### 计算机代写|计算机视觉代写Computer Vision代考|CS763

statistics-lab™ 为您的留学生涯保驾护航 在代写计算机视觉Computer Vision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。我们的专家在代写计算机视觉Computer Vision方面经验极为丰富，各种代写计算机视觉Computer Vision相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (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

## 计算机代写|计算机视觉代写Computer Vision代考|Geometric primitives and transformations

In this section, we introduce the basic 2D and 3D primitives used in this textbook, namely points, lines, and planes. We also describe how 3D features are projected into 2D features. More detailed descriptions of these topics (along with a gentler and more intuitive introduction) can be found in textbooks on multiple-view geometry (Hartley and Zisserman 2004; Faugeras and Luong 2001).
Geometric primitives form the basic building blocks used to describe three-dimensional shapes. In this section, we introduce points, lines, and planes. Later sections of the book discuss curves (Sections $7.3$ and 12.2), surfaces (Section 13.3), and volumes (Section 13.5).
2D points. 2D points (pixel coordinates in an image) can be denoted using a pair of values, $\mathbf{x}=(x, y) \in \mathcal{R}^2$, or alternatively,
$$\mathbf{x}=\left[\begin{array}{l} x \ y \end{array}\right]$$
(As stated in the introduction, we use the $\left(x_1, x_2, \ldots\right)$ notation to denote column vectors.)

2D points can also be represented using homogeneous coordinates, $\tilde{\mathbf{x}}=(\tilde{x}, \tilde{y}, \tilde{w}) \in \mathcal{P}^2$, where vectors that differ only by scale are considered to be equivalent. $\mathcal{P}^2=\mathcal{R}^3-(0,0,0)$ is called the 2D projective space.

A homogeneous vector $\tilde{\mathbf{x}}$ can be converted back into an inhomogeneous vector $\mathbf{x}$ by dividing through by the last element $\tilde{w}$, i.e.,
$$\tilde{\mathbf{x}}=(\tilde{x}, \tilde{y}, \tilde{w})=\tilde{w}(x, y, 1)=\tilde{w} \overline{\mathbf{x}},$$
where $\overline{\mathbf{x}}=(x, y, 1)$ is the augmented vector. Homogeneous points whose last element is $\tilde{w}=0$ are called ideal points or points at infinity and do not have an equivalent inhomogeneous representation.
2D lines. 2D lines can also be represented using homogeneous coordinates $\tilde{\mathbf{I}}=(a, b, c)$. The corresponding line equation is
$$\overline{\mathbf{x}} \cdot \tilde{\mathbf{l}}=a x+b y+c=0 .$$
We can normalize the line equation vector so that $\mathbf{l}=\left(\hat{n}_x, \hat{n}_y, d\right)=(\hat{\mathbf{n}}, d)$ with $|\hat{\mathbf{n}}|=1$. In this case, $\hat{\mathbf{n}}$ is the normal vector perpendicular to the line and $d$ is its distance to the origin (Figure 2.2). (The one exception to this normalization is the line at infinity $\tilde{\mathbf{l}}=(0,0,1)$, which includes all (ideal) points at infinity.)

We can also express $\hat{\mathbf{n}}$ as a function of rotation angle $\theta, \hat{\mathbf{n}}=\left(\hat{n}_x, \hat{n}_y\right)=(\cos \theta, \sin \theta)$ (Figure 2.2a). This representation is commonly used in the Hough transform line-finding algorithm, which is discussed in Section 7.4.2. The combination $(\theta, d)$ is also known as polar coordinates.
When using homogeneous coordinates, we can compute the intersection of two lines as
$$\tilde{\mathbf{x}}=\tilde{\mathbf{l}}_1 \times \tilde{\mathbf{l}}_2,$$
where $\times$ is the cross product operator. Similarly, the line joining two points can be written as
$$\tilde{\mathbf{l}}=\tilde{\mathbf{x}}_1 \times \tilde{\mathbf{x}}_2 .$$
When trying to fit an intersection point to multiple lines or, conversely, a line to multiple points, least squares techniques (Section 8.1.1 and Appendix A.2) can be used, as discussed in Exercise 2.1.

## 计算机代写|计算机视觉代写Computer Vision代考|2D transformations

Having defined our basic primitives, we can now turn our attention to how they can be transformed. The simplest transformations occur in the 2D plane are illustrated in Figure 2.4.
Translation. $2 \mathrm{D}$ translations can be written as $\mathbf{x}^{\prime}=\mathrm{x}+\mathbf{t}$ or
$$\mathbf{x}^{\prime}=\left[\begin{array}{ll} \mathbf{l} & \mathbf{t} \end{array}\right] \overline{\mathbf{x}},$$
where $I$ is the $(2 \times 2)$ identity matrix or
$$\overline{\mathbf{x}}^{\prime}=\left[\begin{array}{cc} \mathbf{I} & \mathbf{t} \ \mathbf{0}^T & 1 \end{array}\right] \overline{\mathbf{x}},$$
where $\mathbf{0}$ is the zero vector. Using a $2 \times 3$ matrix results in a more compact notation, whereas using a full-rank $3 \times 3$ matrix (which can be obtained from the $2 \times 3$ matrix by appending a [0 $\left.0^T 1\right]$ row) makes it possible to chain transformations using matrix multiplication as well as to compute inverse transforms. Note that in any equation where an augmented vector such as $\overline{\mathbf{x}}$ appears on both sides, it can always be replaced with a full homogeneous vector $\tilde{\mathbf{x}}$.

# 计算机视觉代考

## 计算机代写|计算机视觉代写Computer Vision代考|Geometric primitives and transformations

$$\mathbf{x}=\left[\begin{array}{ll} x & y \end{array}\right]$$
（如介绍中所述，我们使用 $\left(x_1, x_2, \ldots\right)$ 表示列向量的符号。)

$$\tilde{\mathbf{x}}=(\tilde{x}, \tilde{y}, \tilde{w})=\tilde{w}(x, y, 1)=\tilde{w} \overline{\mathbf{x}},$$

$$\overline{\mathbf{x}} \cdot \tilde{\mathbf{l}}=a x+b y+c=0 .$$

$$\tilde{\mathbf{x}}=\tilde{\mathbf{l}}_1 \times \tilde{\mathbf{l}}_2$$

$$\tilde{\mathbf{1}}=\tilde{\mathbf{x}}_1 \times \tilde{\mathbf{x}}_2 .$$

## 计算机代写|计算机视觉代写Computer Vision代考|2D transformations

$$\mathbf{x}^{\prime}=\left[\begin{array}{ll} \mathbf{1} & \mathbf{t} \end{array}\right] \overline{\mathbf{x}}$$

$$\overline{\mathbf{x}}^{\prime}=\left[\begin{array}{lll} \mathbf{I} & \mathbf{t} \mathbf{0}^T & 1 \end{array}\right] \overline{\mathbf{x}}$$

## 广义线性模型代考

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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。