Multivariate Calibration with the Delaunay Triangulation Method: Definition of the Calibration Domain

The Delaunay triangulation (DT) method for multivariate calibration is a topological multivariate calibration method. In this paper, we present methods for the definition of the calibration domain. Outliers in the calibration set must be found and deleted and clusters detected. When clusters are found, it may be advantageous to make separate local models. Two methods are proposed. The first, called the DT calibration domain algorithm, is based on finding a kernel of samples that is then extended according to local rules. An alternative is to first eliminate gross outliers and then divide the data set in clusters, if such clusters exist, with Dbscan, a density‐based clustering method. The cluster(s) is (are) then used as kernels(s) and extended with the same rules as the DT calibration domain algorithm to develop DT models for each cluster. The two methods and some of the difficulties that can be encountered with them are demonstrated with three simulated data sets and tested with three real NIR data sets (one agricultural, one food, and one industrial). It is shown that the methods perform well and are at least comparable in prediction performance to partial least squares (PLS).     

Studies on the cell structure of quasicrystals

The geometric and crystallographic ideas for cell models and tilings in non-periodic ordered structures are outlined. The basic concepts, among them the cell geometry and duality in a lattice are explained for the example of a one dimensional section through the root lattice A ₂. The corresponding constructions for 3D icosahedral sections through the 6D face-centered hypercubic lattice, equivalent to the root lattice D ₆, are described. Two different tilings, one with equivalent, one with three inequivalent vertex positions, are derived and discussed.     

Visualizing the dual space of biological molecules

An important part of protein structure characterization is the determination of excluded space such as fissures in contact interfaces, pores, inaccessible cavities, and catalytic pockets. We introduce a general tessellation method for visualizing the dual space around, within, and between biological molecules. Using Delaunay triangulation, a three-dimensional graph is constructed to provide a displayable discretization of the continuous volume. This graph structure is also used to compare the dual space of a system in two different states. Tessellator, a cross-platform implementation of the algorithm, is used to analyze the cavities within myoglobin, the protein-RNA docking interface between aspartyl-tRNA synthetase and tRNA^Asp, and the ammonia channel in the hisH–hisF complex of imidazole glycerol phosphate synthase.     

基于三维重建理论的目标光谱散射特性研究

根据三维重建理论,基于目标的多角度视图,重建了目标表面的三维点云。利用德洛奈三角剖分法结合可见性原理,得到了目标的曲面和曲面面元的法线方向。根据粗糙面散射理论和目标表面的双向反射分布函数(BRDF),结合大气传输软件Modtran计算的某时间、地点的背景光谱辐射亮度,数值分析了目标光谱散射亮度分布特性。以覆盖车衣的汽车为例,重建的三维几何模型误差为4.11%,数值计算了目标在三个波段的光谱散射亮度分布。上述方法可以进一步用于卫星和其他空间目标的光谱辐射、散射特性研究。     

Distance-restricted matching extension in planar triangulations

A graph G is said to have property E(m,n) if it contains a perfect matching and for every pair of disjoint matchings M and N in G with |M|=m and |N|=n, there is a perfect matching F in G such that M⊆F and N∩F=0?. In a previous paper (Aldred and Plummer 2001) [2], an investigation of the property E(m,n) was begun for graphs embedded in the plane. In particular, although no planar graph is E(3,0), it was proved there that if the distance among the three edges is at least two, then they can always be extended to a perfect matching. In the present paper, we extend these results by considering the properties E(m,n) for planar triangulations when more general distance restrictions are imposed on the edges to be included and avoided in the extension.     

On the number of hamiltonian cycles in triangulations with few separating triangles

In this article, we investigate the number of hamiltonian cycles in triangulations. We improve a lower bound of for the number of hamiltonian cycles in triangulations without separating triangles (4‐connected triangulations) by Hakimi, Schmeichel, and Thomassen to a linear lower bound and show that a linear lower bound even holds in the case of triangulations with one separating triangle. We confirm their conjecture about the number of hamiltonian cycles in triangulations without separating triangles for up to 25 vertices and give computational results and constructions for triangulations with a small number of hamiltonian cycles and 1–5 separating triangles.     

2D Centroidal Voronoi Tessellations with Constraints

<正>We tackle the problem of constructing 2D centroidal Voronoi tessellations with constraints through an efficient and robust construction of bounded Voronoi diagrams, the pseudo-dual of the constrained Delaunay triangulation.We exploit the fact that the cells of the bounded Voronoi diagram can be obtained by clipping the ordinary ones against the constrained Delaunay edges.The clipping itself is efficiently computed by identifying for each constrained edge the(connected) set of triangles whose dual Voronoi vertices are hidden by the constraint.The resulting construction is amenable to Lloyd relaxation so as to obtain a centroidal tessellation with constraints.     

提高CCD在激光三角测距中分辨率的方法

激光三角测距系统的精度主要取决于光斑象在探测器上的定位，用ＣＣＤ摄象机作为探测器时，光斑象的定位精度又取决于ＣＣＤ摄象机的分辨率。通常用光斑的采样灰度质心作为象点的准确位置可将ＣＣＤ的分辨率提高到亚象元级，但这种方法存在其固的的局限，边缘灰度跳变与高频干扰噪音影响。     

平面上两个点集间距离的O(nlogn)算法

定理“平面上两个点集的距离所在边是Voronoi图的Delaunay三角剖分中一条边”是本文的核心。在该定理基础上，本文提出如何用Voronoi图的Delaunay三角剖分算法求平面上两个点集的距离．并分析其复杂性．