimization was performed in such a way that the spectral characteristic developed in the Taylor series, HT. With the condition for the elimination of the members of the Tylor series, which greatly affect the ripple of the spectral characteristic, the optimal kernel parameters (aopt, bopt) were determined. The second part of the paper describes an Experiment, in which the interpolation accuracy of the 2P kernel was tested. Convolution interpolation, with the 2P kernel, was performed over the signals from the Test base. The Test base is created with musical signals. By analyzing the interpolation error, which is represented by the Mean Square Error, MSE, the precision of the interpolation was determined. The results (aopt, bopt, MSEmin) are presented on tables and graphs. Detailed comparative analysis showed higher interpolation precision with the proposed 2P interpolation kernel, compared to the interpolation precision with, 1P interpolation kernel. Finally, the numerical values of the optimal kernel parameters, which are determined by the optimization algorithm proposed in this paper, were experimentally verified.

Equally spaced points are optimal for Brownian Bridge kernel interpolation

In this paper we show how ideas from spline theory can be used to construct a local basis for the space of translates of a general iterated Brownian Bridge kernel kβ,ɛ for β∈N, ɛ≥0. In the simple case β=1, we derive an explicit formula for the corresponding Lagrange basis, which allows us to solve interpolation problems without inverting any linear system.We use this basis to prove that interpolation with k1,ɛ is uniformly stable, i.e., the Lebesgue constant is bounded independently of the number and location of the interpolation points, and that equally spaced points are the unique minimizers of the associated power function, and are thus error optimal. In this derivation, we investigate the role of the shape parameter ɛ>0, and discuss its effect on these error and stability bounds.Some of the ideas discussed in this paper could be extended to more general Green kernels.

IMAGE INTEROLATION USING OF THE FIFTH AND SEVENTH ORDER POLYNOMIAL PARAMETER KERNELS

In the first part of the paper, one-parameter (1P), fifth and seventh order polynomial interpolationconvolution kernels, are described. In the second part of the paper an Experiment is described. The precision of theimage interpolation was tested. Interpolation of the Test images from the base, using interpolation kernels, wereperformed. The precision of the interpolation kernels was measured using the mean squared error (MSE). Next,optimum kernel parameter, α, were determined by minimizing MSE. After that, a comparative analysis of theminimum MSE values, for the fifth and seventh order polynomial kernels, was performed. The results are presentedtabularly and graphically.

A Comparison of Processing Schemes for Automotive MIMO SAR Imaging

Synthetic Aperture Radar (SAR) imaging is starting to play an essential role in the automotive industry. Its day and night sensing capability, fine resolution, and high flexibility are key aspects making SAR a very compelling instrument in this field. This paper describes and compares three algorithms used to combine low-resolution images acquired by a Multiple-Input Multiple-Output (MIMO) automotive radar to form an SAR image of the environment. The first is the well-known Fast Factorized Back-Projection (FFBP), which focuses the image in different stages. The second one will be called 3D2D, and it is a simple 3D interpolation used to extract the SAR image from the Range-Angle-Velocity (RAV) data cube. The third will be called Quick&Dirty (Q&D), and it is a fast alternative to the 3D2D scheme that exploits the same intuition. A rigorous mathematical description of each algorithm is derived, and their limits are addressed. We then provide simulated results assessing different interpolation kernels, proving which one performs better. A rough estimation of the number of operations proves that both algorithms can be deployed using a real-time implementation. Finally, we will present some experimental results based on open road campaign data acquired using an eight-channel MIMO radar at 77 GHz, considering the case of a forward-looking geometry.

Design of Low-Artifact Interpolation Kernels by Means of Computer Algebra

We present a number of new piecewise-polynomial kernels for image interpolation. The kernels are constructed by optimizing a measure of interpolation quality based on the magnitude of anisotropic artifacts. The kernel design process is performed symbolically using the Mathematica computer algebra system. An experimental evaluation involving 14 image quality assessment methods demonstrates that our results compare favorably with the existing linear interpolators.

