拓扑结构

The surface representation in discrete form and its differential computation are important issues in computer graphics and geometric design.

0引言一般来说，曲面的一阶微分量是指曲面的切平面方向和法向量，二阶微分量是指曲面的曲率等有关量·它们作为重要的曲面信息度量指标，在计算机图形学，机器人视觉和计算机辅助设计等领域发挥了重要的作用·传统的曲面是连续形式的参数曲面和隐式曲面，其微分量的计算已经有了较完备的方法·随着激光测距扫描等三维数据采样技术和硬件设备的长足进步，以及图形工业对任意拓扑结构光滑曲面造型的需求日益迫切，离散形式的曲面———细分曲面、网格曲面和点云曲面正在逐渐成为计算机图形学和几何设计领域的新宠·于是，对这种离散形式的曲面如何估

This work opened up the new field of differential topology .

这工作开放微分拓扑结构新领域。

With this approach, a mathematical model of ASVG is developed. The method is simple and can be used to analyze the detailed internal properties of an ASVG. It overcomes the disadvantages of the two methods generally used, one is a method for modeling an ASVG by getting differential equations according to the topology of the ASVG circuit, which is very complicated and it is difficult to get a unified model expression of an ASVG; the other is a method for modeling an ASVG by considering the whole ASVG as a voltage source, which is too simple to analyze the detailed internal properties of ASVG.

该方法既克服了根据ASVG装置拓扑结构列写微分方程组的建模方法过于复杂且不易获得统一模型表达式的缺点，同时又克服了将ASVG装置等效为电压源的建模方法太简单而无法用于分析ASVG装置内部性质的缺点，具有建模简单又能分析ASVG装置的内部性质的优点。

Based on complex network theory, the qualitative analysis of the topology of NCW is carried out by establishing a four-tier gird diorama. Then we discovered that NCW has inherent scale-free feature.

基于复杂网络理论，通过建立四重网格立体模型，定性分析了网络中心战的拓扑结构，从中发现其具有无尺度的基本特征。

In this algorithm,by restricting the selection rule of a discrete time series,an appropriate discrete model of satellite time-varying topological networks can be obtained.

卫星网络是一种特殊的时变网络，由于卫星本身的特点，网络的拓扑结构、各边的权值都随时间变化而变化。

First, the satellite constellation topology and the satellite network are introduced in this paper. A comprehensive overview on LEO satellite network routing algorithm research status is given, including the comparisons of several major LEO satellite network routing protocols like DT-DVTR(Discrete Time Dynamic Virtual Topology Routing)、AR and FSA.

本文首先介绍了卫星星座的拓扑结构和卫星网络的组网方式，对LEO卫星网络路由算法研究现状进行了综述，对主要的几种LEO卫星网络路由协议如DT-DVTRDiscrete Time Dynamic Virtual Topology Routin(来源：554fABC论文网www.abclunwen.comg、AR和FSA等进行了详细的比较并论述了它们具有的优点和存在的缺点。

They point out that volume control topologies are not perfectly linear, nor are buffer stages perfectly noiseless and distortionless.

他们指出，音量控制拓扑结构不完全线性的，也不是完美的缓冲阶段噪声和失真。

Plenty of samples is provided for training BP neural network by traditional design method and the topology structure is built using forward propagating data and backward propagating error data, which is applied to optimal design of parallel double broken line pulley in order to accomplish the mapping between main parameter of hoisting mechanism of gantry crane and the related parameters of parallel double broken line pulley.

