Least cost distance analysis for spatial interpolation

Spatial interpolation allows creation of continuous raster surfaces from a subsample of point-based measurements. Most interpolation approaches use Euclidean distance measurements between data points to generate predictions of values at unknown locations. However, there are many spatially distributed data sets that are not properly represented by Euclidean distances and require distance measures which represent their complex geographic connectivity. The problem of defining non-Euclidean distances between data points has been solved using the network-based solutions, but such techniques have historically relied on a network of connected line segments to determine point-to-point distances. While these vector-based solutions are computationally efficient, they cannot model more complex 2- and 3-dimensional systems of connectivity. Here, we use least-cost-path analyses to define distances between sampled points; a solution that allows for arbitrarily complex systems of connectivity to be interpolated. We used least-cost path distances in conjunction with the inverse distance weighting interpolation for a proof-of-concept interpolation of water temperature data in a complex deltaic river system. We compare our technique to Euclidean distance interpolation, and demonstrate that our technique, which follows connectivity rules, yields are more realistic interpolation of water temperature.     

Residual-based specification of a hidden random field included in a hierarchical spatial model

A method for specifying a hidden random field (HRF) included in a hierarchical spatial model is proposed. In hierarchical models of interest the first stage describes, conditional on a realization of the HRF, a response variable which is observable on a continuous spatial domain; the second stage models the HRF which reflects unobserved spatial heterogeneity. The question which is investigated is how can the HRF be modeled, i.e. specified. The method developed to address this question is based on residuals obtained when the base model, i.e. the hierarchical model in which the HRF is assumed constant, is fitted to data. It is shown that the residuals are linked with the HRF, and the link is used to specify the HRF. The method is applied to simulated data in order to assess its performance, and then to real data on radionuclide concentrations on Rongelap Island.     

基于误差控制的自适应3次B样条曲线插值

针对现有曲线插值算法不能有效压缩型值点的缺陷,研究了一种自适应三次B样条曲线插值算法。从型值点序列中选用最少的点插值一条初始曲线,基于提出的点到曲线的最小距离计算方法,分别计算各非插值点对应的插值误差,并从中提取最大插值误差。若最大误差大于给定的误差阈值,则将其对应的型值点加入插值型值点序列,重新插值曲线,直到最大插值误差满足误差要求。与现有曲线插值算法相比,该算法可以在保证插值精度的前提下有效压缩数据量。     

Free-form surface machining error compensation applying 3D CAD machining pattern model

The article presents a methodology for compensating for systematic influences of computer numerical control (CNC) machining processes on free-form surfaces. The proposed procedure is performed off-line by introducing corrections compensating for these influences to machining programs. The effect of systematic influences of machining are deterministic deviations of surfaces. CAD models of these deviations, averaged for a number of surfaces machined under repeatable conditions, represent a machining pattern model (MPM) which serves as the basis for performing compensation. The basis for developing such models is surface deviations determined during coordinate measurements carried out along a regular grid of points. For estimating surface MPMs, a methodology is proposed in which regression analysis, spatial statistics methods, an iterative procedure, and NURBS modeling are applied. An MPM with the opposite sign was used for compensating systematic influences of the ball-end milling process by modifying the nominal geometry data and correcting the machining program. The results of machining error compensation carried out on the basis of a previously developed MPM were compared to the results of compensation performed on the basis of raw measurement data as well as to the results these after compensation on the basis of a model of deterministic deviations for the surface under study.     

Adaptive-feedrate interpolation for parametric curves with a confined chord error

Recently, modern manufacturing systems have been designed which can machine arbitrary parametric curves while greatly reducing data communication between CAD/CAM and CNC systems. However, a constant feedrate and chord accuracy between two interpolated points along parametric curves are generally difficult to achieve due to the non-uniform map between curves and parameters. A speed-controlled interpolation algorithm with an adaptive feedrate is proposed in this paper. Since the chord error in interpolation depends on the curve speed and the radius of curvature, the feedrate in the proposed algorithm is automatically adjusted so that a specified limit on the chord error is met. Both simulation and experimental results for non-uniform rational B-spline (NURBS) examples are provided to verify the feasibility and precision of the proposed interpolation algorithm.     