An adaptive residual sub-sampling algorithm for kernel interpolation based on maximum likelihood estimations

In this paper we propose an enhanced version of the residual sub-sampling method (RSM) in Driscoll and Heryudono (2007) for adaptive interpolation by radial basis functions (RBFs). More precisely, we introduce in the context of sub-sampling methods a maximum profile likelihood estimation (MPLE) criterion for the optimal selection of the RBF shape parameter. This choice is completely automatic, provides highly reliable and accurate results for any RBFs, and, unlike the original RSM, guarantees that the RBF interpolant exists uniquely. The efficacy of this new method, called MPLE-RSM, is tested by numerical experiments on some 1D and 2D benchmark target functions.

Inferring potential landscapes from noisy trajectories of particles within an optical feedback trap

SummaryWhile particle trajectories encode information on their governing potentials, potentials can be challenging to robustly extract from trajectories. Measurement errors may corrupt a particle’s position, and sparse sampling of the potential limits data in higher energy regions such as barriers. We develop a Bayesian method to infer potentials from trajectories corrupted by Markovian measurement noise without assuming prior functional form on the potentials. As an alternative to Gaussian process priors over potentials, we introduce structured kernel interpolation to the Natural Sciences which allows us to extend our analysis to large datasets. Structured-Kernel-Interpolation Priors for Potential Energy Reconstruction (SKIPPER) is validated on 1D and 2D experimental trajectories for particles in a feedback trap.

On construction of prediction intervals for heteroscedastic regression

In a real-world regression problem, the variance usually varies with the location, which brings difficulties in prediction of the response. Existing heteroscedastic regression methods suffer from inaccurate estimation and/or high computational complexity, and cannot be used to construct satisfactory prediction intervals for small or large data. This article focuses on the problem of constructing prediction intervals of the response under heteroscedastic regression models. We apply the reconstruction approach to parameterize the mean and variance functions as forms of kernel interpolation, and use the maximum likelihood estimation method to estimate the parameters. Our method allows a small number of parameters in the parameterization forms, and only requires low computational cost. Based on these estimators and some Bayesian modifications, we provide three classes of prediction intervals. Numerical experiments for both small and large datasets indicate that they are very competitive compared with existing heteroscedastic regression methods in terms of coverage rate and computational complexity.

A hybrid smoothed particle hydrodynamics coupled to a fictitious domain method for particulate flows and its application in a three-dimensional printing process

A hybrid smoothed particle hydrodynamics (SPH) coupled to a direct-forcing fictitious domain (FD) scheme is proposed for the simulation of particulate flows. The new method is effective in calculating the particle-fluid interaction forces and uses a kernel interpolation function to realize the momentum exchange between fluids and particles. A higher-order interpolation scheme is applied to preserve the consistency and accuracy of the kernel function. We first test our method by simulating the benchmark of flow past a cylinder at Reynolds number ranging from 20 to 200 and obtain the convergent results, including accurate lift and drag coefficients, Strouhal number, length of the recirculation bubble, and separation angle. Subsequently, we verify our new method for the typical particulate flows, including the motion of a neutrally-buoyant cylinder in Couette flow, the motion of a neutrally-buoyant cylinder in a planar Poiseuille flow, the sedimentation of a circular cylinder in a channel, and the motion of a neutrally-buoyant slender particle in Couette flow. A good agreement with the existing experimental data, with other numerical results, and with available theoretical solutions is obtained indicating the accuracy and the robustness of the new method. Subsequently, our SPH-FD is applied to simulate a slender fiber in a three-dimensional (3D) printing process, showing a good potential and advantages in simulating particulate flows of some industrial processes.

