## 机器视觉代写|图像处理作业代写Image Processing代考|Ice Edge Detection

statistics-lab™ 为您的留学生涯保驾护航 在代写图像处理Image Processing方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写图像处理Image Processing代写方面经验极为丰富，各种代写图像处理Image Processing相关的作业也就用不着说。

• 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

The gradient, which is the first-order derivative, has a direction toward the most rapid change in intensity. The gradient of a digital image with pixel value $f(x, y)$ is defined as the vector:
$$\nabla f=\left[\begin{array}{l} G_{x} \ G_{y} \end{array}\right]=\left[\begin{array}{l} \frac{\partial f}{\partial x} \ \frac{\partial f}{\partial y} \end{array}\right]$$
and the gradient magnitude is given by:
$$|\nabla f|=\sqrt{G_{x}^{2}+G_{y}^{2}}=\sqrt{\left(\frac{\partial f}{\partial x}\right)^{2}+\left(\frac{\partial f}{\partial y}\right)^{2}}$$

while the direction of the gradient vector is given by the angle:
$$\theta=\angle f=\arctan \left(\frac{G_{x}}{G_{y}}\right)$$
with respect to the $x$-axis, where for implementation we use the arctan() function for correct quadrant mapping.

For computational efficiency, the gradient magnitude is sometimes approximated by using the squared gradient magnitude:
$$\nabla f \approx G_{x}^{2}+G_{y}^{2}$$
$$\nabla f \approx\left|G_{x}\right|+\left|G_{y}\right|$$
where these two approximations also preserve the relative changes in intensity scales.
The gradient of an image can be used for the detection of edges in the image; it requires the calculation of the partial derivatives $G_{x}$ and $G_{y}$ at every pixel location in the image. To directly estimate the partial derivatives $G_{x}$ and $G_{y}$ is one of the key issues in this method. The discrete approximation of partial derivatives over a neighborhood about a point is required. For example, it is a common and simple way to form the running difference of pixels along rows and columns of the image, which gives the approximation:
\begin{aligned} &\frac{\partial f}{\partial x}(x, y) \approx f(x+1, y)-f(x, y) \ &\frac{\partial f}{\partial y}(x, y) \approx f(x, y+1)-f(x, y) \end{aligned}
To implement the derivatives over an entire image, the edge detector, which is a local image processing method designed to detect edge pixels, filters the image with convolution kernels. So, the Equations $4.6 \mathrm{a}$ and $4.6 \mathrm{~b}$ can then be implemented for all pertinent values of $x$ and $y$ by filtering $f(x, y)$ with the simple 1-dimensional convolution kernels shown in Figure 4.1.

## 机器视觉代写|图像处理作业代写Image Processing代考|LAPLACIAN

Similar to the first-order derivative, the second-order derivative, which is the Laplacian of the image, is defined as:
$$\nabla^{2} f=\frac{\partial^{2} f}{\partial x^{2}}+\frac{\partial^{2} f}{\partial y^{2}}$$
The second-order derivative along the $x$ direction can be approximated by differentiating Equation $4.6 \mathrm{a}$ with respect to $x$, e.g.:
\begin{aligned} \frac{\partial^{2} f}{\partial x^{2}}(x, y) & \approx \frac{\partial G_{x}(x, y)}{\partial x} \ &=\frac{\partial f(x+1, y)}{\partial x}-\frac{\partial f(x, y)}{\partial x} \ & \approx[f(x+2, y)-f(x+1, y)]-[f(x+1, y)-f(x, y)] \ &=f(x+2, y)-2 f(x+1, y)+f(x, y) \end{aligned}

Since this approximation is centered about the pixel $(x+1, y)$, however, we replace $x$ with $x-1$ and obtain the result:
$$\frac{\partial^{2} f}{\partial x^{2}}(x, y) \approx f(x+1, y)+f(x-1, y)-2 f(x, y)$$
This is the desired approximation to the second partial derivative centered about the pixel $(x, y)$. Similarly,
$$\frac{\partial^{2} f}{\partial y^{2}}(x, y) \approx f(x, y+1)+f(x, y-1)-2 f(x, y)$$
Combining Equations $4.11$ and $4.12$ two equations into a single operator according to Equation $4.9$ gives an approximation of the Laplacian:
$$\nabla^{2} f(x, y)=f(x-1, y)+f(x+1, y)+f(x, y-1)+f(x, y+1)-4 f(x, y)$$
This expression simply measures the weighted differences between a pixel and its 4-neighbors, and it can be implemented by using the kernel in Figure 4.4(a).

Sometimes it is desired to give more weight to the center pixels in the neighborhood, and Equation $4.13$ can be extended to include the diagonal terms, for instance, using the kernel in Figure 4.4(b).

## 机器视觉代写|图像处理作业代写Image Processing代考|MORPHOLOGICAL EDGE DETECTION

Morphology refers to geometrical characteristics related to the form and structure of objects, such as size, shape, and orientation. In image processing, mathematical morphology involves geometric analysis of shapes and textures in images based on some simple mathematical concepts from set theory. It is used to extract image components that are useful in representation and description of region shapes, such as boundaries, skeletons, convex hull, etc.

Morphological operators work with an image and a structuring element. The structuring element is a small set or subimage used to probe the given image for specific properties. It is also known as a kernel, and can be represented as a matrix of 0 s and Is. Values of 1 in the matrix indicate the points that belong to the structuring element, while values of 0 indicate otherwise. The structuring element has a desired shape, such as square, rectangle, disk, diamond, etc. The origin of a structuring element identifies the pixel of interest (the pixel being processed), and it must be clearly specified. The origin is typically at the center of gravity; however, it could be located at any desired position of the structuring element. Figure $4.7$ shows examples of different structuring elements of various sizes with their origins highlighted in the corresponding geometric centers.

## 图像处理代考

∇F=[GX G是]=[∂F∂X ∂F∂是]

|∇F|=GX2+G是2=(∂F∂X)2+(∂F∂是)2

θ=∠F=反正切⁡(GXG是)

∇F≈GX2+G是2

∇F≈|GX|+|G是|

∂F∂X(X,是)≈F(X+1,是)−F(X,是) ∂F∂是(X,是)≈F(X,是+1)−F(X,是)

## 机器视觉代写|图像处理作业代写Image Processing代考|LAPLACIAN

∇2F=∂2F∂X2+∂2F∂是2

∂2F∂X2(X,是)≈∂GX(X,是)∂X =∂F(X+1,是)∂X−∂F(X,是)∂X ≈[F(X+2,是)−F(X+1,是)]−[F(X+1,是)−F(X,是)] =F(X+2,是)−2F(X+1,是)+F(X,是)

∂2F∂X2(X,是)≈F(X+1,是)+F(X−1,是)−2F(X,是)

∂2F∂是2(X,是)≈F(X,是+1)+F(X,是−1)−2F(X,是)

∇2F(X,是)=F(X−1,是)+F(X+1,是)+F(X,是−1)+F(X,是+1)−4F(X,是)

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 机器视觉代写|图像处理作业代写Image Processing代考|Ice Pixel Detection

statistics-lab™ 为您的留学生涯保驾护航 在代写图像处理Image Processing方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写图像处理Image Processing代写方面经验极为丰富，各种代写图像处理Image Processing相关的作业也就用不着说。

• 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

## 机器视觉代写|图像处理作业代写Image Processing代考|THRESHOLDING

The pixels in the same region have similar intensity. Based on that ice is whiter than water, the pixel values are normally very different between ice and water pixels, and thresholding is thus a natural choice to segment ice regions from water regions.
The thresholding method is based on the pixel’s grayscale value. It extracts the objects from the background and converts the grayscale image into a binary image. Assuming that an object is brighter than the background, the object and background pixels have intensity levels grouped into two dominant modes. The threshold $T$ is selected to distinguish the objects from the background. A pixel is marked as “object” if its value is greater than the threshold value and as “background” otherwise, that is:
$$g(x, y)= \begin{cases}1 & \text { if } f(x, y)>T \ 0 & \text { if } f(x, y) \leq T\end{cases}$$
where $g(x, y)$ and $f(x, y)$ are the pixel intensity values located in the $x^{\text {th }}$ row, $y^{\text {th }}$ column of the binary and grayscale image, respectively. This turns the grayscale image into a binary image.

