基于子图的随机图点覆盖2度点核化研究

点覆盖问题虽然可以在参数计算理论的架构内求精确解,但是目前在理论及应用上有一定的局限性.根据不同度的顶点之间及顶点与边的关系,提出随机图参数化点覆盖问题的d-核化可决策性及2度点三角形子图的计数方法;通过研究子图对顶点的共享关系,分析2度顶点核化过程中核及度分布演变的动态过程,得出随机图2度点核化强度与2度点概率关系及2度点核化可决策性的两个推论: 2度点核化算法对2度点分布概率约为0.75的随机图的核化强度最高;对顶点度概率分布为φ(x)的随机图的参数化点覆盖问题(G,k),当k小于某一与φ(x)有关的值时,它是2-核化可决策的.仿真结果证实,该理论能够把握2度点核化的内在机制,提供随机图上这一NP完全问题的求解方法,也为参数计算在已知度分布的一类不确定问题中的应用提供了可能.     

一种提取目标图像最小外接矩形的快速算法

在图像分类与识别算法研究中,目标几何特征的提取通常需要计算目标图像的最小外接矩形以获取长、宽等属性。针对该特点,提出一种利用顶点链码与离散格林理论相结合的方式提取目标图像的最小外接矩形的算法。该算法只需根据顶点链中垂直或水平方向上的点坐标即可求出目标的面积、形心和主轴。基于顶点链码和离散格林的主轴法和旋转法可快速求出目标的最小外接矩形。实验结果表明,旋转法的运算速度是现有算法的2倍左右,主轴法的速度又比旋转法快速2倍左右。     

建筑运维阶段信息模型的轻量化方法

BIM 技术引入我国以来,在建设项目中的普及率远低于推广的力度,导致这种现 状的原因之一,是贯穿全生命周期的BIM 模型拥有大量的数据,对计算机的要求过高。通过利 用Revit API 外部功能扩展方式实现二次开发,以及使用网格模型简化算法从内外两方面分别对 建筑运维阶段信息模型进行轻量化处理,降低使用时对硬件的要求,使BIM 全生命周期模型更 加具有普适性,对BIM 在国内的发展具有相当的意义。实验结果证实,该方法能够在不影响运 维阶段使用的情况下,实现建筑信息模型的轻量化。     

基于立方体染色的排课表模型

根据立方体染色思想,建立排课表模型,引入关联锁原理,将排课表约束条件转化为立方体点线面关系,增强该模型的收敛性,从而更好地解决排课问题。分析结果表明,在教师、课程、学生等信息已知的情况下,该模型可给出教学资源消耗的最小值,达到合理利用教学资源的目的。     

基于顶点存储类型的多边形填充算法

提出了一种基于顶点存储类型的多边形填充算法。该算法将多边形顶点和新生成的交点划分为三种类型进行存储,然后由过顶点的扫描线将多边形分割成若干个梯形区域分别进行填充。此算法只涉及过顶点的扫描线,且多边行边上的像素点坐标可以直接从边的直线方程中获得,从而使得该算法大大降低了计算的复杂性。     

曲面三角网格模型顶点法矢计算与交互式分割

本文给出一种三角网格模型顶点法矢计算公式,该公式采用网格模型中三角片面积与顶角角度综合加权,其计算精度高于现有的面积加权计算方法．另外,本文还提出了一种简便灵活的任意拓扑曲面三角网格模型交互式分割方法．利用该方法,可有效地将任意拓扑三角网格模型分割为几个与盘形拓扑同胚的区域,为后续处理提供方便。     

基于STL文件的Laplacian网格优化算法

针对直接重构得到且以STL文件格式存储的网格模型质量不高的问题, 提出了一种基于Laplacian坐标的网格模型全局优化算法。该算法在提高三角面片质量的同时可以很好地保持原网格模型的局部几何特征, 其核心思想是通过在最小二乘意义下求解由权重控制的包含顶点位置和拉普拉斯坐标双重约束的线性系统来对网格顶点进行重新定位。从实验结果可以看出, 该算法较以往的Lapacian优化算法在对网格细节特征的保持上有一定优势。     

Deletion, replacement and mean-shift for diagnostics in linear mixed models

Deletion, replacement and mean-shift model are three approaches frequently used to detect influential observations and outliers. For general linear model with known covariance matrix, it is known that these three approaches lead to the same update formulae for the estimates of the regression coefficients. However if the covariance matrix is indexed by some unknown parameters which also need to be estimated, the situation is unclear. In this paper, we show under a common subclass of linear mixed models that the three approaches are no longer equivalent. For maximum likelihood estimation, replacement is equivalent to mean-shift model but both are not equivalent to case deletion. For restricted maximum likelihood estimation, mean-shift model is equivalent to case deletion but both are not equivalent to replacement. We also demonstrate with real data that misuse of replacement and mean-shift model in place of case deletion can lead to incorrect results.     

Finding a minimal cover for binary images: An optimal parallel algorithm

Given a black-and-white image, represented by an array of n × n binary-valued pixels, we wish to cover the black pixels with aminimal set of (possibly overlapping) maximal squares. It was recently shown that obtaining aminimum square cover for a polygonal binary image with holes is NP-hard. We derive an optimal parallel algorithm for theminimal square cover problem, which for any desired computation timeT in [logn,n] runs on an EREW-PRAM with (n/T) processors. The cornerstone of our algorithm is a novel data structure, the cover graph, which compactly represents the covering relationships between the maximal squares of the image. The size of the cover graph is linear in the number of pixels. This algorithm has applications to problems in VLSI mask generation, incremental update of raster displays, and image compression.The research reported here forms part of the author's doctoral dissertion, submitted to Cornell University in May 1989. This work was partially supported by NSF Grant DC1-86-02256, IBM Agreement 12060043, and ONR Contract N00014-83-K-0640. A preliminary version of this paper was presented at the 26th Annual Allerton Conference on Communications, Control, and Computing, Monticello, IL, September 28–30, 1988.