A‐ULMPM: An Adaptively Updated Lagrangian Material Point Method for Efficient Physics Simulation without Numerical Fracture

AbstractWe present an adaptively updated Lagrangian Material Point Method (A‐ULMPM) to alleviate non‐physical artifacts, such as the cell‐crossing instability and numerical fracture, that plague state‐of‐the‐art Eulerian formulations of MPM, while still allowing for large deformations that arise in fluid simulations. A‐ULMPM spans MPM discretizations from total Lagrangian formulations to Eulerian formulations. We design an easy‐to‐implement physics‐based criterion that allows A‐ULMPM to update the reference configuration adaptively for measuring physical states, including stress, strain, interpolation kernels and their derivatives. For better efficiency and conservation of angular momentum, we further integrate the APIC [JSS*15] and MLS‐MPM [HFG*18] formulations in A‐ULMPM by augmenting the accuracy of velocity rasterization using both the local velocity and its first‐order derivatives. Our theoretical derivations use a nodal discretized Lagrangian, instead of the weak form discretization in MLS‐MPM [HFG*!!18], and naturally lead to a “modified” MLS‐MPM in A‐ULMPM, which can recover MLS‐MPM using a completely Eulerian formulation. A‐ULMPM does not require significant changes to traditional Eulerian formulations of MPM, and is computationally more efficient since it only updates interpolation kernels and their derivatives during large topology changes. We present end‐to‐end 3D simulations of stretching and twisting hyperelastic solids, viscous flows, splashing liquids, and multi‐material interactions with large deformations to demonstrate the efficacy of our new method.

Retinal fundus image superresolution generated by optical coherence tomography based on a realistic mixed attention GAN.

Optical coherence tomography (OCT) is widely used to diagnose retinal diseases. However, due to the limited resolution of OCT imaging systems, the quality of fundus images displayed is not satisfactory, which hinders the diagnosis of patients by ophthalmologists. This is an inevitable problem of OCT imaging systems, but few people have given attention to it. We attempt to solve this problem through deep learning methods. In this paper, we propose a single-image superresolution (SISR) model that is based on a generative adversarial network (GAN) for restoring low-resolution (LR) OCT fundus images to high-resolution (HR) counterparts. To obtain more realistic images, we craft the training data set by obtaining the real blur kernels of the LR images instead of using the bicubic interpolation kernel. The baseline of our generator is similar to that of an enhanced superresolution generative adversarial network (ESRGAN), but we creatively propose a mixed attention block (MAB). In contrast to other superresolution (SR) tasks, to adapt to the characteristics of OCT imaging systems, our network can reconstruct LR images with different upscaling factors in the height and widthdirections. The results of qualitative and quantitative experiments prove that our model is capable of reconstructing retinal fundus images clearly andaccurately. We propose a new GAN model for enhancing the quality of displayed OCT retinal fundus images and achieve state-of-the-artresults.

GPGM-SLAM: a Robust SLAM System for Unstructured Planetary Environments with Gaussian Process Gradient Maps

Simultaneous Localization and Mapping (SLAM) techniques play a key role towards long-term autonomy of mobile robots due to the ability to correct localization errors and produce consistent maps of an environment over time. Contrarily to urban or man-made environments, where the presence of unique objects and structures offer unique cues for localization, the apperance of unstructured natural environments is often ambiguous and self-similar, hindering the performances of loop closure detection. In this paper, we present an approach to improve the robustness of place recognition in the context of a submap-based stereo SLAM based on Gaussian Process Gradient Maps (GPGMaps). GPGMaps embed a continuous representation of the gradients of the local terrain elevation by means of Gaussian Process regression and Structured Kernel Interpolation, given solely noisy elevation measurements. We leverage the imagelike structure of GPGMaps to detect loop closures using traditional visual features and Bag of Words. GPGMap matching is performed as an SE(2) alignment to establish loop closure constraints within a pose graph. We evaluate the proposed pipeline on a variety of datasets recorded on Mt. Etna, Sicily and in the Morocco desert, respectively Moon- and Mars-like environments, and we compare the localization performances with state-of-the-art approaches for visual SLAM and visual loop closure detection.