利用传统的设计方法为BP神经网络的学习提供足够样本集，然后通过正向传播和误差反向传播建立BP神经网络的拓扑结构，并将其应用于平行双折线卷筒的智能设计中，以完成龙门起重机起升机构主要设计参数与平行双折线卷筒相关参数的映射，提高设计的质量和效率，为龙门起重机关键零部件的智能设计提供一个新的途径。

It solves the problem that the unitary contour presentation can not correctly extract face contour in a face image which suffers from scale, rotation etc. The definition of the internal and external energy function is provided. At the same time, the global matching algorithm and local matching algorithm is given. The experiment shows that this presentation and the accompanying matching algorithm can be used to extract the face contour very well. So the image segmentation can be implemented by using it.②By analyzing the recognition principle of PCA method, we can conclude that the face images coming from different surrounding consist of different face image space. This is the essential reason that makes the generality of PCA method worse. Also, we give a measurement means to measure the distance from different face image space, so we can analyze face image space more conveniently.③We also construct various scale models and rotation pose models to detect the scale and rotating angle of face image to be recognized. The experiment results show that the detecting precision is very high. So it is good for face image feature extraction and face image representation.④Similarly, we construct local feature models of face image and utilize them to detect the local feature of face image. At the same time, we put forward a novel face image local feature detection algorithm, locating step by step. The experiment results show that this method can accurately detect the location of local face feature in a image.⑤A novel face image presentation model, dual attribute graph , is put forward. Firstly, it utilizes attribute graph to present the face image, then exact the local principal component coefficient and Gabor transform coefficient of thc pixels which corresponds to the nodes of the graph as the attribute of the nodes. This representation fully makes use of the statistical characteristic of the local face feature and utilizes Gabor transform to present the topographical structure of face image. So DAG has more general property.⑥Based on the DAG presentation, we give a DAG matching function and matching algorithm. During the design of the function and algorithm, the noise factor, e. g., lighting, scale and rotation pose are considered and tried to be eliminated. So the algorithm can give more general property.⑦A general face image recognition system is implemented. The experiment show the system can get better recognition performance under the noise surrounding of lighting, scale and rotation pose.

本文在上述研究的基础上，取得了如下主要研究成果：①构造了一个通用的人脸轮廓模型表示，解决了由于人脸图象尺度、旋转等因素而使得仅用单一轮廓表示无法正确提取人脸轮廓的问题，并给出了模型内、外能函数的定义，同时给出了模型的全局与局部匹配算法，实验表明，使用这种表示形式以及匹配算法，能够较好地提取人脸图象的轮廓，可实际用于人脸图象的分割；②深入分析了PCA方法的识别机制，得出不同成象条件下的人脸图象构成不同的人脸图象空间的结论，同时指出这也是造成PCA方法通用性较差的本质原因，并给出了不同人脸空间距离的一种度量方法，使用该度量方法能够直观地对人脸图象空间进行分析；③构造了各种尺度模板、旋转姿势模板以用于探测待识人脸图象的尺度、旋转角度，实验结果表明，探测精确度很高，从而有利于人脸图象特征提取，以及图象的有效表示；④构造了人脸图象的各局部特征模板，用于人脸图象局部特征的探测；同时提出了一种新的人脸图象局部特征探测法---逐步求精定位法，实验结果表明，使用这种方法能够精确地得到人脸图象各局部特征的位置；⑤提出了一种新的人脸图象表示法---双属性图表示法；利用属性图来表示人脸图象，并提取图节点对应图象位置的局部主成分特征系数以及Gabor变换系数作为图节点的属性，这种表示方法充分利用了人脸图象的局部特征的统计特性，并且使用Gabor变换来反映人脸图象的拓扑结构，从而使得双属性图表示法具有较强的通用性；⑥在双属性图表示的基础上，给出双属性图匹配函数及匹配算法，在函数及算法设计过程中，考虑并解决了光照、尺度、旋转姿势变化等因素对人脸图象识别的影响，使得匹配算法具有较强的通用性；⑦设计并实现了一个通用的人脸图象识别系统，实验结果表明，该系统在图象光照、尺度、旋转姿势情况下，得到了较好的识别效果。

Duality principle is a powerful tool for the analysis of topological structure of power electronic circuits.

对偶原理是分析电力电子电路拓扑结构的有力工具。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。