When a constant threshold value is used over the entire image, it is called global thresholding. Otherwise, it is called variable thresholding, which allows the threshold to vary across the image.

## 机器视觉代写|图像处理作业代写Image Processing代考|GLOBAL THRESHOLDING

When the intensity distributions of objects and background pixels in an image are sufficiently distinct, it is possible to use a global threshold applicable for the entire image. The key to using the global thresholding is in how to select the threshold value, for which there are several different methods.

As mentioned in Section 2.2, image histogram is a useful tool for thresholding. If a histogram has a deep and sharp valley (local minima) between two peaks (local maxima), e.g., the bimodal histogram as shown in Figure 3.1, that represent objects and background, respectively, an appropriate value for the threshold will be in the valley between the two peaks in the histogram.

For example, as seen in Figure 3.2, the histogram of the grayscale sea ice image in Figure 3.2(a) clearly has two distinct modes, one for the objects (sea ice) and the other for the background (water). A suitable threshold for separating these two modes can be chosen at the bottom of this valley. As a result, it is easy to choose a threshold $T=125$ that separates them. Then the grayscale image can be converted into the binary image as shown in Figure $3.2(\mathrm{c})$, and the ice concentration is thereby estimated as $41.47 \%$.

This method is very simple. However, it is often difficult to detect the valley bottom precisely, especially when the image histogram is “noisy”, causing many local minima and maxima. Often the objects and background modes in the histogram are not distinct, making it more difficult to determine where the background intensities end and the object intensities begin. Furthermore, in most applications there are usually enough variability between images such that, even if a global thresholding is feasible, an algorithm capable of automatically estimating the threshold value for each image will be most accurate.

## 机器视觉代写|图像处理作业代写Image Processing代考|Otsu thresholding

To automatically select an optimal value for the threshold, Otsu proposed a method from the viewpoint of discriminant analysis; it directly approaches the feasibility of evaluating the “goodness” of the threshold [114].

Let $[0,1,2, \cdots, L-1]$ denote the $L$ intensity levels for a given image with size $M \times N$, and let $n_{i}$ denote the number of pixels with intensity $i$. The total number of pixels in the image, denoted by $n$, is then:
$$n=M \times N=\sum_{i=0}^{L-1} n_{i}$$
To examine the formulation of this method, the histogram is normalized as a discrete probability density function:
$$p_{i}=\frac{n_{i}}{n}, \quad p_{i} \geq 0, \sum_{i=0}^{L-1} p_{i}=1$$
Now suppose that a threshold $t(0<t<L-1)$ is chosen to divide the pixels into two classes $C_{0}$ and $C_{1}$, where $C_{0}$ is the set of pixels with levels $[0,1, \cdots, t]$, and $C_{1}$ is the set of pixels with levels $[t+1, t+2, \cdots, L-1]$. Then the probabilities of class $C_{0}$ occurrence is given by the cumulative sum:
$$P_{0}(t)=P\left(C_{0}\right)=\sum_{i=0}^{l} p_{i}$$
Similarly, the probability of class $C_{1}$ occurrence is given by
$$P_{1}(t)=P\left(C_{1}\right)=\sum_{i=l+1}^{L-1} p_{i}=1-P_{0}(t)$$
The mean intensity of the pixels in class $C_{0}$ is given by:
\begin{aligned} m_{0}(t) &=\sum_{i=0}^{t} i P\left(i \mid C_{0}\right) \ &=\sum_{i=0}^{t} i \frac{P\left(C_{0} \mid i\right) P(i)}{P\left(C_{0}\right)} \ &=\frac{1}{P_{0}(t)} \sum_{i=0}^{t} i p_{i} \end{aligned}
where $P\left(C_{0} \mid i\right)=1, P(i)=p_{i}$, and $P\left(C_{0}\right)=P_{0}(t)$. Similarly, the mean intensity of the pixels in class $C_{1}$ is given by:
\begin{aligned} m_{1}(t) &=\sum_{i=l+1}^{L-1} i P\left(i \mid C_{0}\right) \ &=\frac{1}{P_{1}(t)} \sum_{i=l+1}^{L-1} i p_{i} \end{aligned}

## 机器视觉代写|图像处理作业代写Image Processing代考|THRESHOLDING

G(X,是)={1 如果 F(X,是)>吨 0 如果 F(X,是)≤吨

## 机器视觉代写|图像处理作业代写Image Processing代考|Otsu thresholding

n=米×ñ=∑一世=0大号−1n一世

p一世=n一世n,p一世≥0,∑一世=0大号−1p一世=1

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 机器视觉代写|图像处理作业代写Image Processing代考|BILINEAR INTERPOLATION

statistics-lab™ 为您的留学生涯保驾护航 在代写图像处理Image Processing方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写图像处理Image Processing代写方面经验极为丰富，各种代写图像处理Image Processing相关的作业也就用不着说。

• 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

## 机器视觉代写|图像处理作业代写Image Processing代考|BILINEAR INTERPOLATION

The bilinear interpolation, also called first-order interpolation, calculates the intensity value for any point $(u, v)$ in the input image by using a low-degree polynomial of the form:
$$f(u, v)=\sum_{m=0}^{1} \sum_{n=0}^{1} a_{m n} u^{m} v^{n}$$
where the function $f$ gives the intensity value at $(u, v), a_{m n}(m, n=0,1)$ are coefficients determined by the four nearest neighbors.

When the intensity values of the four nearest neighbors are known, the general idea of the bilinear interpolation is to use linear interpolations along the $x$ – and $y$ directions to determine the intensity value at $(u, v)$. As exemplified in Figure $2.24, P$ denotes the interpolated point for which an intensity value must be calculated, $(u, v)$

are its coordinates mapped from the output image by Equation $2.33$, and $P_{1}, P_{2}, P_{3}$, and $P_{4}$ are its four nearest neighbors in the input image with the coordinates $(i, j)$, $(i, j+1),(i+1, j)$, and $(i+1, j+1)$, respectively. The bilinear interpolation first interpolates linearly along the $x$-direction to find the values at $Q_{1}$ and $Q_{2}$ :
\begin{aligned} &f\left(Q_{1}\right)=(j+1-v) f\left(P_{1}\right)+(v-j) f\left(P_{2}\right) \ &f\left(Q_{2}\right)=(j+1-v) f\left(P_{3}\right)+(v-j) f\left(P_{4}\right) \end{aligned}
then interpolates linearly along $y$-direction to obtain the value of $P$ :
\begin{aligned} f(P)=&(i+1-u) f\left(Q_{1}\right)+(u-i) f\left(Q_{2}\right) \ =&(i+1-u)\left[(j+1-v) f\left(P_{1}\right)+(v-j) f\left(P_{2}\right)\right] \ &+(u-i)\left[(j+1-v) f\left(P_{3}\right)+(v-j) f\left(P_{4}\right)\right] \ =&(i+1-u)(j+1-v) f\left(P_{1}\right)+(i+1-u)(v-j) f\left(P_{2}\right) \ &+(u-i)(j+1-v) f\left(P_{3}\right)+(u-i)(v-j) f\left(P_{4}\right) \end{aligned}
which gives:
$$f(P)=[i+1-u \quad u-i]\left[\begin{array}{cc} f\left(P_{1}\right) & f\left(P_{2}\right) \ f\left(P_{3}\right) & f\left(P_{4}\right) \end{array}\right]\left[\begin{array}{c} j+1-v \ v-j \end{array}\right]$$

## 机器视觉代写|图像处理作业代写Image Processing代考|BICUBIC INTERPOLATION

The bicubic interpolation, also called third-order interpolation, calculates the intensity value of any point $(u, v)$ in the input image by reconstructing a surface among its four nearest neighbors based on their intensity values, the derivatives in both $x$ – and $y$-directions, and the cross derivatives.