Pixel-driven computation of parallel and fan-beam projections of a digital image based on pixel-representation using a new formula

BackgroundThe computation of the projections of a digital image – modelled as a superposition of square pixels – is essential in several algorithms in computed tomography, and also in many machine vision applications. Projections of digital images are computed through the ray-driven approach. Current pixel-driven methods, though simpler, involve interpolation kernels in the projection-domain – not based on the exact Radon transform (RT) of a square. MethodsA new analytical formula – for the line-integral of the unit pixel – simpler than that published previously, is derived. The formula allows easy, pixel-driven computation of the RT of a digital image based on the pixel model i.e., Riemann-sum approximation to the line integral. The method naturally allows pixel-driven backprojection, based on the same (pixel) model. The approach is extended to computing projections over divergent (fan-) beams, and its application as a generalized version of the traditional Hough transform, is discussed. ResultsThe Radon transform of the unit-pixel match that of a digital square image. The RT, of a mathematical phantom consisting of a superposition of elliptical disks, compares well with that based on analytical formula. A comparative study with the pixel driven approach with interpolation in the projection-domain, and its important variant, is included. The fan-beam projections of the square image and the phantom are presented. The applicability of the RT in estimating the Hough transform over precise lines, is shown. ConclusionThe new formula, a simplified version of that of Deans, is useful in pixel-driven computation of parallel and fan-beam projections based on Riemann-sum approximation, which is exact in the case of the common pixel-based image model. Pixel-driven approach is amenable to parallel, and also region-of-interest computation. The method is useful in CT as well as machine vision applications.

On Particle Shifting Techniques (PSTs): Analysis of existing laws and proposition of a convergent and multi-invariant law

This paper addresses the Particle Shifting Technique (PST) in the SPH schemes. Improving the accuracy of SPH schemes leads to particle clustering along the flow streamlines which turns to be detrimental for the simulations. PSTs aim at avoiding this adverse effect by slightly disordering the particles, allowing to retrieve a regular particle distribution within the kernel interpolation support. The gain in accuracy is such that this technique is now commonly adopted by the SPH practitioners, however the conditions that should be respected by a PST are not clearly discussed in the literature. In this paper, such conditions are exposed and their fulfillment by the main existing PSTs of the literature is analyzed. None of these existing PSTs fully satisfying these conditions, a novel PST is introduced. The proposed PST is validated for three different SPH schemes on 2D and 3D test cases, in presence of free-surface and solid boundaries.

Coherence-Induced Bias Reduction in Synthetic Aperture Sonar Along-Track Micronavigation

Subwavelength motion estimation is vital for the production of focused synthetic aperture sonar (SAS) imagery. The required precision is obtainable from the sonar data itself through a process termed micronavigation. Along-track micronavigation is achieved by a similar technique to that used in correlation velocity logs (CVLs), where sparse estimates of the spatial coherence function are interpolated to estimate the location of the peak coherence and hence estimate the interping vehicle motion. However, along-track micronavigation estimates made using this technique are biased, which limits the utility of these measurements for long-term navigation of autonomous underwater vehicles (AUVs). Three sources of along-track motion estimation bias are considered in this article. First, imperfect temporal registration between the signals results in coherence estimates that are negatively biased as a function of the temporal offset. Second, the sparse estimates of the spatial coherence function are obtained by cross-correlation of complex baseband signals, a process which is known to result in positively biased coherence estimates, especially when the true coherence is low. Finally, mismatches between the underlying spatial coherence function and the interpolation kernel used to estimate the peak coherence location also result in along-track micronavigation bias. In this article, we describe and evaluate three methods for reducing along-track micronavigation bias. We introduce a temporal registration of the signals before coherence estimation, which reduces the impact of negative coherence bias due to temporal offsets. The remaining coherence estimation bias is reduced by combining multiple coherence estimates in a Bayesian coherence estimator. Additionally, an improved interpolation kernel is derived with a significantly improved fit compared to the current gold standard Gaussian interpolation kernel. The improvements in along-track micronavigation accuracy are demonstrated using two simulated data sets, which both allow comparison with ground truth. The first involves direct simulation of the spatial coherence from a given interping geometry using the pulse-echo formulation of the van Cittert–Zernike theorem, while the second involves simulation of raw sonar echo data using a point-scatterer model. Using these simulations, a reduction in along-track micronavigation bias of 48.5%–99.5% is demonstrated, with reductions in along-track micronavigation error standard deviation of up to 34%. This improvement expands the potential for SAS-equipped AUVs to reduce their long-term navigation drift, facilitating longer underwater transits, improved target localization, and reduced track misalignment in repeat-pass operations.