无人机DEM测点插值算法的矿区沉陷测绘技术

为实现对矿区沉陷深度的精准测量,完善测绘技术的具体实施方案,针对无人机DEM测点插值算法的矿区沉陷测绘技术展开研究;根据DEM测点获取结果,实施分维值测定处理,再以此为基础,确定插值拐点所处区域,实现对无人机DEM测点插值算法应用流程的完善;联合像控点布设原则,定义空中三角区域,并通过推导径向插值基函数的方式,建立矿区沉陷区域的地理模型;在空间坐标系转换条件的基础上,确定矢量数据叠加的处理结果,再结合像片倾角与旋偏角的实际取值,求解测量精度评价指标,完成无人机DEM测点插值算法的矿区沉陷测绘技术实施方法的设计;实验结果表明,上述测绘技术方法作用下,沉陷深度测量结果与矿区真实沉陷深度之间的差值不超过1 m,符合精准测量的应用需求,对于测绘实施方案的完善可以起到一定的促进性影响作用。     

Error analysis of the derivative of rational interpolation with a linear denominator

This paper deals with the approximation properties of the derivatives of rational cubic interpolation with a linear denominator. Error expressions of the derivatives of interpolating functions are derived, convergence is established and the optimal error coefficient c _i is proved to be symmetric about the parameters of the rational interpolation. The unified integral form of the error of the second derivative in all subintervals is obtained. A simple expression of the jump of the second derivative at the knots and the conditions for the interpolating function to be C ² in the interpolating interval are given.     

大规模数字高程模型的可视化研究

根据细节层次模型（LOD）的设计思想,提出了大规模数字高程模型的数据组织和可视化方法。该方法在数据分页算法和细节层次模型相结合的基础上,采用视区计算和边界融合算法,实现了地形的快速绘制。实验证明该方法实现了高性能绘制大规模数字高程模型。     

Kinematic analysis and error modeling of TAU parallel robot

The TAU robot presents a new configuration of parallel robots with three degrees of freedom. This robotic configuration is well adapted to perform with a high precision and high stiffness within a large working range compared with a serial robot. It has the advantages of both parallel robots and serial robots. In this paper, the kinematic modeling and error modeling are established with all errors considered using Jacobian matrix method for the robot. Meanwhile, a very effective Jacobian approximation method is introduced to calculate the forward kinematic problem instead of Newton–Raphson method. It denotes that a closed form solution can be obtained instead of a numerical solution. A full size Jacobian matrix is used in carrying out error analysis, error budget, and model parameter estimation and identification. Simulation results indicate that both Jacobian matrix and Jacobian approximation method are correct and with a level of accuracy of micron meters. ADAMS's simulation results are used in verifying the established models.     

Hermite interpolation with a pair of spirals

The Hermite interpolation problem in the plane considered here is to join two points and to match given unit tangent vectors and signed curvatures at the two points with various G² curves consisting of a pair of spirals. The rotation of the tangent vector of the interpolating curve from one point to the other is restricted to being less than π. The necessary and sufficient conditions for the existence of each of the various curves are given.     

基于DEM的水库三维可视化研究

利用库区纸质地形图建立了高精度的数字高程模型，进行了精度分析、地形因子分析、可视性分析和库容计算。并结合ASP和VRML技术实现了基于网络的三维可视化系统，包括计算结果可视化与查询、图形数据可视化和库区虚拟场景可视化。实现了对深层次水利信息的获取和形象表达。     

Spatial interpolation of McArthur's Forest Fire Danger Index across Australia: Observational study

Fire danger indices are used by fire management agencies to assess fire weather conditions and issue public warnings. The most widely used fire danger indices in Australia are the McArthur Fire Forest Danger Index and the Grassland Fire Danger Index. These indices are calculated at weather stations using measurements of weather variables and fuel information. For a vast country like Australia when assessing the risk of severe fire weather events, it is also important to calculate the spatial distribution of these indices considering the extreme tail of the distribution. The spatial distribution of one of the fire weather danger indices regularly used in Australia is presented in this paper. In particular, we present the spatial distribution of the long-term tendency of extreme values of the McArthur Forest Fire Danger Index (FFDI). This indicator of fire weather conditions was assessed by calculating the return period of its extreme values by fitting extreme value distributions to data sets of FFDI at 78 recording stations around Australia. The spatial distribution of these return periods was obtained by using spatial interpolation algorithms with the recording stations measurements. Two conventional and two new algorithms based on machine-learning techniques were tested. This study shows that the best interpolation results for the FFDI can be obtained by using a combination of random forest and inverse distance weighting interpolation algorithms. The spatial distribution of the seasonal FFDI return period shows that the highest FFDI over large parts of southern Australia occurs during the summer months whilst in northern Australia it occurs in spring. The results also show that the FFDI in eastern Australia, the most populated region of the country, is higher inland than in the coastal areas particularly during spring and summer.     