Similar to the bilinear interpolation, the bicubic interpolation calculates the intensity value for a point $(u, v)$ by fitting a cubic polynomial:
$$f(u, v)=\sum_{m=0}^{3} \sum_{n=0}^{3} a_{m n} u^{m} v^{n}$$
where $a_{m n}(m, n=0,1,2,3)$ are coefficients determined by its $4 \times 4$ nearest neighbors in the input image, that is, the four nearest neighbors of the point $(u, v)$ (empty circles as seen in Figure 2.25), and their horizontal, vertical, and diagonal neighboring pixels (black dots as seen in Figure 2.25). The latter are used to calculate the first-order derivatives in both $x$ – and $y$-directions and the cross derivative at each of the four nearest neighbors of point $(u, v)$. Then 8 first-order derivatives in both the $x$ – and $y$ directions and 4 cross derivatives, together with 4 intensity values at the four nearest neighbors of point $(u, v)$ give a linear system of 16 equations to determine the 16 coefficients of $a_{m n}$ in Equation $2.39$ [122].

## 机器视觉代写|图像处理作业代写Image Processing代考|Bicubic interpolation

Instead of directly calculating the solution of this linear system, typically by some matrix inversion, an alternative approach is to use a cubic convolution interpolation kernel that is composed of piecewise cubic polynomials defined on the subintervals $(-2,-1),(-1,0),(0,1)$, and $(1,2)[78]$. Assume the coordinates of the four nearest neighbors of point $(u, v)$ in the input image are $(i, j),(i, j+1),(i+1, j)$, and $(i+$ $1, j+1)$. Then the interpolated pixel intensity may be expressed in the compact form [121]:
$$f(u, v)=\sum_{m=-1}^{2} \sum_{n=-1}^{2} f(u+m, v+n) r_{c}{(m+i-u)} r_{c}{-(n+j-v)}$$
36
Sea Ice Image Processing with MATLAB
where $r_{c}(x)$ denotes a bicubic interpolation function, given by :
$$r_{c}(x)= \begin{cases}(a+2)|x|^{3}-(a+3)|x|^{2}+1, & \text { if } 0 \leq|x| \leq 1 \ a|x|^{3}-5 a|x|^{2}+8 a|x|-4 a, & \text { if } 1<|x| \leq 2 \ 0, & \text { if }|x|>2\end{cases}$$
where $a$ is the weighting factor that can be used as a tuning parameter to obtain a best visual interpolation result [118].

Compared with the bilinear interpolation, the bicubic interpolation method extends the influence of more neighboring pixels, and it takes not only the intensity values but also the intensity derivatives into account. Therefore, this method can produce more clear result than the bilinear interpolation method; however, at the expense of more computational complexity.

## 机器视觉代写|图像处理作业代写Image Processing代考|BILINEAR INTERPOLATION

F(在,在)=∑米=01∑n=01一种米n在米在n

F(问1)=(j+1−在)F(磷1)+(在−j)F(磷2) F(问2)=(j+1−在)F(磷3)+(在−j)F(磷4)

F(磷)=(一世+1−在)F(问1)+(在−一世)F(问2) =(一世+1−在)[(j+1−在)F(磷1)+(在−j)F(磷2)] +(在−一世)[(j+1−在)F(磷3)+(在−j)F(磷4)] =(一世+1−在)(j+1−在)F(磷1)+(一世+1−在)(在−j)F(磷2) +(在−一世)(j+1−在)F(磷3)+(在−一世)(在−j)F(磷4)

F(磷)=[一世+1−在在−一世][F(磷1)F(磷2) F(磷3)F(磷4)][j+1−在 在−j]

## 机器视觉代写|图像处理作业代写Image Processing代考|BICUBIC INTERPOLATION

F(在,在)=∑米=03∑n=03一种米n在米在n

## 机器视觉代写|图像处理作业代写Image Processing代考|Bicubic interpolation

F(在,在)=∑米=−12∑n=−12F(在+米,在+n)rC(米+一世−在)rC−(n+j−在)
36使用 MATLAB进行

rC(X)表示双三次插值函数，由 给出：
rC(X)={(一种+2)|X|3−(一种+3)|X|2+1, 如果 0≤|X|≤1 一种|X|3−5一种|X|2+8一种|X|−4一种, 如果 1<|X|≤2 0, 如果 |X|>2

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 机器视觉代写|图像处理作业代写Image Processing代考|CHAIN CODE

statistics-lab™ 为您的留学生涯保驾护航 在代写图像处理Image Processing方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写图像处理Image Processing代写方面经验极为丰富，各种代写图像处理Image Processing相关的作业也就用不着说。

• 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

## 机器视觉代写|图像处理作业代写Image Processing代考|CHAIN CODE

Chain codes are a notation for recording the list of boundary pixels of an object. The chain code uses a logically connected sequence of straight-line segments with specified length and direction to represent the boundary [45]. A chain code can be created by tracking a boundary in some direction, say clockwise, and assigning a direction to the segments connecting every pair of pixels. The direction of each segment is coded by using a 4- or 8 -connected numbering scheme, as shown in Figure 2.18. An example of the representations of an object boundary by using 4 – and 8 directional chain codes are shown in Figure 2.19.

Figure $2.18$ Numbering scheme of the chain code.
Taking an 8 -connected numbering scheme, for example, each code indicates the change of angular direction (in multiples of $45^{\circ}$ ) from one boundary pixel to the next. The even codes $0,2,4$, and 6 correspond to horizontal and vertical directions, while the odd codes $1,3,5$, and 7 correspond to the diagonal directions. The boundary has changed direction when a change occurs between two consecutive chain codes, and the change in the code direction usually indicates a corner on the boundary. By using the chain code, a complete description of an object boundary can be represented by the coordinates of the starting point together with the list of chain codes leading to subsequent boundary pixels, as shown in Figure $2.20$. This representation of a list of boundary pixels becomes more succinct than using all boundary pixels’ coordinates.
However, the chain code depends on the starting point, and different starting points result in different chain codes for the same boundary. To address this, the chain code for a boundary can be normalized with respect to the starting point by treating it as a circular or periodic sequence of direction numbers, and redefining the starting point such that the resulting sequence of numbers is of minimum magnitude.

## 机器视觉代写|图像处理作业代写Image Processing代考|IMAGE INTERPOLATION

An image gives the intensity values at the integral lattice locations, that is, the coordinates of each pixel are both integers. Image interpolation is the process of using known pixel intensity values to estimate the values at arbitrary locations other than those defined exactly by the integral lattice locations.

Image interpolation is a fundamental operation in image processing and has been widely used in image zooming, rotating, geometric calibration, etc. For example, as seen in Figure 2.22, suppose the input image coordinates $(x, y)$ are assigned to another pair of image coordinates $(\eta, \xi)$ by some coordinate transformation T:
$$(\eta, \xi)=\mathrm{T}{(x, y)}$$
Then the intensity values of the input image also have to be assigned to the corresponding locations of the transformed image. However, with the coordinate transform $\mathrm{T}$, some output pixels with coordinates calculated by Equation $2.32$ may be located between the integer-valued grid points in the $x y$-plane. Thus, the image interpolation techniques are applied to determine the intensity values at those in-between locations. Note also that two or more pixels in the input image can be mapped into the same pixel in the output image by the coordinate transform, in which case the image interpolation techniques can be used to combine multiple input pixel values into a common output pixel value.

