函数图

Peaks(30); N=16;% number of contour lines and their colors clf % clear the current figure view(3)% set view to 3-D hold on % hold blank screen setgca,' ColorOrder ',hsv(N % use colors from default hsv colormap contour3 % draw N contour lines grid,xlabel(' X-axis '),ylabel(' Y-axis '),zlabel(' Z-axis ') title(' CONTOUR3 of PEAKS ') hold off

输出见图 18.17。图 18.17 函数 PEAKS 的三维等值线图现在，各条等值线的颜色沿着 z 轴的变化和网格图曲面图网格图和曲面图网格图曲面图一样。

The course contains four sections as follows: mathematical logic (including basic concepts of propositional logic and predicate logic, propositional calculuses and inference theories), set theory (including set algebras, relations, functions and cardinal numbers), algebraic structure (including algebraic systems, semigroups and groups, rings and fields, lattices and Boolean algebras), graph theory (including basic concepts of graph, Euler graphs and Hamiltonian graphs, trees, planar graphs and coloring graphs, some special vertex subsets and edge subsets).

本课程包含四部分内容：数理逻辑（包含命题逻辑与一阶逻辑的基本概念、等值演算以及推理理论），集合论（包含集合代数、二元关系、函数和基数），代数结构（包含代数系统、半群与群、环与域、格与布尔代数），图论（包含图的基本概念、欧拉图与哈密顿图、树、平面图及图的着色、图的某些特殊的顶点子集与边子集）。

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。

After certifying the irreality of ideal filtering function, we can get a better filter selecting a proper window function. Comparing two actual filters, we designate a good"Panama hat"filtering function. Meanwhile, an effectively linear interpolating function is introduced to raise the image reconstruction quality. Describing its realizing steps on the micro-computer briefly, we reconstructed some images from the anlogue projections of some models. The number of projection views is 180, 100 same interval parallel lines per view; the size of reconstructed images is 64×64 pixels with 64 gray levels; the reconstructing speeds are 40" on PC-386 and 12"on PC-486, respectively; each pixel is 0.31mm.

在证明了理想滤波器的不可实现性之后，得知通过选择适当的窗函数可获得很好的滤波函数，经过两个实际滤波器的效果对比，我们选取了较好的"巴拿马帽"形滤波函数，同时也介绍了一个有效的提高重建质量的线性内插函数，概要地叙述了平行射束图象重建的计算机具体实现步骤后，对几个物体的模拟投影数据进行了重建：投影角为180°，每视角下有100个平行投影数据点，在386微机上重建尺寸为64×64，时间约为40秒；在486/33MHz微机上只用了12秒，图象的象点精度是0.31mm。

The prerequisite of the correct use of karnaugh map is to full in the map with the given logic function correctly. Karnaugh map can be used to transform logic function into various simplest expressions and check the race and hazard of logic function. It has a wider range of important applications in the analysis and design of combinational logic circuit and sequential logic circuit.

正确运用卡诺图的前提是把给定的逻辑函数正确填图，可以利用卡诺图将逻辑函数化简为各种最简表达式；可以用来检查逻辑函数的竞争冒险等；在组合逻辑电路和时序逻辑电路的分析与设计中更有广泛的重要应用。

In part two, the optical spatiotemporal pattern in ring optic cavity is investigated. Using delay feedback with spatial perturbation method, the system shows roll, square, hexagon, homocentric circle,"honeycomb"and"snowflower" pattern with different spatial perturbation functions. Different patterns can be coexist and compete each other with the same perturbation function, which is the new character of this optical system with delay feedback.

第二部分，利用延时反馈的空间微扰方法研究了环形腔中二能级介质的光学时空斑图的控制，在不同的微扰函数作用下，出现了滚筒状、四方形、六角形、蜂窝状、同心圆以及"雪花"状等不同的斑图，并且在相同的微扰函数下出现了不同斑图之间的竞争，这种竞争是我们发现的这一具有空间微扰的延时反馈非线性光学系统光学斑图的新特征。

In part two, the optical spatiotemporal pattern in ring optic cavity is investigated. Using delay feedback with spatial perturbation method, the system shows roll, square, hexagon, homocentric circle,"honeycomb"and"snowflower" pattern with different spatial perturbation functions. Different patterns can be coexist and compete each other with the same perturbation function, which is the new character of this optical system with delay feedback.

第二部分，利用延时反馈的空间微扰方法研究了环形腔中二能级介质的光学时空斑图的控制，在不同的微扰函数作用下，出现了滚筒状、四方形、六角形、蜂窝状、同心圆以及&雪花&状等不同的斑图，并且在相同的微扰函数下出现了不同斑图之间的竞争，这种竞争是我们发现的这一具有空间微扰的延时反馈非线性光学系统光学斑图的新特征。

In the incontinuous cutting, the wave shape of milling can be looked as periodic function. When the milling wave shape with single-tooth was looked as impulse function, by the Fourier Transform, we can find out that it is composed of sine wave with a given frequency and a series of integer multiple frequency. Discussing on the power function is a major tache for studying on the cutting capability of the complex three-dimension groove milling inserts, so to know the facts that affect the single-tooth milling spectral value, and to observe the dynamic milling wave property from the composition of the power spectral, thus we can design and optimize grooves.

在断续切削中，铣削波形可被看作周期函数，将单齿铣削波形看成为脉冲函数，经过傅立叶变换，可以表示为一个按特定的基本频率变动的正弦波形的分量和许多个按基本频率的整数倍而变动的正弦波形的分量叠加而成，讨论所获得的频谱函数，是研究三维复杂槽型铣刀片切削性能的主要环节，以便了解影响单齿铣削波形幅值谱图的各种因素，并从功率谱图的组成情况来考察动态铣削波形的特性，从而进行槽型的设计和优选。

It is useful to design their algorithm.For an arbitrary P of the reals,we defin

从数学理论上来讲，我们称函数f为图G的一个P-控制函数是指：在图G-中定义函数f：V→P，即对图G的顶点进行赋权，若对于V中任何一个顶点v，我们有f≥1成立。w=f=∑_f，我们称min{w|f为图G的

More importantly, we propose a data-dependent parameterization method in which optimal parameterization in the lighting and viewing space that minimizes the modeling error is obtained.

我们使用了多变量的球面迳向基底函数核心当作我们双向贴图函数模型的核心并且使用了资料相关的重新参数化方法得到在光源及视点空间的最佳参数以增进我们双向贴图函数模型的近似度。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。