## 计算机代写|计算机视觉代写Computer Vision代考|CS518

2023年2月3日

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
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## 计算机代写|计算机视觉代写Computer Vision代考|Particle Filter

The Kalman filter requires that the state equation is linear and the state distribution is Gaussian. These requirements are not always met in practice. Particle filter is an effective algorithm for solving non-linear problems. The basic idea is to use random samples (these samples are called “particles”) propagated in the state space to approximate the posterior probability distribution (PPD) of the system state, thereby obtaining the estimated value of system state. The particle filter itself represents a sampling method by which a specific distribution can be approximated through a time structure. Particle filters are also often referred to as sequential Monte Carlo methods, guided filtering, etc. In the research of image technology, it is also called CONditional DENSity propagATION (CONDENSATION).

Suppose a system has a state $X_t=\left{\boldsymbol{x}1, \boldsymbol{x}_2, \ldots, \boldsymbol{x}_t\right}$, where the subscript represents time. At time $t$, there is a probability density function that represents the possible situation of $\boldsymbol{x}_t$, which can be represented by a group of particles (a group of sampling states), and the appearance of particles is controlled by its probability density function. In addition, there are a series of observations related to the probability of state $X_t, Z_t=\left{z_1, z_2, \ldots, z_t\right}$, and a Markov hypothesis that the probability of $\boldsymbol{x}_t$ depends on the previous state $\boldsymbol{x}{t-1}$, which can be expressed as $P\left(\boldsymbol{x}t \mid \boldsymbol{x}{t-1}\right)$.

Conditional density diffusion is an iterative process. At each step, a set of $N$ samples $s_i$ with weight $w_i$ are maintained, namely
$$S_t=\left{\left(s_{t i}, w_{t i}\right)\right} \quad i=1,2, \cdots, N \quad \sum_i w_i=1$$
These samples and weights together represent the probability density function of the state $X_t$ given the observation $Z_t$. Unlike the Kalman filter, the distribution does not need to meet the constraints of single-mode, Gaussian distribution, etc. and can be multi-mode. Now it is necessary to derive $S_t$ from $S_{t-1}$.

## 计算机代写|计算机视觉代写Computer Vision代考|Mean Shift and Kernel Tracking

The mean shift represents the mean vector of the shift. The mean shift is a non-parametric technique that can be used to analyze complex multi-modal feature spaces and determine feature clusters. It assumes that the distribution of clusters in its central part is dense, and it iteratively calculates the mean value of the density kernel (corresponding to the centroid or the center of gravity of the cluster, which is also the most frequent value in a given window) to achieve the goal.

The principle and steps of the mean shift method are introduced below with the help of Fig. 5.12, where the dots in each figure represent the feature points in the 2-D feature space (actually maybe higher dimensional). First, randomly select an initial region of interest (initial window) and determine its centroid (as shown in Fig. 5.12a). It can also be regarded as drawing a ball with this point as the center (drawing a circle in 2-D). The radius of the ball or circle should be able to contain a certain number of data points, but not all data points can be included. Next, search for a region of interest with a greater density of surrounding points, and determine its centroid (equivalent to moving the center of the ball to a new position, which is the average position of all points in this radius), and then move the window to this position that is determined by the centroid, where the displacement vector between the original centroid and the new centroid corresponds to mean shift (as shown in Fig. 5.12b). Repeat the above process to continuously move the mean (the result is that the ball/circle will gradually approach the region with greater density) until convergence (as shown in Fig. 5.12c). The position of the last centroid here determines the maximum value of the local density, that is, the most frequent value of the local probability density function.

Mean shift technique can also be used for moving object tracking. At this time, the region of interest corresponds to the tracking window, and a feature model is required for the tracked object. The basic idea of using the mean shift technique for object tracking is to continuously move the object model in the tracking window to search for the position with the largest correlation value. This is equivalent to moving the window to coincide (converge) with the centroid when determining the cluster center.

# 计算机视觉代考

## 计算机代写|计算机视觉代写Computer Vision代考|Particle Filter

$X_{-} t=\backslash$ left $\left{\backslash\right.$ boldsymbol ${x} 1$, Iboldsymbol ${x} _2$, VIdots, Ibolds $}$
，其中下标代表时间。在时间 $t$ ，有一个概率密度函数代 表可能的情况 $\boldsymbol{x}t$ ，可以用一组粒子（一组采样状态）来 表示，粒子的出现是由它的概率密度函数控制的。此 外，还有一系列与状态概率相关的观察 $\mathrm{X} t \mathrm{t}$, Z_t $t=\backslash$ left $\left{z{-} 1, z_2\right.$ 2,Vdots, z_t tright $}$ ， 以及一个马尔可 夫假设，即 $\boldsymbol{x}t$ 取决于之前的状态 $\boldsymbol{x} t-1$, 可以表示为 $P(x t \mid x t-1)$ 条件密度扩散是一个迭代过程。在每一步，一组 $N$ 样本 $s_i$ 有重量 $w_i$ 被维持，即 $\mathrm{S}{-} \mathrm{t}=\backslash \operatorname{left}\left{\backslash \operatorname{left}\left(\mathrm{S}{-}{\mathrm{t}}, \mathrm{w} _{\mathrm{t} i} \backslash\right.\right.$ right $) \backslash$ right $} \backslash$ quad $i=1,2, \backslash \mathrm{cd}$ 这些样本和权重一起代表了状态的概率密度函数 $X_t$ 鉴于 观察 $Z_t$. 与卡尔曼滤波器不同的是，分布不需要满足单 模、高斯分布等约束，可以是多模。现在需要导出 $S_t$ 从 $S{t-1}$

## 计算机代写|计算机视觉代写Computer Vision代考|Mean Shift and Kernel Tracking

Mean shift 技术也可以用于运动目标跟踪。此时感兴趣区域对应于跟踪窗口，需要对跟踪对象建立特征模型。利用均值漂移技术进行目标跟踪的基本思想是在跟踪窗口中不断移动目标模型，寻找相关值最大的位置。这相当于在确定聚类中心时移动窗口使其与质心重合（收敛）。

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。