## 机器视觉代写|图像处理作业代写Image Processing代考|NEAREST NEIGHBOR INTERPOLATION

The nearest neighbor interpolation, also called zero-order interpolation, assigns to each output pixel the intensity value of its nearest neighbor in the input image. To perform nearest neighbor interpolation method, the coordinates of every pixel in the output image, denoted as $(m, n)$, are first mapped into the input image by:
$$(u, v)=\mathrm{T}^{-1}{(m, n)}$$
where $(u, v)$ becomes the corresponding coordinates in the input image. Then the intensity value of the pixel located at $(m, n)$ in the output image is set as the value of the pixel that has the shortest distance to $(u, v)$ in the input image. This process is illustrated by Figure $2.23$.The nearest neighbor interpolation method is computationally very simple and fast. However, this method only uses the value of the pixel that is closest to the interpolated location, without taking account of the influence of other neighboring pixels. As a result, this method may produce severe mosaic and saw-tooth effect.

(这,X)=吨(X,是)

(在,在)=吨−1(米,n)

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 机器视觉代写|图像处理作业代写Image Processing代考|SET OPERATIONS ON BINARY IMAGES

statistics-lab™ 为您的留学生涯保驾护航 在代写图像处理Image Processing方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写图像处理Image Processing代写方面经验极为丰富，各种代写图像处理Image Processing相关的作业也就用不着说。

• 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

## 机器视觉代写|图像处理作业代写Image Processing代考|SET OPERATIONS ON BINARY IMAGES

Since a binary image is a matrix containing object pixels of value 1 and background pixels of value 0 , it can simply be represented as the set of those coordinate vectors

$(x, y)$ of the pixels that have value of 1 in the binary image, given by:
$$G={(x, y) \mid g(x, y)=1}$$
where $(x, y)$ are pairs of spatial coordinates, $g(x, y)$ is the pixel value $(0$ or 1$)$ at $(x, y)$, and $G$ represents the set of image pixels describing the object of interest. All other image pixels are assigned to the background.

Let $\mathbb{Z}$ be the set of integers. Let the elements of a binary image be represented by a set $A \subseteq \mathbb{Z} \times \mathbb{Z}$, whose elements are 2-dimensional vectors of the form $(x, y)$, which are spatial coordinates. If a set contains no elements, it is called an empty set or a null set, denoted by $\varnothing$. If $\omega=(x, y)$ is an element of $A$, then it is written as:
$$\omega \in A$$
otherwise, it is written as:
$\omega \notin A$
If every element of a set $A$ is also an element of a set $B$, then $A$ is said to be a subset of $B$ and written as:
$$A \subseteq B$$
A set $B$ of pixel coordinates $\omega$ that satisfy a particular condition is written as:
$$B={\omega \mid \text { condition }}$$
The universe set, $\mathbb{U}$, is the set of all elements in a given application. In image processing, the universe is typically defined as the rectangle containing all the pixels in an image.

The complement (or inverse) of $A$, denoted as $A^{c}$, is the set of all elements of $U$ that do not belong to set $A$, given by:
$$A^{c}={\omega \mid \omega \notin A}=\mathbb{U}-A$$
The complement of the binary image $A$ is the binary image that exchanges black and white, that is, 0 -valued pixels set to 1 -valued and 1 -valued pixels set to 0 -valued.
The union of two sets $A$ and $B$, denoted as $A \cup B$, is the set of all elements that belong to either $A, B$, or both, given by:
$$A \cup B={\omega \in A \text { or } \omega \in B}$$
The union of two binary images $A$ and $B$, is a binary image in which the pixels’ values are 1 if the corresponding input pixels’ values are 1 in $A$ or in $B$.

Similarly, the intersection of two sets $A$ and $B$, denoted as $A \cap B$, is the set of all elements that belong to both $A$ and $B$, given by:
$$A \cap B={\omega \in A \text { and } \omega \in B}$$
The intersection of two binary images $A$ and $B$ is a binary image where the pixels’ values are 1 if the corresponding input pixels’ values are 1 in both $A$ and $B$.

## 机器视觉代写|图像处理作业代写Image Processing代考|SET OPERATIONS ON GRAYSCALE IMAGES

When dealing with grayscale images, the set must represent an image with pixels having more than two values. The image intensity value is the third dimension besides the two spatial dimensions $x$ and $y$. A grayscale image can be represented as a binary image in a 3 -dimensional space, with the third dimension representing image intensities. The intensity values can be viewed as heights at each pixel above the $x y$-plane, according to a function $z=g(x, y)$ corresponds to a surface in the 3 dimensional space. Thus, a grayscale image can be represented as a set given by:
$$G={(x, y, z) \mid z=g(x, y)}$$
Because grayscale images are 3-dimensional sets, where the first two dimensions define the spatial coordinates and the third dimension denotes the grayscale intensity value, the preceding set operations for binary images are not applicable for grayscale images. Let the elements of a grayscale image be represented by a set $A \subseteq \mathbb{Z} \times \mathbb{Z} \times \mathbb{Z}$, whose elements are 3 -dimensional vectors of the form $(x, y, z)$, where the intensity value $z$ is also an integer value within the interval $\left[0,2^{k}-1\right]$ with $k$ defined as the number of bits used to represent $z$. The complement of $A$ is defined as the pairwise differences between a constant and the intensity of every pixel in an image, given by:
$$A^{c}={(x, y, L-z) \mid(x, y, z) \in A}$$
where $L=2^{k}-1$ is a constant. $A^{c}$ is an image of the same size as $A$; however, its pixel intensities have been inverted by substracting them from the constant $L$.

The union of two grayscale sets (images) $A$ and $B$ is defined as the maximum of corresponding pixel pairs, given by:
$$A \cup B=\left{\max _{z}(a, b) \mid a \in A, b \in B\right}$$
The outcome of $A \cup B$ is an image of the same size as these two images, formed from the maximum intensity between pairs of spatially corresponding elements.

## 机器视觉代写|图像处理作业代写Image Processing代考|LOGICAL OPERATIONS

The logical operations are derived from Boolean algebra, which is a mathematical approach to describe propositions whose outcome would be either TRUE or FALSE. The logical operations consist of three basic operations: NOT, OR, and AND. The terms NOT, OR, and AND are commonly used to denote complementation, union, and intersection, respectively. The NOT operation simply inverts the input value, that is, the output is FALSE if the input is TRUE, and it sets to TRUE if the input is FALSE. The OR operation produces the output TRUE if either one of the inputs is TRUE, and FALSE if and only if all the inputs are FALSE. The AND operation produces the output TRUE if and only if all inputs are TRUE, and FALSE otherwise. Any other logic operator, such as NAND, NOR, and XOR, etc., can be implemented by using only these three operators.

In image processing, the logic operations compare corresponding pixels of input images of the same size and generate an output image of the same size. When dealing with binary images, consisting of only 1 -valued object pixels and 0 -valued background pixels, the TRUE and FALSE states in logic operations correspond directly to the pixel values 1 and 0 , respectively. Hence, the logic operations can be applied in a straight forward manner on binary images using the rules from logical truth tables, as shown in Table $2.1$, to the pixel values from a pair of input images (or a single input image in the case of NOT operation).

## 机器视觉代写|图像处理作业代写Image Processing代考|SET OPERATIONS ON BINARY IMAGES

(X,是)二值图像中值为 1 的像素数，由下式给出：
G=(X,是)∣G(X,是)=1

ω∈一种

ω∉一种

## 机器视觉代写|图像处理作业代写Image Processing代考|SET OPERATIONS ON GRAYSCALE IMAGES

G=(X,是,和)∣和=G(X,是)

A \cup B=\left{\max _{z}(a, b) \mid a \in A, b \in B\right}A \cup B=\left{\max _{z}(a, b) \mid a \in A, b \in B\right}

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 机器视觉代写|图像处理作业代写Image Processing代考|DISTANCE TRANSFORM

statistics-lab™ 为您的留学生涯保驾护航 在代写图像处理Image Processing方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写图像处理Image Processing代写方面经验极为丰富，各种代写图像处理Image Processing相关的作业也就用不着说。

• 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

## 机器视觉代写|图像处理作业代写Image Processing代考|DISTANCE TRANSFORM

Distance transform is an important tool in image processing, and it is normally only applied to binary images that consist of object and background pixels. A distance transform of a binary image specifies the distance from every pixel to the nearest background pixel. In other words, the distance transform converts a binary image into a grayscale image where each object pixel has a value corresponding to the minimum distance from the background. The resulting grayscale image is a so-called distance map.

