随机函数

In this paper, the theory, algorithm, and experiment of automatic object detection and tracking are studied in depth. It is firstly pointed out that the essential of Mean Shift method is a special Newton-Gaussian method. A new method named Fast Mean Shift is established to stretch the conservative step of Mean Shift method. The convergence and validity of this new method are proved in theory. And it is also proved that the convergence speed of Fast Mean Shift is faster than that of Mean Shift. The contrast experiments of searching the maximum possibility density of random of data sets in plane and 3D space are done. The results show that this new method can reduce the iterations greatly. A new object tracking method based on Fast Mean Shift is built to improve the object tracking performance, which is shown in the face tracking experiment with the tennis sequence provided by the Ohio State University, and the car tracking experiment with the car sequence provided by Kalsruhe University. The face trcking experiment with highly noised images show that the object tracking method based on Fast Mean Shift has strong anti-jamming ability. A new fast color object detection technology based on characteristic color is established, which use characteristic color distribution to compute the characteristic color vector of any area in an image quickly. With the high performance search method, the fast object detection is achieved. At last, using object tracker based on Fast Mean Shift and color object detector based on characteristic color with the Kalman filter, PID controller, searial communication and other technologies, automatic object detection and tracking system with control system is built. The availability and anti-jamming ability of this system are verified by some object detection and tracking tests in different scenes.

本文对目标自动识别与跟踪进行了理论、计算、试验三方面的深入研究，主要包括：首次指出了目标跟踪技术中常用的均值迁移方法的本质为一种特殊的高斯-牛顿方法，改进了均值迁移方法步长取值保守的弱点，建立了快速均值迁移方法，证明了该方法的收敛性、有效性以及收敛速度优于均值迁移方法；进行了平面和3维随机分布数据集的最大概率密度搜索对比试验，试验结果表明，快速均值迁移方法大大减少了迭代次数；建立了基于快速均值迁移的目标跟踪方法，利用俄亥俄州立大学提供的乒乓球序列图像和卡斯鲁厄大学的汽车序列图像，对人脸和汽车目标跟踪性能分别进行了对比试验，并进行了高噪声人脸图像目标跟踪试验，结果表明，基于快速均值迁移的目标跟踪方法有效提高了目标跟踪性能，具有很强的抗干扰能力；建立了一种新型彩色目标自动识别方法，采用特征色彩分布函数实现了对任意图像区域特征色彩矢量的快速计算，建立了高效的搜索方法，实现了彩色目标的快速识别；将基于快速均值迁移方法的目标跟踪方法、基于特征色彩的目标识别方法与卡尔曼滤波、PID控制、串行通讯等技术结合，建立了带有控制系统的快速目标自动识别与跟踪系统，并在不同场景下进行了目标自动识别与跟踪试验，验证了快速目标自动识别与跟踪系统的有效性和抗干扰能力。

It is usually required to calculate the mean and the standard deviation of the function of random variables in many engineering problems.

引言在工程实践中，经常会遇到需要计算随机变量函数特征值的问题。

The paper deals with the mean square value of dynamic loads for automobiles with two degrees of freedom by means of random vibration theory and derives an analytieal formula according to Jordan lemma.

运用随机振动理论，研究了二自由度汽车车轮的动载荷均方值，由约旦复变函数引理，推出一个解析公式。

A differential equation describing this stochastic process is derived, and a statistical distribution function of microcrack size is obtained.

本文导出了描述这种随机过程的微分方程，利用微裂缝形成长大的位错机理，解出了微裂缝大小的统计分布函数。

Computation of Laplace transforms is an important component of multifrac-tal analysis, and the moment generating function for occupation time of stochastic processes is the Laplace transforms of occupation time.

拉普拉斯变换的计算是重分形分析的一个重要组成部分，随机过程逗留时的矩母函数是逗留时的拉普拉斯变换。

The major contribution of this thesis is introduce and develop Moment Generating Function Approach to performance analysis of Arbitrary Stochastic Petri Nets In which firing delays of transitions can be either deterministic or arbitrarily distributed random variable with a moment generating function.

在ASPN中，变迁的激活时延即可以是确知的或具有矩母函数的任意分布的随机变量。

In the proof,the tools of the conditional moment generating function and the differentiation on a net for the study on strong limit theorems in the random selection system are applied.

在证明中采用了一种把网微分法与条件矩母函数相结合应用于随机选择系统强极限定理研究的一种途径。

In part 3, utilizing the existing Lipschitz results and the property of Yosida approximation of monotone and continuous function, we prove the existence and uniqueness theorem of a general backward stochastic differential equation with monotone and continuous coefficient.

第三部分在系数仅满足单调连续这样一个新条件下，我们综合运用单调连续函数的Yosida逼近的性质以及Lipschitz条件下的已有结果，证明了一般形式的倒向随机微分方程解的存在唯一性。

This dissertation proves that the class of monotone increase functions is PAC solvable while the class of single peak functions is non-PAC solvable under a GA with reproduction and a mutation operator which mutate according to a pre-set order.

本文提出了概率意义上近似收敛可解的概念，并证明了随机行走和狄拉克δ函数都是非PAC可解的，证明了任何问题在只有杂交算符或变异算符的遗传算法下都是非PAC可解的。

We obtain the risk process involved in this model,the statistical properties of the surplus process,and statistical features of the claim numbers and the probability distribution of the total amount of compensation.The three types of business of the risk model is given when the number of claims obey Poisson distribution and negative binomial distribution.We make a comparison between the risk model built in the thesis and the classic risk models with independent claim numbers when the amount of claims obey Weillbull distribution and Exponential distribution.The results have a good practical significance.

其次，考虑不同险种间的相互关系，建立了一种含有主副理赔的风险分析模型；借助随机过程和经典风险理论，对该风险模型所涉及的风险过程、盈余过程的统计特性以及理赔总额的概率分布、数字特征和矩母函数进行解析研究，给出了主理赔次数服从泊松分布和负二项分布的这种风险模型的具体实例，并在理赔额变量服从Weillbul分布和Exponential分布的情况下，把文中所建风险模型和理赔次数相互独立的风险模型作了比较，所得结果有很好的现实意义。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。