关键词： 数学形态学   图象处理   模式识别   图象分割   算法  

摘要： 图象分割在图象分析、机器视觉、目标识别中都将直接影响到后续的理解和识别工作。本文着重讨论了基于数学形态学变换的图象分割算法，提出了基于图象最大内切圆的数学形态学形状描述图象分割算法和基于目标最小闭包结构元素的数学形态学形状描述图象分割算法。

关键词： 数学思想方法   数学素质教育   化归   数形结合   新大纲   乘法法则   思维能力   乘法分配律   数学素养   运算法则  

摘要： 九年义务教育数学新大纲明确指出：“初中数学的基本知识主要是初中代数、几何中的概念、法则、性质、公式、定理，以及由其内容所反映出来的数学思想和方法．”这是加强数学素质教育的一项新举措．与传统教材相比，新教材无疑是从根本上着意全面提高学生的“数学素质”．...

关键词： mathematical programs with equilibrium constraints   sequential quadratic programming   linear complementarity  

摘要： This paper presents a sequential quadratic programming algorithm for computing a stationary point of a mathematical program with linear complementarity constraints. The algorithm is based on a reformulation of the complementarity condition as a system of semismooth equations by means of Fischer-Burmeister functional, combined with a classical penalty function method for solving constrained optimization problems. Global convergence of the algorithm is established under appropriate assumptions. Some preliminary computational results are reported.

关键词： 聚类算法   数学形态学   空间数据库   模式识别  

摘要： 聚类算法能从空间数据库中直接发现一些有意义的聚类结构而不需要背景知识，是空间数据发掘和知识发现的重要手段。在分析已有聚类算法的基础上，提出了一种基于数学形态学的聚类算法，该算法能够处理任意形状的聚类，采用启发式方法自动确定最优聚类数。同时，该算法也可以在矢量型空间数据库中得到实现。试验表明算法是可行和有效的，且能处理存在噪音的数据。

关键词： algebraic invariants   free form objects   recognition   pose estimation   implicit polynomials  

摘要： Implicit polynomials can be used for describing a large variety of curved shapes. In most of the earlier works, the emphasis had been on the use of second degree implicit polynomials. To describe more complex curves and surfaces, it is necessary that higher degree implicit polynomials be used. In this paper, we have proposed a tensor based approach for obtaining affine and Euclidean invariants from the coefficients of higher degree implicit polynomials. Our approach is more general and computationally efficient than the matrix based approaches for obtaining invariants. For the Euclidean case, the algorithm can be used for both recognition and pose estimation. In this paper, we have demonstrated our approach for obtaining invariants of 2-D shapes using third and fourth degree implicit polynomials. (C) 1997 Pattern Recognition Society. Published by Elsevier Science Ltd.

摘要： The trie, or digital tree, is a standard data structure for representing sets of strings over a given finite alphabet. Since Knuth's original work (1973), these data structures have been extensively studied and analyzed. In this paper, we present an algebraic approach to the analysis of average storage and average time required by the retrieval algorithms of trie structures under the prefix model. This approach extends the work of Flajolet et al. for other models which, unlike the prefix model, assume that no key in a sample set is the prefix of another. As the main application, we analyze the average running time of two algorithms for computing set intersections.

关键词： 分解算法   凸多面体   数学规划  

摘要： 分析讨论了一种数学规划的分解算法，并在凸多面体分析的基础上，讨论了Ｄａｎｔｚｉｇ－Ｗｏｌｆ算法及其改进．

关键词： 算筹   筹算   算法   数学机械化  

摘要： 本文从现代计算机技术的角度来分析中国传统数学机械化的“硬件系统”和“软件系统”。重点论述算筹是中国传统数学机械化的物质基础，优越的计算工具和十进位置值制记数法为数学机械化提供了得天独厚的条件；而制定算法是数学的根本，也可以说是中华民族的价值观在数学中的表现，变换技术和改进算法是数学机械化的核心内容。中国传统数学的算法化倾向以及算筹的不断改进、完善，又促使机械化水平的提高和计算技术的长期发达。

关键词： 极限分析   凸函数   刚塑性结构   数学规划算法  

摘要： 从塑性极限分析理论的上限定理出发，将理想刚塑性结构极限分析问题归化为求：ｆ（ｘ１，ｘ２，…，ｘｎ）＝∑Ｒｉ＝１∑ｎｊ＝１ａｉｊｘｊ＋ｂｉ的凸函数的最小值及最小值点的问题，给出了解决上述问题的数学规划算法。

关键词： Shannon-type techniques   Fourier interpolation   Aperture synthesis   Reconstruction  

摘要： A new class of phase-calibration algorithms is presented. The originality of these algorithms, as well as their efficiency, results from certain particular structures, the analysis of which calls on algebraic graph theory. The corresponding optimization process, which is based on the principle of the trust-region methods, proves to be well suited to these structures. The main message that emerges from the study is very clear: The traditional notions of phase closure imaging can be understood and refined in a wider framework. The implications of this research therefore concern all the fields in which the notion of phase closure plays a key role: weak-phase imaging in optical interferometry, radio imaging, remote sensing by aperture synthesis, etc. (C) 1998 Optical Society of America.