Assume $f$ is a binary image, in which the pixels with a value of ‘ 0 ‘ indicate the background while the pixels with a value of ‘ 1 ‘ indicate the object. Let $B=$ ${p \mid f(p)=0}$ be the set of background pixels and $O={p \mid f(p)=1}$ be the set of object pixels. The distance transform of a binary image $f, D(p)$, can be given by [39]:
$$D(p)= \begin{cases}0, & \text { if } p \in B \ \min _{q \in B} d(p, q), & \text { if } p \in O\end{cases}$$
where function $d$ is a distance function or metric which is to determine the distance between pixels.

For pixels $p, q$, and $r$ in an image, a distance function $d$ satisfies the following three criteria [128]:

1. Positive definite: $d(p, q) \geq 0(d(p, q)=0$ iff $p=q)$
2. Symmetric: $d(p, q)=d(q, p)$
3. Triangular: $d(p, r) \leq d(p, q)+d(q, r)$There are several types of distance metrics in image processing. The three most important ones are: Euclidean, city-block, and chessboard.

## 机器视觉代写|图像处理作业代写Image Processing代考|PERFORMANCE OF THE DISTANCE METRICS

Figure 2.14 Effects of different distance transforms.
denoted by the operator ‘ $*$ ‘, is defined as:
\begin{aligned} h(x, y) &=\omega(x, y) * f(x, y) \ &=\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \omega(u, v) f(x-u, y-v) \mathrm{d} u \mathrm{~d} v \end{aligned}
In image processing, where an image is represented by a set of pixels, convolution is a local operation that replaces each pixel in an image by a linear combination of its neighbors. The impulse response $\omega(x, y)$ is then referred to as a convolution kernel, and the convolution becomes the calculation of the sum of products of the kernel coefficients with the intensity values in the region encompassed by the kernel. The convolution of a kernel $\omega(x, y)$ of size $m \times n$ with an image $f(x, y)$ is given by:
\begin{aligned} h(x, y) &=\omega(x, y) * f(x, y) \ &=\sum_{s=-\frac{1}{2}}^{\frac{1}{2}} \sum_{t=-\frac{4}{2}}^{\frac{n}{2}} \omega(s, t) f(x-s, y-t) \end{aligned}
For each pixel $(x, y)$ in the image, the convolution value $h(x, y)$ is the weighted sum of the pixels in the neighborhood about $(x, y)$, where the individual weights are the corresponding coefficients in the convolution kernel. This procedure involves translating the convolution kernel to pixel $(x, y)$ in the image, multiplying each pixel in

the neighborhood by a corresponding coefficient in the convolution kernel, and summing the multiplications to obtain the response at each pixel $(x, y)$. Figure $2.15$ gives an example of convolution of an image with a $3 \times 3$ kernel. In this example, the response of the kernel at the center point $(x, y)$ of the $3 \times 3$ image neighborhood is given by:
\begin{aligned} h(x, y)=& \omega(-1,-1) f(x-1, y-1)+\omega(-1,0) f(x-1, y) \ &+\omega(-1,1) f(x-1, y+1)+\omega(0,-1) f(x, y-1) \ &+\omega(0,0) f(x, y)+\omega(0,1) f(x, y+1)+\omega(1,-1) f(x+1, y-1) \ &+\omega(1,0) f(x+1, y)+\omega(1,1) f(x+1, y+1) \end{aligned}

## 机器视觉代写|图像处理作业代写Image Processing代考|SET AND LOGICAL OPERATIONS

Since a binary image is a matrix containing object pixels of value 1 and background pixels of value 0 , it can simply be represented as the set of those coordinate vectors

$(x, y)$ of the pixels that have value of 1 in the binary image, given by:
$$G={(x, y) \mid g(x, y)=1}$$
where $(x, y)$ are pairs of spatial coordinates, $g(x, y)$ is the pixel value ( 0 or 1$)$ at $(x, y)$, and $G$ represents the set of image pixels describing the object of interest. All other image pixels are assigned to the background.

Let $\mathbb{Z}$ be the set of integers. Let the elements of a binary image be represented by a set $A \subseteq \mathbb{Z} \times \mathbb{Z}$, whose elements are 2-dimensional vectors of the form $(x, y)$, which are spatial coordinates. If a set contains no elements, it is called an empty set or a null set, denoted by $\varnothing$. If $\omega=(x, y)$ is an element of $A$, then it is written as:
$\omega \in A$
otherwise, it is written as:
$\omega \notin A$
If every element of a set $A$ is also an element of a set $B$, then $A$ is said to be a subset of $B$ and written as:
$$A \subseteq B$$
A set $B$ of pixel coordinates $\omega$ that satisfy a particular condition is written as:
$$B={\omega \mid \text { condition }}$$
The universe set, $\mathbb{U}$, is the set of all elements in a given application. In image processing, the universe is typically defined as the rectangle containing all the pixels in an image.

The complement (or inverse) of $A$, denoted as $A^{c}$, is the set of all elements of $U$ that do not belong to set $A$, given by:
$$A^{c}={\omega \mid \omega \notin A}=\mathbb{U}-A$$
The complement of the binary image $A$ is the binary image that exchanges black and white, that is, 0 -valued pixels set to 1 -valued and 1 -valued pixels set to 0 -valued.
The union of two sets $A$ and $B$, denoted as $A \cup B$, is the set of all elements that belong to either $A, B$, or both, given by:
$$A \cup B={\omega \in A \text { or } \omega \in B}$$
The union of two binary images $A$ and $B$, is a binary image in which the pixels’ values are 1 if the corresponding input pixels’ values are 1 in $A$ or in $B$.

Similarly, the intersection of two sets $A$ and $B$, denoted as $A \cap B$, is the set of all elements that belong to both $A$ and $B$, given by:
$$A \cap B={\omega \in A \text { and } \omega \in B}$$
The intersection of two binary images $A$ and $B$ is a binary image where the pixels’ values are 1 if the corresponding input pixels’ values are 1 in both $A$ and $B$.

## 机器视觉代写|图像处理作业代写Image Processing代考|DISTANCE TRANSFORM

D(p)={0, 如果 p∈乙 分钟q∈乙d(p,q), 如果 p∈这

1. 正定：d(p,q)≥0(d(p,q)=0当且当p=q)
2. 对称：d(p,q)=d(q,p)
3. 三角形：d(p,r)≤d(p,q)+d(q,r)图像处理中有几种类型的距离度量。最重要的三个是：欧几里得、城市街区和棋盘。

## 机器视觉代写|图像处理作业代写Image Processing代考|PERFORMANCE OF THE DISTANCE METRICS

H(X,是)=ω(X,是)∗F(X,是) =∫−∞∞∫−∞∞ω(在,在)F(X−在,是−在)d在 d在

H(X,是)=ω(X,是)∗F(X,是) =∑s=−1212∑吨=−42n2ω(s,吨)F(X−s,是−吨)

H(X,是)=ω(−1,−1)F(X−1,是−1)+ω(−1,0)F(X−1,是) +ω(−1,1)F(X−1,是+1)+ω(0,−1)F(X,是−1) +ω(0,0)F(X,是)+ω(0,1)F(X,是+1)+ω(1,−1)F(X+1,是−1) +ω(1,0)F(X+1,是)+ω(1,1)F(X+1,是+1)

## 机器视觉代写|图像处理作业代写Image Processing代考|SET AND LOGICAL OPERATIONS

(X,是)二值图像中值为 1 的像素数，由下式给出：
G=(X,是)∣G(X,是)=1

ω∈一种

ω∉一种

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 机器视觉代写|图像处理作业代写Image Processing代考|IMAGE HISTOGRAM

statistics-lab™ 为您的留学生涯保驾护航 在代写图像处理Image Processing方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写图像处理Image Processing代写方面经验极为丰富，各种代写图像处理Image Processing相关的作业也就用不着说。

• 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

## 机器视觉代写|图像处理作业代写Image Processing代考|IMAGE HISTOGRAM

The histogram of an image is a statistic showing the distribution of the pixel intensity values. For an image with $L$ possible intensity levels in the range of $[0, L-1]$, the histogram is the number of pixels in the image at each different intensity level, defined as the discrete function:
$$h\left(r_{k}\right)=n_{k}$$
where $r_{k}$ is the $k^{\text {th }}$ intensity level in the interval $[0, L-1]$, and $n_{k}$ is the number of pixels in the image whose intensity level is $r_{k}$. Note that $L=2^{B}$ where $B$ is the bit depth of the image.

