收敛

Experiment in this paper validates the convergence of the improved Mean Shift algorithm, contrast convergence rate of improved Mean Shift algorithm with convergence rate of traditional Mean Shift algorithm.

本文的实验也进一步验证了改进的Mean Shift算法的收敛性，并对比了改进前后的Mean Shift算法的收敛速度。

Li Xiangru found an error in Comuniciu's proof of Mean Shift convergence, and gave an indirect condition for its convergence.

李乡儒指出了Comuniciu关于算法收敛性证明中的错误，并给出了一个算法收敛的间接条件。

The research of its convergence of Mean Shift algorithm is the foundation of its application. Comaniciu and Li Xiang-ru have respectively provided the proof for the convergence of Mean Shift but they both made a mistake in their proofs.

作为迭代算法，Mean Shift的收敛性研究是应用的基础，而Comaniciu和李乡儒分别证明了Mean Shift的收敛性，但证明过程存在错误。

Exponential distribution ; estimation of parameters ; strong convergence rate ; mean square convergence rate ; indicators of reliability ; Monte-Carlo simulation

指数分布；参数估计；强收敛速度；均方收敛速度；可靠性指标；蒙特卡罗模拟

The convergence of the mean shift procedure to the closest mode of the underlying distribution is proven, both for the Epanechnikov kernel and the general case of kernels with convex and monotonic decreasing profile. The smooth trajectory property of the mean shift is also demonstrated.

均值平移算法对于Epanechnikov 核函数的收敛性在本文中得到了证明，进而推出均值平移算法收敛的充要条件是核函数具有凸的、单调递减性质的轮廓；揭示了均值平移过程运动轨迹的平滑性。

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。

The non-reference-signal's adaptive digital filter algorithm of multi-sensor data fusion in the course of adaptive filter can be done without reference signals. It can adjust convergence constant automatically, it can also be recurred with real gradient value. Thus the field to apply the adaptive filter is widened, the convergence speed of the adaptive filter is sped up, the weighted disadjustmend is decreased, so that the last error of mean square approaches its minimum value more.

这章研究的基于多传感器数据融合无参考信号的自适应数字滤波算法其在自适应滤波过程中具有不用参考信号与自动调整收敛因子及使用实际梯度值进行递推的特点，这样不仅可扩大自适应滤波的使用范围，而且还使自适应滤波的收敛速度加快有效地减小权失调，从而使最后的均方误差更接近于其最小值。

It is improved to solve the prematurely and stagnation problems of traditional Ant Colony Optimization in the paper. First, mean value method is used to update pheromone to avoid premature convergence which leads to non-globally optimal solution. Second, Pheromone is updated by Best Track to speed the rate of convergence which will help to avoid locally optimal solution.

本文针对基本蚁群算法比较容易陷入早熟和停滞，对现有蚁群算法的信息素更新规则进行了改进，一是采用平均值法更新信息素，避免算法过早收敛于非全局最优解；二是采用最佳路径法更新信息素，可加快收敛速度，并使算法跳出局部最优解。

In order to speed up the convergence speed, the each one step of the Landwber iteration is discomposed into the matrix computation and solution and a quick iteration scheme is given for the matrix computation. The relevant accelerated algorithm is given too. Numerical example proves that the accelerated algorithm can quicken convergence speed, reduce the calculation burden, and overcome the obstacle of application of Landweber method of iterated regularization.

为了加快Landweber迭代收敛速度，将每一步Landweber迭代分解为矩阵计算和求解，对矩阵计算部分设计了一种快速迭代格式，并给出了相应的加速算法，通过数值实验验证了这种算法能够大大加快收敛速度，有效的减少计算量，解决了Landweber迭代正则化方法在实际应用中的障碍。

The choice of step-length strongly affects the convergence rate of the Gradient Method, the classical Gradient Method—the method of steepest descent converges rather slowly in most cases, the poor behavior of the method is due to the optimal choice of step-length.

步长的选取对梯度法的收敛速度影响非常大，经典的梯度法-最速下降法在大多数情况下收敛得相当慢的原因在于最优步长的选取。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。