## 计算机代写|计算机视觉代写Computer Vision代考|COSC428

2022年12月24日

couryes-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
couryes™为您提供可以保分的包课服务

## 计算机代写|计算机视觉代写Computer Vision代考|Object-centered projection

When working with long focal length lenses, it often becomes difficult to reliably estimate the focal length from image measurements alone. This is because the focal length and the distance to the object are highly correlated and it becomes difficult to tease these two effects apart. For example, the change in scale of an object viewed through a zoom telephoto lens can either be due to a zoom change or to a motion towards the user. (This effect was put to dramatic use in some scenes of Alfred Hitchcock’s film Vertigo, where the simultaneous change of zoom and camera motion produces a disquieting effect.)

This ambiguity becomes clearer if we write out the projection equation corresponding to the simple calibration matrix $\mathbf{K}$ (2.59),
\begin{aligned} & x_s=f \frac{\mathbf{r}_x \cdot \mathbf{p}+t_x}{\mathbf{r}_z \cdot \mathbf{p}+t_z}+c_x \ & y_s=f \frac{\mathbf{r}_y \cdot \mathbf{p}+t_y}{\mathbf{r}_z \cdot \mathbf{p}+t_z}+c_y, \end{aligned}
where $\mathbf{r}_x, \mathbf{r}_y$, and $\mathbf{r}_z$ are the three rows of $\mathbf{R}$. If the distance to the object center $t_z \gg|\mathbf{p}|$ (the size of the object), the denominator is approximately $t_z$ and the overall scale of the projected object depends on the ratio of $f$ to $t_z$. It therefore becomes difficult to disentangle these two quantities.
To see this more clearly, let $\eta_z=t_z^{-1}$ and $s=\eta_z f$. We can then re-write the above equations as
\begin{aligned} & x_s=s \frac{\mathbf{r}_x \cdot \mathbf{p}+t_x}{1+\eta_z \mathbf{r}_z \cdot \mathbf{p}}+c_x \ & y_s=s \frac{\mathbf{r}_y \cdot \mathbf{p}+t_y}{1+\eta_z \mathbf{r}_z \cdot \mathbf{p}}+c_y \end{aligned}
(Szeliski and Kang 1994; Pighin, Hecker et al. 1998). The scale of the projection $s$ can be reliably estimated if we are looking at a known object (i.e., the 3D coordinates $p$ are known). The inverse distance $\eta_z$ is now mostly decoupled from the estimates of $s$ and can be estimated from the amount of foreshortening as the object rotates. Furthermore, as the lens becomes longer, i.e., the projection model becomes orthographic, there is no need to replace a perspective imaging model with an orthographic one, since the same equation can be used, with $\eta_z \rightarrow 0$ (as opposed to $f$ and $t_z$ both going to infinity). This allows us to form a natural link between orthographic reconstruction techniques such as factorization and their projective/perspective counterparts (Section 11.4.1).

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

The above imaging models all assume that cameras obey a linear projection model where straight lines in the world result in straight lines in the image. (This follows as a natural consequence of linear matrix operations being applied to homogeneous coordinates.) Unfortunately, many wide-angle lenses have noticeable radial distortion, which manifests itself as a visible curvature in the projection of straight lines. (See Section 2.2.3 for a more detailed discussion of lens optics, including chromatic aberration.) Unless this distortion is taken into account, it becomes impossible to create highly accurate photorealistic reconstructions. For example, image mosaics constructed without taking radial distortion into account will often exhibit blurring due to the misregistration of corresponding features before pixel blending (Section $8.2$ ).

Fortunately, compensating for radial distortion is not that difficult in practice. For most lenses, a simple quartic model of distortion can produce good results. Let $\left(x_c, y_c\right)$ be the pixel coordinates obtained after perspective division but before scaling by focal length $f$ and shifting by the image center $\left(c_x, c_y\right)$, i.e.,
\begin{aligned} x_c & =\frac{\mathbf{r}_x \cdot \mathbf{p}+t_x}{\mathbf{r}_z \cdot \mathbf{p}+t_z} \ y_c & =\frac{\mathbf{r}_y \cdot \mathbf{p}+t_y}{\mathbf{r}_z \cdot \mathbf{p}+t_z} . \end{aligned}
The radial distortion model says that coordinates in the observed images are displaced towards (barrel distortion) or away (pincushion distortion) from the image center by an amount proportional to their radial distance (Figure 2.13a-b). ${ }^6$ The simplest radial distortion models use low-order polynomials, e.g.,
\begin{aligned} & \hat{x}_c=x_c\left(1+\kappa_1 r_c^2+\kappa_2 r_c^4\right) \ & \hat{y}_c=y_c\left(1+\kappa_1 r_c^2+\kappa_2 r_c^4\right), \end{aligned}
where $r_c^2=x_c^2+y_c^2$ and $\kappa_1$ and $\kappa_2$ are called the radial distortion parameters. ${ }^7$ This model, which also includes a tangential component to account for lens decentering, was first proposed in the photogrammetry literature by Brown (1966), and so is sometimes called the Brown or BrownConrady model. However, the tangential components of the distortion are usually ignored because they can lead to less stable estimates (Zhang 2000).
After the radial distortion step, the final pixel coordinates can be computed using
\begin{aligned} & x_s=f \hat{x}_c+c_x \ & y_s=f \hat{y}_c+c_y . \end{aligned}

# 计算机视觉代考

## 计算机代写|计算机视觉代写Computer Vision代考|Object-centered projection

$$x_s=f \frac{\mathbf{r}_x \cdot \mathbf{p}+t_x}{\mathbf{r}_z \cdot \mathbf{p}+t_z}+c_x \quad y_s=f \frac{\mathbf{r}_y \cdot \mathbf{p}+t_y}{\mathbf{r}_z \cdot \mathbf{p}+t_z}+c_y$$

$$x_s=s \frac{\mathbf{r}_x \cdot \mathbf{p}+t_x}{1+\eta_z \mathbf{r}_z \cdot \mathbf{p}}+c_x \quad y_s=s \frac{\mathbf{r}_y \cdot \mathbf{p}+t_y}{1+\eta_z \mathbf{r}_z \cdot \mathbf{p}}+c_y$$
(Szeliski 和 Kang 1994；Pighin、Hecker 等人 1998) 。投影比例尺 $s$ 如果我们正在查看已知对象（即 $3 \mathrm{D}$ 坐标 $p$ 是已知的）。反距离 $\eta_z$ 现 在大部分与估计值脱钧 $s$ 并且可以根据物体旋转时的透视㜚短量来估 算。此外，随若镜头变长，即投影模型变为正交模型，无需将途视成 像模型替换为正交模型，因为可以使用相同的方程式， $\eta_z \rightarrow 0$ (相对 于 $f$ 和 $t_z$ 都趋于无穷大) 。这使我们能够在因式分解等正交重建技术与 其对应的投影/遷视技术之间形成自然联系（第 $11.4 .1$ 节)。

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

$$x_c=\frac{\mathbf{r}_x \cdot \mathbf{p}+t_x}{\mathbf{r}_z \cdot \mathbf{p}+t_z} y_c \quad=\frac{\mathbf{r}_y \cdot \mathbf{p}+t_y}{\mathbf{r}_z \cdot \mathbf{p}+t_z} .$$

$$\hat{x}_c=x_c\left(1+\kappa_1 r_c^2+\kappa_2 r_c^4\right) \quad \hat{y}_c=y_c\left(1+\kappa_1 r_c^2+\kappa_2 r_c^4\right)$$

$$x_s=f \hat{x}_c+c_x \quad y_s=f \hat{y}_c+c_y$$

## 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。