全景图像几何畸变校正的算法研究及其软件实现

对于360°视场的全景图像,本文提出了分别对其进行切向和径向畸变校正的处理算法,并用插值处理提高处理精度。达到了将全景图像恢复为常规视场平面像的目的。它是进一步图像分析的前期工作。     

Birkhoff系统的Hojman定理的几何基础

研究了Birkhoff系统的Hojman定理的几何基础.建立了系统的运动微分方程和Hojman守恒 定理，利用现代微分几何给出了Birkhoff系统的Hojman定理的一个证明. 关键词： Birkhoff系统 Hojman定理 对称性 微分几何     

NECESSARY CONDITIONS FOR OPTIMAL CONTROLS OF SEMILINEAR ELLIPTIC VARIATIONAL INEQUALITIES INVOLVING STATE CONSTRAINT

This paper deals with maximum principle for some optimal control problem governed by some elliptic variational inequalities. Some state constraints are discussed. The basic techniques used here are based on those in [1] and a new penalty functional defined in this paper.     

THE RELATIONSHIP BETWEEN PROJECTIVE GEOMETRIC AND RATIONAL QUADRATIC B-SPLINE CURVES

For two rational quadratic B-spline curves with same control vertexes, the cross ratio of four eollinear points are represented; which are any one of the vertexes, and the two points that the ray initialing from the vertex intersects with the corresponding segments of the twocurves, and the point the ray intersecting with the connecting line between the two neighboring vertexes. Different from rational quadratic Beeier curves, the value is generally related with the loeation of the ray, and the necessary and sufficient condition o5 the ratio being independent of the ray‘s loeation is showed. Alsn another cross ratio o5 the following four collinear points are suggested, i.e. one vertex, the points that the ray from the initlal vertex intersects respectivdy with the curve segmentt the line connecting the segments end points, and the line connecting the two neighboring vertexes. This cross ratio is concerned only whh the ray‘s location, butnot with the weights of the curve. Furthermore, the cross ratio is projective invariant under the projective transformation between the two segments.     

李群,拓扑与微分几何

该文介绍严志达院士的若干工作，以庆贺他的八十寿辰．     

带圆周约束的Steiner树问题

本文首先考虑了带圆周约束的Steiner树问题．设欧氏平面上有一圆，平面上有n个点，所成点集为N，该问题是要在圆周上找一点P，使NU{P}这n 1个点的Steiner树之长度达到最短．本文对干n=2的情形给出解．另一方面，鉴干问题的复杂性为NP-C，作者提出了一个近似解，并证明了近似解的性能比为（3的平方根）／2。     

横向放大率法确定复合光学系统的基点

介绍了应用测量横向放大率确定两薄透镜组成的复合光学系统基点的方法。由于采用线阵光电耦合器件（CCD）测量物经光学系统成像的横向放大率，提高了测量精度。     

一类求解线性约束非线性规划问题的可行方向法

Wilson,Han和Powell提出的序列二次规划方法(简称SQP方法)是求解非线性规划问题的一个著名方法,这种方法每次迭代的搜索方向是通过求解一个二次规划子问题得到的,本文受[1]启发,得到二次规划子问题的一个近似解,进而给出了一类求解线性约束非线性规划问题的可行方向法,在约束集合满足正则性的条件下,证明了该算法对五种常用线性搜索方法具有全局收敛性。     

几何位相非线性变化的实验研究

本文报道了Pancharatnam位相非线性变化的实验研究，实验结果与理论预言符合得很好。Pancharatnam位相的这种非线性可能在光开关中得到应用。