Optimization of the 3p keys kernel parameters by minimizing the ripple of the spectral characteristic

The ideal interpolation kernel is described by the sinc function, and its spectral characteristic is the box function. Due to the infinite length of the ideal kernel, it is not achievable. Therefore, convolutional interpolation kernels of finite length, which should better approximate the ideal kernel in a specified interval, are formed. The approximation function should have a small numerical complexity, so as to reduce the interpolation execution time. In the scientific literature, great attention is paid to the polynomial kernel of the third order. However, the time and spectral characteristic of the third-order polynomial kernels differs significantly from the shape of the ideal kernel. Therefore, the accuracy of cubic interpolation is lower. By optimizing the kernel parameters, it is possible to better approximate the ideal kernel. This will increase the accuracy of the interpolation. The first part of the paper describes a three-parameter (3P) Keys interpolation kernel, r. After that, the algorithm for optimizing the parameters of the 3P Keys kernel, is shown. First, the kernel is disassembled into components, and then, over each kernel component, Fourier transform is applied. In this way the spectral characteristic of the 3P Keys kernel, H, was determined. Then the spectral characteristic was developed in the Taylor series, HT. With the condition for the elimination of the members of the Taylor series, which greatly affect the ripple of the spectral characteristic, the optimal kernel parameters (?opt, ?opt, gopt) were determined. The second part of the paper describes an experiment, in which the interpolation accuracy of the 3P Keys kernel, was tested. Parametric cubic convolution (PCC) interpolation, with the 3P kernel, was performed over the images from the Test database. The Test database is created with standard Test images, which are intensively used in Digital Image Processing. By analyzing the interpolation error, which is represented by the Mean Square Error, MSE, the accuracy of the interpolation was determined. The results (?opt, ?opt, gopt, MSEmin) are presented on tables and graphs. Detailed comparative analysis showed higher interpolation accuracy with the proposed 3P Keys interpolation kernel, compared to the interpolation accuracy with, 1P Keys and 2P Keys interpolation kernels. Finally, the numerical values of the optimal kernel parameters, which are determined by the optimization algorithm proposed in this paper, were experimentally verified.