渐进插值的LOOP曲面细分*

目前很多细分方法都存在不能用同一种方法处理封闭网格和开放网格的问题。对此,一种新的基于插值技术的LOOP曲面细分方法,其主要思想就是给定一个初始三角网格M,反复生成新的顶点,新顶点是通过其相邻顶点的约束求解得到的,从而构造一个新的控制网格M,在取极限的情况下,可以证明插值过程是收敛的;因为生成新顶点使用的是与其相连顶点的约束求解得到的,本质上是一种局部方法,所以,该方法很容易定义。它在本地方法和全局方法中都有优势,能处理任意顶点数量和任意拓扑结构的网格,从而产生一个光滑的曲面并忠实于给定曲面的形状,其控制     

An adaptive mesh refinement of quadrilateral finite element meshes based upon an a posteriori error estimation of quantities of interest: modal response

Modal analysis is commonly performed in a vehicle development process to assess dynamic responses of structure designs. This paper presents an adaptive quadrilateral refinement process for modal analysis of elastic shells based upon a posteriori error estimation in natural frequencies. The process provides engineers with an estimation of their modal analysis quality and an effective adaptive refinement tool for quadrilateral meshes. The effectiveness of the process is demonstrated on the eigenvalue analyses of two numerical examples, a shock tower cap and a roof structure. It shows that the solution error in the frequency of interest is effectively reduced through the adaptive refinement process, and the resulting frequency of interest converges to the solution of a very fine model.     

Statistical analysis of positioning error of a CNC milling machine

The characteristics of the positioning error of a NC milling machine were studied through statistical analysis. It was found that (1) the mean of the error is significantly affected by the table position, (2) the variances of the error at different table positions are from the same population, and (3) the effect of the feedrate on positioning error is not significant. Also, a software correction technique was applied and workpiece error was decreased by 40%.     

Consistency and error analysis of Prior-Knowledge-Based Kernel Regression

Incorporating prior knowledge (PK) into learning methods is an effective means to improve learning performance. The consistency and error theories of PK-based methods, which are of great theoretical importance, are still far from well established. Concentrating on the PK-based kernel regression, this paper proposes a methodology of analyzing the consistency and error. This methodology converts the specific methods firstly to a unified optimization problem and then to a unified solution expression, and a general consistency and error analysis tool is proposed and applied. A few examples are given to illustrate the analysis procedure.     

Light mesh: soft shadows as interpolation of visibility

The light meshes (LM) method is a modification of the recursive ray tracing algorithm (RRTA). In this paper we consider an original procedure of shadow calculations, which allows soft shadows to be obtained. The light meshes method can be integrated easily into existing implementations of RRTA as a supplementary technique or plug-ins. In comparison with conventional RRTA the suggested technique allows us to: (a) build soft shadows, (b) speed up a process of shadow calculations, (c) simulate main effects of diffuse interreflections, (d) omit the ambient term. Obviously, visual results of the LM method differ slightly from those calculated with the help of the basic RRTA.

A light mesh is a point set in the 3D space of a scene. In practice, it is approximated by a finite set of points, as a rule, by evenly spaced grids. At each mesh point we compute illuminance, which characterizes some kind of “light field intensity” in the scene space. Then an important part of resulting illumination of a scene object point is obtained by the interpolation of the stored values of nearby mesh points.

Experiments show that the approach proposed reduces computational time with respect to the ray tracing algorithm if a scene contains a lot of light sources and/or an image has a large resolution.     

多尺度有理分形的图像插值算法

目的图像插值是图像处理中的重要问题,为了提高纹理图像的放大质量,结合以往的有理函数的插值算法,提出一种新的基于有理分形函数的图像插值算法。方法对于输入图像,首先,运用中值滤波和直方图均衡化对输入图像预处理;其次,通过毯子覆盖法求出图像的多尺度分形特征值,进行纹理区域和平滑区域的划分;最后,在纹理区域采用有理分形插值函数,在平滑区域采用有理插值函数。结果对于一般图像,本文算法与NARM(nonlocal autoregressive model),NEDI(new edge-directed interpolation)相当,在纹理区域较多的图像中,本文算法在峰值信噪比(PSNR)和结构相似性(SSIM)数值上较对比算法进一步提高,在视觉效果上,图像对比度明显增强,在Barbara,Truck等的对比图像中,峰值信噪比均提高了0.5 1 dB。结论本文插值算法利用多尺度分形特征将图像划分区域,在不同区域采用不同的插值模型。优化模型参数使得插值质量进一步提高。实验表明本文算法能够对纹理和非纹理区域有效划分对纹理的信息保持优于传统算法,获得了较好的主客观效果。     

A distribution-free geometric upper bound for the probability of error of a minimum distance classifier

An upperbound to the probability of error per class in a multivariate pattern classification is derived. The bound, given by

$\text{P(E|class w}{}_{\mathrm{i}}\text{)≤}\text{N}\text{R}{}^2{}_{\mathrm{i}}$

is derived with minimal assumptions; specifically the mean vectors exist and are distinct and the covariance matrices exist and are non-singular. No other assumptions are made about the nature of the distributions of the classes. In equation (i) N is the number of features in the feature (vector) space and R_i is a measure of the “radial neighbourhood” of a class. An expression for R_i is developed. A comparison to the multivariate Gaussian hypothesis is presented.