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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

## CS代写|图像处理作业代写Image Processing代考|Mode Filter

The mode value represents the most likely value in a distribution. The mean, median, and mode values are all relative to the region covered by the mask. Similar to the mean filter or median filter, the mode filter takes the most-frequency value in the mask as the output of the filter.

Using the mode filter can not only eliminate noise (especially impulse noise) but also sharpen the edge of the object. This is because, in the neighborhood close to the edge, the mode filter will move the mode closer to the center of the edge, thereby making the edge sharper. This can be explained as follows: the pixels on the background side of any edge mainly have background gray values, so the output of the mode filter is the gray value of the background; while the pixels on the foreground side of any edge mainly have foreground gray values, so the output of the mode filter is the gray value of the foreground. In this way, at a certain point on the edge, the main peak of the local grayscale distribution changes from the background to the foreground or from the foreground to the background, thereby tending to enhance the edge. This is different from averaging filter, which blurs the edges. Averaging filtering will produce an edge profile with a mixture of background and foreground gray levels, which will reduce the local contrast between these two regions.

The grayscale distribution in a region can be represented by the histogram of the region, and the mean, median, and mode are all closely related to the histogram. The mean value of the histogram of a region also gives the mean gray value of the region. The median value of the histogram of a region also gives the median gray value of the region. The mode value of the histogram of a region is the gray value with the largest statistical value. If the histogram is symmetrical and there is only one peak, then the mean, median, and mode are all the same. If there is only one peak in the histogram, but the left and right are asymmetric, then the mode value corresponds to that peak, and the median is always closer to the mode value than the mean.

Figure $2.13$ gives a histogram of an image to show the positional relationship between the mean, median, and mode.

In Figure 2.13, the position of the mode value is $7=\arg {\max [H(z)]}$, and the position of the median value is $6($ as $1+3+4+5+6=9+8+2$ ), and the position of the mean value is $5.69=$ $(1 \times 1+2 \times 3+3 \times 4+4 \times 5+5 \times 6+6 \times 7+7 \times 9+8 \times 8+9 \times 2) /(1+2+3+4+5+6+7+8+9)=256 / 45)$. It can be seen that the position of the median value is closer to the position of the mode value than the position of the mean value.

Direct detection of the mode value may be inaccurate due to the influence of noise. If the median value has been determined, the median position can be used to further determine the mode position. The method of truncating median filtering can be used here. First, according to the median value, cut the longer part of the tail to make it the same length as the un-truncated part, then calculate the median value of the remaining part, and then cut it off as above so that the iteration will gradually approach the mode position. Here the relationship that the median position is closer to the mode position than the mean position is used.

## CS代写|图像处理作业代写Image Processing代考|Interactive Filtering

The use of the aforementioned various filters to eliminate periodic noise requires prior knowledge of the frequency of the noise so that it is possible to design the filter to automatically eliminate noise. In practice, if the frequency of periodic noise is not known in advance, the spectral amplitude map $G(u, v)$ of the degraded image can be displayed. Since the noise of a single frequency will produce two bright spots far away from the origin of the coordinate on the spectrum amplitude map, it is easy to rely on visual observation to interactively determine the position of the pulse component in the frequency domain and use a band-stop filter to eliminate them at this position. This kind of human-computer interaction can improve the flexibility and efficiency of the filtering process.

In practice, the periodic noise often has multiple frequency components, for which the main frequency needs to be extracted. This requires placing a band-pass filter $H(u, v)$ at the position corresponding to each bright spot in the frequency domain. If we can construct a $H(u, v)$ that allows only components related to the interference pattern to pass, then the Fourier transform of this pattern is:
$$P(u, v)=H(u, v) G(u, v)$$
To build such a $H(u, v)$, many judgments are needed to determine whether each bright spot is an interference bright spot. So this work often needs to be done interactively by observing the spectrum display of $G(u, v)$. When a filter is determined, the periodic noise can be obtained by the following equation:
$$p(x, y)=F^{-1}{H(u, v) G(u, v)}$$
If the $p(x, y)$ can be completely determined, then subtracting $p(x, y)$ from $g(x, y)$ can provide $f(x, y)$. In practice, only a certain approximation of this pattern can be obtained. To reduce the influence of the components that are not considered in the estimation of $p(x, y)$, the weighted $p(x, y)$ can be subtracted from $g(x, y)$ to obtain an approximation of $f(x, y)$ :
$$f_e(x, y)=g(x, y)-w(x, y) p(x, y)$$
In the above equation, $w(x, y)$ is called the weight function. By changing it, the optimal noise elimination result can be obtained in a certain sense.

# 图像处理代考

## CS代写|图像处理作业代写Image Processing代考|Interactive Filtering

p(X,是)=F−1H(在,在)G(在,在)

F和(X,是)=G(X,是)−在(X,是)p(X,是)

## 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。

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