For a grayscale image that has $L$ different possible intensities, $L$ numbers will be displayed in its histogram to show the distribution of pixels among those grayscale values. An example of the histogram of an 8-bit grayscale image, which has 256 possible intensity levels, is shown in Figure 2.7. For a color image, three individual histograms of red, green, and blue channels can be taken, as shown in Figure $2.8$.
A histogram is usually normalized by dividing all elements of $h\left(r_{k}\right)$ by the total number of pixels in the image, denoted by $n$ :
\begin{aligned} p\left(r_{k}\right) &=\frac{h\left(r_{k}\right)}{n} \ &=\frac{n_{k}}{M \times N} \end{aligned}
for $k=0,1, \cdots, L-1$. Note also that $n=M \times N$, where $M$ and $N$ are the row and column dimensions of the image. From basic probability, $p\left(r_{k}\right)$ gives the probability of occurrence of intensity level $r_{k}$ in an image.

## 机器视觉代写|图像处理作业代写Image Processing代考|PIXEL NEIGHBORHOODS

The neighborhood of a pixel plays an important role in image processing; it is often required for many operations, such as denoise, interpolation, edge detection, and morphology etc. The 4-neighbors and 8 -neighbors are two common pixel neighborhoods that are used to process an image.

The 4-neighbors of a pixel $p$ located at $(x, y)$ are a set of pixels that connected vertically and horizontally to $p$. As seen in Figure $2.9$ (a), the 4-neighbors of $p$ are

denoted by $N_{4}(p)$, and given by:
$$(x+1, y),(x-1, y),(x, y+1),(x, y-1)$$
in terms of pixel coordinates. Each 4-neighbor of $p$ is a unit distance from $p$.
The four pixels that connected diagonally to $p$ are called diagonal neighbors $(D-$ neighbors). As seen in Figure $2.9$ (b), the diagonal neighbors of $p$, denoted by $N_{D}(p)$, are given by:
$$(x+1, y+1),(x+1, y-1),(x-1, y+1),(x-1, y-1)$$
and each of them is at Euclidean distance of $\sqrt{2}$ from $p$.
The 8-neighbors of a pixel $p$ include its four 4-neighbors and four diagonal neighbors as seen in Figure $2.9(\mathrm{c})$, and they are denoted by $N_{8}(p)$.

Be aware that some of the points in $N_{4}(p), N_{D}(p)$, and $N_{8}(p)$ fall outside the image if $p$ lies on the border of the image.

Let $V$ be a set of intensity values that is used to define adjacency. It specifies a criterion of similarity that the intensity values of adjacent pixels shall satisfy. For example, $V=1$ when the adjacent pixels are 1 -valued for a binary image. $V$ could also be a subset of the 256 intensity values for an 8 -bit grayscale image. Two pixels $p$ and $q$ with the intensity values from $V$ are said to be:
(a) 4-adjacent, if $q \in N_{4}(p)$.
(b) 8 -adjacent, if $q \in N_{8}(p)$.
(c) $m$-adjacent (mixed adjacent), if
(i) $q \in N_{4}(p)$, or
(ii) $q \in N_{D}(p)$ and $N_{4}(p) \cap N_{4}(q)=\varnothing$ (the set $N_{4}(p) \cap N_{4}(q)$ has no pixels whose intensity values are from $V$ ).

Mixed adjacency is a modification of 8 -adjacency. It is used to eliminate the ambiguities that often arise when 8 -adjacency is used (this will be explained in Section 2.3.3).

## 机器视觉代写|图像处理作业代写Image Processing代考|IMAGE HISTOGRAM

H(rķ)=nķ

p(rķ)=H(rķ)n =nķ米×ñ

## 机器视觉代写|图像处理作业代写Image Processing代考|PIXEL NEIGHBORHOODS

(X+1,是),(X−1,是),(X,是+1),(X,是−1)

(X+1,是+1),(X+1,是−1),(X−1,是+1),(X−1,是−1)

(a) 4-相邻，如果q∈ñ4(p).
(b) 8 – 相邻，如果q∈ñ8(p).
(i)q∈ñ4(p), 或
(ii)q∈ñD(p)和ñ4(p)∩ñ4(q)=∅（该集ñ4(p)∩ñ4(q)没有强度值来自的像素在 ).

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 机器视觉代写|图像处理作业代写Image Processing代考|Digital Image Processing Preliminaries

statistics-lab™ 为您的留学生涯保驾护航 在代写图像处理Image Processing方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写图像处理Image Processing代写方面经验极为丰富，各种代写图像处理Image Processing相关的作业也就用不着说。

• 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

## 机器视觉代写|图像处理作业代写Image Processing代考|Digital Image Processing Preliminaries

A digital image in a 2-dimensional discrete space is the sampling and quantization of a 2 -dimensional continuous space, being a projection of a picture of objects and background in 3-dimensional space. A digital image is composed of 2 -dimensional array elements arranged in rows and columns. Those elements are the so-called pixels, and each of them holds a particular value to represent the picture at its location.
For a mathematical expression, a digital image can be represented as a function $f(x, y)$, where $(x, y)$ are integers and $f$ is a mapping that assigns an intensity value to each distinct pair of coordinates $(x, y)$. A digital image with $M$ rows and $N$ columns, which we say that the image is of size $M \times N$, can also be represented as a matrix:
$$f=\left[\begin{array}{cccccc} f(1,1) & f(1,2) & \cdots & f(1, y) & \cdots & f(1, N) \ f(2,1) & f(2,2) & \cdots & f(2, y) & \cdots & f(2, N) \ \vdots & \vdots & \ddots & \vdots & \ddots & \vdots \ f(x, 1) & f(x, 2) & \cdots & f(x, y) & \cdots & f(x, N) \ \vdots & \vdots & \ddots & \vdots & \ddots & \vdots \ f(M, 1) & f(M, 2) & \cdots & f(M, y) & \cdots & f(M, N) \end{array}\right]$$
where $f(x, y)(1 \leq x \leq M, 1 \leq y \leq N)$ is the finite and quantized value that represent the gray scale or color of the image at the point $(x, y)$.

In this chapter, some beforehand knowledge about digital image processing relevant to the sea ice image processing algorithms presented in this book is introduced.

## 机器视觉代写|图像处理作业代写Image Processing代考|The CMY and CMYK color spaces

The CMY (cyan, magenta, and yellow) color model is a subtractive color representation. It is typically used in color printing because cyan, magenta, and yellow are the primary colors of pigments. The CMY color model can be transformed from the RGB model by:
$$\left[\begin{array}{c} C \ M \ Y \end{array}\right]=\left[\begin{array}{l} 1 \ 1 \ 1 \end{array}\right]-\left[\begin{array}{l} R \ G \ B \end{array}\right]$$
where the tristimulus values in the RGB color model are normalized to the range $[0,1]$. Figure $2.4$ presents the CMY components of the color image shown in Figure $2.3$.