珠江口伶仃洋中华白海豚栖息地利用对海岸线等变迁的响应

PDF HTML阅读 XML下载 导出引用 引用提醒 珠江口伶仃洋中华白海豚栖息地利用对海岸线等变迁的响应 DOI: 10.5846/stxb202101070066 作者: 作者单位: 作者简介: 通讯作者: 中图分类号: 基金项目: 中国水产科学研究院南海水产研究所中央级公益性科研院所基本科研业务费专项资金资助（2017YB20）；广东省科技计划项目（2019B121201001）；农业农村部财政项目"中华白海豚保护行动计划" Long-term changes in habitat use of Indo-Pacific humpback dolphins (Sousa chinensis) in response to anthropogenic coastline shift in Lingding Bay of Pearl River Estuary, China Author: Affiliation: Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:沿岸鲸豚类栖息地易受人类活动的干扰，导致其分布和核心栖息地发生变化。珠江口-漠阳江口中华白海豚种群是目前所知全球范围内最大的种群，其中伶仃洋水域是其重要的栖息地。近年来，珠江口伶仃洋周边城市发展带来的人类活动增加，白海豚的生存压力日益增大，分析伶仃洋中华白海豚对栖息地环境变化的响应，研究对应的保护策略显得非常迫切。以多源陆地资源卫星Landsat为数据源，通过影像分析近43年珠江口伶仃洋围填海造成的海域流失，结合近20年来采用截线抽样法收集的海豚观测数据，运用含障碍核插值（Kernel interpolation with barriers）方法，分析白海豚的分布及核心栖息地的变化。结果显示：1986-2015年期间，研究区域内流失的海域面积为344.08km2；目击分布离人工海岸线的平均距离大于自然海岸线的平均距离，目击分布到自然海岸线和人工海岸线的平均距离均在减小，表明过去20年白海豚的栖息地使用选择发生了一些变化，被迫适应人类活动的干扰；1997-2016年白海豚的分布范围呈现先增加后减小，白海豚栖息地使用的重心偏向伶仃洋东部水域，核心栖息地趋向主航道和无人海岛附近水域萎缩，可能是海豚因海域食物资源减少而迫不得已的选择。不同时期，珠江口中华白海豚国家级自然保护区所覆盖的核心栖息地比例呈递减趋势，占比由79.9%下降到49.4%，当前有必要对保护区范围和功能区作出一些优化调整，以适应栖息地使用的变化格局。 Abstract:Cetacean living coastal habitat often suffer from anthropogenic disturbance, which would change their original distribution and core habitat use. Pearl River Estuary-Moyang River Estuary (PRE-MRE) population is the largest known (putative) population of Indo-Pacific humpback dolphin in the world. Lingding Bay is a critical habitat of PRE-MRE population, where human activities have become frequently in recent years and dolphin survival pressure is increasing. Analysis the response of Indo-Pacific humpback dolphin to environment change and making corresponding conservation strategy are urgent. This research mainly discussed coastal waters loss process in the past 43 years from sea reclamation in the Lingding Bay using the multi-source Landsat imageries. To examine the change of distribution and core habitat of dolphins, a new kernel density estimation approach that accounted for physical barriers to movements was applied with sighting records from line-transect surveys during past 20 years. Our results showed that about 344.08 km2 waters became unavailable from 1986 to 2015; average proximity of sighting sites to artificial shoreline was farther than to natural shoreline and average proximity of sighting sites to artificial shoreline and natural shoreline decreased, which indicated that dolphin habitat use changed and dolphin had to adapt anthropogenic disturbance; habitat use of dolphin focused on eastern Lingding Bay waters and distribution range reached peak in 2005-2006, but fell sharply in 2015-2016; dolphin's core habitat approaching main channels and around undeveloped islands might be the only option result from resource depletion. The proportion of core habitat showed a decreasing trend in the Chinese White Dolphin National Nature Reserve of Guangdong Pearl River Estuary, which decreased from 79.9% to 49.4% in different period. We recommend that the government should adjust current protected range to fulfill the change pattern from habitat use. 参考文献 相似文献 引证文献

Spectral characteristics of two parameter fifth degree polynomial convolution kernel

In this paper, the spectral characteristic of a polynomial two parameter convolutional fifth-order interpolation kernel is determined. The spectral characteristic is determined as follows. First, the kernel is decomposed into components. After that, the spectral characteristics of each kernel component were calculated using the Fourier transform. Finally, the spectral characteristic of the interpolation two parameter kernel using a combination of the spectral components of the kernels and the kernel parameters, a and b, is formed. Through a numerical example and a graphical representation of the spectral characteristics of the one parameter and two parameter kernels, greater similarity of the spectral characteristics of the 2 P kernel, relative to the ideal box characteristic, is shown.

Greedy sampling and approximation for realizing feedback control for high dimensional nonlinear systems

The problem of closed-loop control for high dimensional nonlinear systems is considered. Three different types of kernel interpolation surrogates for the optimal feedback policy are compared. The data for this comes from open-loop controlled solutions. Here, additional information about the system originating from the Pontryagin Maximum Principle is exploited. The starting position for the open-loop control is adaptively selected by a geometric greedy selection criterion, and a so-called vectorial kernel orthogonal greedy algorithm is performed to set up the surrogate. With this procedure we can overcome the curse of dimensionality and still receive a very precise, robust and real-time capable feedback control.

Solving a class of variable order nonlinear fractional integral differential equations by using reproducing kernel function

<abstract><p>In this paper, reproducing kernel interpolation collocation method is explored for nonlinear fractional integral differential equations with Caputo variable order. In order to testify the feasibility of this method, several examples are studied from the different values of parameters. In addition, the influence of the parameters of the Jacobi polynomial on the numerical results is studied. Our results reveal that the present method is effective and provide highly precise numerical solutions for solving such fractional integral differential equations.</p></abstract>