In practice, to produce true black color for printing without using excessive amounts of CMY pigments, black, called the key (K), is added as a fourth color, giving rise to the CMYK color model. The conversion between the CMYK and RGB is given by [121]:
$$\left[\begin{array}{l} C \ M \ Y \ K \end{array}\right]=\left[\begin{array}{l} 1 \ 1 \ 1 \ 0 \end{array}\right]-\left[\begin{array}{l} R \ G \ B \ 0 \end{array}\right]-K_{b}\left[\begin{array}{c} u \ u \ u \ -b \end{array}\right]$$
where
$$K_{b}=\min {1-R, 1-G, 1-B}$$
and $u(0 \leq u \leq 1)$ is the under-color removal factor, and $b(0 \leq b \leq 1)$ is the darkness factor.

## 机器视觉代写|图像处理作业代写Image Processing代考|The HSI color space

Alternative to the RGB, CMY and CMYK color spaces, a hue-saturation color coding method, HSI (hue, saturation, and intensity), is also commonly used, particularly in the image processing algorithms based on color descriptions. Hue is an attribute that describes a pure color, while saturation (purity) is a measure of the degree to which pure color is diluted by white light. The HSI color model decouples the intensity component from the hue and saturation in a color image [49], and it can be obtained from the RGB color model by [121]:
$$\begin{gathered} {\left[\begin{array}{c} I \ V_{1} \ V_{2} \end{array}\right]=\left[\begin{array}{ccc} \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \ \frac{-1}{\sqrt{6}} & \frac{-1}{\sqrt{6}} & \frac{2}{\sqrt{6}} \ \frac{1}{\sqrt{6}} & \frac{-1}{\sqrt{6}} & 0 \end{array}\right]\left[\begin{array}{l} R \ G \ B \end{array}\right]} \ H=\arctan \left(\frac{V_{2}}{V_{1}}\right) \ S=\sqrt{V_{1}^{2}+V_{2}^{2}} \end{gathered}$$
Figure $2.5$ presents the HSI components of the color image shown in Figure $2.3$.

## 机器视觉代写|图像处理作业代写Image Processing代考|Digital Image Processing Preliminaries

F=[F(1,1)F(1,2)⋯F(1,是)⋯F(1,ñ) F(2,1)F(2,2)⋯F(2,是)⋯F(2,ñ) ⋮⋮⋱⋮⋱⋮ F(X,1)F(X,2)⋯F(X,是)⋯F(X,ñ) ⋮⋮⋱⋮⋱⋮ F(米,1)F(米,2)⋯F(米,是)⋯F(米,ñ)]

## 机器视觉代写|图像处理作业代写Image Processing代考|The CMY and CMYK color spaces

CMY（青色、品红色和黄色）颜色模型是一种减色表示。它通常用于彩色印刷，因为青色、品红色和黄色是颜料的原色。CMY 颜色模型可以通过以下方式从 RGB 模型转换：
[C 米 是]=[1 1 1]−[R G 乙]

[C 米 是 ķ]=[1 1 1 0]−[R G 乙 0]−ķb[在 在 在 −b]

ķb=分钟1−R,1−G,1−乙

## 机器视觉代写|图像处理作业代写Image Processing代考|The HSI color space

[一世 在1 在2]=[131313 −16−1626 16−160][R G 乙] H=反正切⁡(在2在1) 小号=在12+在22

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 机器视觉代写|图像处理作业代写Image Processing代考|APPLICATIONS OF DIGITAL IMAGE PROCESSING TECHNIQUES FOR ICE PARAMETER IDENTIFICATION

statistics-lab™ 为您的留学生涯保驾护航 在代写图像处理Image Processing方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写图像处理Image Processing代写方面经验极为丰富，各种代写图像处理Image Processing相关的作业也就用不着说。

• 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

## 机器视觉代写|图像处理作业代写Image Processing代考|ICE PARAMETER IDENTIFICATION

Digital images were first used for transferring newspaper pictures between London and New York in the early 1920 s, where the pictures were coded for the submarine cable transmission and reconstructed by a special telegraph printer at the receiving end. The concept of digital image processing became meaningful and many of the digital image processing capabilities were developed in the $1960 \mathrm{~s}$ when both hardware and software of computer technology were developed powerful enough to carry out image processing algorithms. In the 1970 s, digital image processing techniques began to be used in the space program, medical imaging, remote sensing, and astronomy as cheaper and dedicated computer hardware became available. Until now, with the rapid development of computer technology, the use of digital image processing techniques has been growing by leaps and bounds, and has achieved success in many applications such as remote sensing, industrial inspection, medicine, biology, astronomy, law enforcement, defense, etc. [48].

In most cases, human manual interpretation is simply impossible, and the only feasible solution for information extraction from images is through digital image processing by a computer. Digital image processing algorithms, implemented by computers, are important to replace humans in the interpretation of image data. Many image processing algorithms have been developed for the analysis of sea ice statistics and ice properties from remotely sensed sea ice images, and in this section we will give an overview of some of the relevant literature in this field.

## 机器视觉代写|图像处理作业代写Image Processing代考|ICE CONCENTRATION CALCULATION

From Equation 1.1, it is clear that the estimation of ice concentration by using ice imagery data is equivalent to the discrimination of ice pixels from water pixels. Due to the fact that ice is normally brighter than water, a thresholding approach is typically used for extracting ice from water pixels $[54,169,185]$. For instance, Markus and Dokken [103] propose that sea ice pixels can be determined by adapting thresholds between ice and open water based on local intensity distributions, while Johannessen et al. [70] introduces an algorithm of sea ice concentration retrieval from ERS (European Remote Sensing) SAR (Synthetic Aperture Radar) images by using two thresholds to separate open water from thick ice.

Ice concentration derivation is usually associated with ice type classification, since all types of sea ice should be taken into account for calculating ice concen-tration. Hence, the algorithms for classifying ice types, such as unsupervised and supervised classification [169], texture features [89], and neural networks [77], etc., can also be used for calculating ice concentration. The ice concentration is then derived by summing up the concentrations of multiple ice types existing in the ice image.

## 机器视觉代写|图像处理作业代写Image Processing代考|SEA ICE TYPE CLASSIFICATION

Unsupervised and supervised classification algorithms are popular for sea ice type classification $[81,55,42,143,133,112,138,43,142,181]$. In an unsupervised classification approach, pixels are assigned to classes based on their spectral properties, without the user having any prior knowledge of the existence of those classes; while in a supervised classification approach, pixels are grouped based on the knowledge of the user by providing sample classes to train the classifier [71]. Hughes [64] examined the use of an unsupervised $k$-means clustering method for automatic classification of the data from $7 \mathrm{SSM} / \mathrm{I}$ channels, and he demonstrated that it is possible to obtain classifications of the different ice regimes both in the seasonal and perennial ice cover by clustering using emissivities from all channels. Dabboor and Shokr [37] proposed an iteratively supervised classification approach that utilized a complex Wishart distribution-based likelihood ratio (LR) and a spatial context criterion to discriminate sea ice types for polarimetric SAR data.

Image features, particularly texture features that characterize local and statistical properties of regions in an image, have been widely used in the classification of sea ice types $[63,138,31,142,26,27]$. Several research works have been done on gray-level co-occurrence matrices (GLCM) texture analysis [56] for sea ice image classification $[138,101,89]$. Many important parameters need to be defined for GLCM. Soh and Tsatsoulis [142] quantitatively evaluated GLCM texture parameters and representations, and they determined best textural parameters and representations for mapping texture features of SAR sea ice imagery. They also developed three GLCM implementations and evaluated these developed implementations by a supervised Bayesian classifier on sea ice textural contexts. Other texture analysis methods, such as Gabor, and Markov random fields (MRF), can also used in sea ice image classification. Clausi [25] compared the ability of texture features based on GLCM, Gabor, MRF, and the combination of these three methods for classifying SAR sea ice image.

Neural networks have also been applied to classifying sea ice types $[74,14,181]$. For examples, Comiso [33] utilized a back-propagation neural network to improve the classification by using the unsupervised ISODATA cluster analysis results to train the system. Hara et al. [55] developed a neural network that employed the learning vector quantization (LVQ) method to perform the initial clustering and improved the results by an iterative maximum likelihood (ML) method for the classification of sea ice in SAR imagery. Pedersen et al. [119] used a feed-forward back propagation neural network with 3 layers for sea ice type classification based on texture features.
Besides the classification methods mentioned above, Yu and Clausi [180] developed a so-called iterative region growing using semantics (IRGS) algorithm that

combined image segmentation and classification for classifying the operational SAR sea ice imagery. In this IRGS algorithm, the watershed algorithm [167] was first used to segment the image into small homogeneous regions, then the MRF-based labeling and the region merging processes were performed iteratively until the merging cannot be performed further. The IRGS algorithm has been applied to polygons from sea ice maps provided by the Canadian Ice Service (CIS) for classifying sea ice types [112], and further extended for polarimetric SAR image classification by incorporating a polarimetric feature model based on the Wishart distribution and modifying key steps [179].

It should be noted that the works mentioned above mainly classified sea ice into first-year, multi-year, and young ice. Those sea ice types are different from the ice types that we classify in this book, as described in Section 1.2.2.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 机器视觉代写|图像处理作业代写Image Processing代考|RESEARCH BACKGROUND

statistics-lab™ 为您的留学生涯保驾护航 在代写图像处理Image Processing方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写图像处理Image Processing代写方面经验极为丰富，各种代写图像处理Image Processing相关的作业也就用不着说。

• 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

## 机器视觉代写|图像处理作业代写Image Processing代考|RESEARCH BACKGROUND

Sea ice, defined as any form of ice that forms as a result of sea water freezing [91], occurs primarily in the polar regions and covers approximately $7 \%$ of the total area of the world’s oceans [168]. Sea ice is turbulent because of wind, wave, and temperature fluctuations, and it influences the movement of ocean waters, fluxes of heat, and circulation between atmosphere and ocean [1]. Sea ice plays important roles in climatology, meteorology, oceanography, physics, maritime navigation, marine biology, Arctic (and Antarctic) offshore operations, and world trade [137]. For example, if gradual warming melts sea ice over time, the abnormal changes in the amount of sea ice can affect the habitats of the animals that live in the polar regions, and it can disrupt normal atmosphere/ice/ocean momentum transfer and heat exchange that thereby may lead to further changes in global climate [2]. Moreover, the prevalence of sea ice will be a determining factor to human activities in the Arctic regions, such as scientific voyages, oil and gas activities, and Arctic shipping through the availability of the Arctic sailing routes from northern European to northern Pacific ports.

Ice concentration, ice floe size distribution, and ice types are important parameters in the field observations of sea ice. Because the sizes of the ice floes and brash ice can range from about one meter to a few kilometers, the temporally and spatially continuous field observations of sea ice are necessary for safe marine activities and understanding of the Arctic climate change. To that end, one of the most efficient ways to observe the ice conditions in the oceans is by using satellite, aerial, or nautical imagery and applying digital image processing techniques to the ice image data.
The analysis of image information obtained from remote sensors can reduce or suppress the ambiguities, incompleteness, uncertainties, and errors of the object and the environment via various processing techniques. It can also make the information of the object and environment more accurate and reliable by maximizing the use of image information from a variety of information sources, obtaining a more comprehensive and distinct environment. Therefore, various types of remotely sensed data and imaging technologies have been aiding the development of sea ice observation. Particularly the satellite observing systems and corresponding data processing algorithms have been widely used in the determination of sea ice parameters, such as extracting ice concentration $[141,34,136,79]$, classifying ice types $[59,26,144,14,180,47]$, and analyzing ice floe properties $[7,86,145]$. Nowadays the ice concentration data on a global scale has become available on a daily basis due to the development of microwave satellite sensors. According to this innovation, it has become possible to monitor the variability of sea ice extent on a global basis. However, it is still a big issue to predict the sea ice behavior in the numerical sea ice model due to the lack of our knowledge about the sub-grid scale information of in the JZ20-2 oil-gas field of the Liaodong Bay, and by this system, ice thickness, ice concentration, and ice velocity of the whole ice period in the Bohai Sea were determined continuously during the winter of $2009-2010$.

## 机器视觉代写|图像处理作业代写Image Processing代考|ICE CONCENTRATION

Ice concentration $(I C)$ is the ratio of ice on unit area of sea surface. To obtain $I C$ from a visual ice image, only the visible ice can be considered, including brash ice and, if visible in the image, submerged ice. With the image area, the height of the image taken above the ice sheet, and the segmentation, which is the identification of the ice pixels from the water pixels, the actual area of sea ice and sea surface can be derived. However, the actual domain area is not necessary for calculating the ice concentration.

In simplified terms, ice concentration from a digital visible image is, in this book, defined as the area covered by visible ice observable in the 2-dimensional image, taken vertically from above, over the total sea surface domain area of the image.
A digital image is a numerical representation of a 2-dimensional picture as a finite set of values called pixels. Hence, ice concentration can be derived by calculating the fraction of the number of pixels of visible ice to the total number of pixels within the image domain. An image may contain parts of land or other non-relevant areas. Thus, the domain area is an effective area within the image after the non-relevant parts have been removed. The ice concentration is then given by:
\begin{aligned} I C &=f(\text { image area, height above ice sheet, segmentation }) \ &=\frac{\text { Area of all visible ice within domain }}{\text { Actual domain area }} \ &=\frac{\text { Number of pixels of visible ice in the image domain }}{\text { Total number of pixels in the image domain }} \end{aligned}

## 机器视觉代写|图像处理作业代写Image Processing代考|ICE TYPES

Various types of sea ice can be found in ice-covered regions, and different types of sea ice have different physical properties. As defined in Løset et al. [91]:

• Floe is any relatively flat piece of sea ice $20 \mathrm{~m}$ or more across. It is subdivided according to horizontal extent. A giant flow is over $10 \mathrm{~km}$ across; a vast floe is 2 to $10 \mathrm{~km}$ across; a big floe is 500 to $2000 \mathrm{~m}$ across; a medium floe is 100 to $500 \mathrm{~m}$ across; and a small floe is 20 to $100 \mathrm{~m}$ across.
• Ice cake is any relatively flat piece of sea ice less than $20 \mathrm{~m}$ across.
• Brash ice is accumulations of floating ice made up of fragments not more than $2 \mathrm{~m}$ across and the wreckage of other forms of ice. It is common between colliding floes or in regions where pressure ridges have collapsed.
• Slush is snow that is saturated and mixed with water on land or ice surfaces, or as a viscous floating mass in water after heavy snowfall.
In this book, for simplicity, the size of the sea ice piece is the only criterion to distinguish ice floe and brash ice. That is, any relatively flat piece of sea ice $2 \mathrm{~m}$ or more across is considered as “ice floe”, while any relatively flat piece of sea ice less than $2 \mathrm{~m}$ across is considered as “brash ice (piece)”. The residual of ice pixels are considered as “slush”.

## 机器视觉代写|图像处理作业代写Image Processing代考|ICE TYPES

• 浮冰是任何相对平坦的海冰20 米或更多。它是根据水平范围细分的。一个巨大的流程结束了10 ķ米穿过; 巨大的浮冰是 2 到10 ķ米穿过; 一大块浮冰是 500 到2000 米穿过; 中等漂浮物是 100 到500 米穿过; 一个小浮冰是 20 到100 米穿过。
• 冰糕是任何相对平坦的海冰，小于20 米穿过。
• 碎冰是由不超过2 米穿过和其他形式的冰的残骸。在碰撞的浮体之间或在压力脊塌陷的区域中很常见。
• 雪泥是在陆地或冰面上饱和并与水混合的雪，或者是大雪后在水中形成的粘性漂浮块。
在本书中，为简单起见，海冰块的大小是区分浮冰和碎冰的唯一标准。也就是说，任何相对平坦的海冰2 米或更大的海冰被认为是“浮冰”，而任何相对平坦的海冰小于2 米横跨被认为是“碎冰（片）”。冰像素的残差被认为是“slush”。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。