## 计算机代写|计算机视觉代写Computer Vision代考|CS766

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
• (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|Plane plus parallax (projective depth)

In general, when using the $4 \times 4$ matrix $\tilde{\mathbf{P}}$, we have the freedom to remap the last row to whatever suits our purpose (rather than just being the “standard” interpretation of disparity as inverse depth). Let us re-write the last row of $\tilde{\mathbf{P}}$ as $\mathbf{p}_3=s_3\left[\hat{\mathbf{n}}_0 \mid c_0\right]$, where $\left|\hat{\mathbf{n}}_0\right|=1$. We then have the equation
$$d=\frac{s_3}{z}\left(\hat{\mathbf{n}}_0 \cdot \mathbf{p}_w+c_0\right),$$

where $z=\mathbf{p}_2 \cdot \overline{\mathbf{p}}_w=\mathbf{r}_z \cdot\left(\mathbf{p}_w-\mathbf{c}\right)$ is the distance of $\mathbf{p}_w$ from the camera center $C$ (2.25) along the optical axis $Z$ (Figure 2.11). Thus, we can interpret $d$ as the projective disparity or projective depth of a 3D scene point $\mathbf{p}_w$ from the reference plane $\hat{\mathbf{n}}_0 \cdot \mathbf{p}_w+c_0=0$ (Szeliski and Coughlan 1997; Szeliski and Golland 1999; Shade, Gortler et al. 1998; Baker, Szeliski, and Anandan 1998). (The projective depth is also sometimes called parallax in reconstruction algorithms that use the term plane plus parallax (Kumar, Anandan, and Hanna 1994; Sawhney 1994).) Setting $\hat{\mathbf{n}}_0=\mathbf{0}$ and $c_0=1$, i.e., putting the reference plane at infinity, results in the more standard $d=1 / z$ version of disparity (Okutomi and Kanade 1993).

Another way to see this is to invert the $\tilde{\mathbf{P}}$ matrix so that we can map pixels plus disparity directly back to $3 \mathrm{D}$ points,
$$\tilde{\mathbf{p}}_w=\tilde{\mathbf{P}}^{-1} \mathbf{x}_s .$$
In general, we can choose $\tilde{\mathbf{P}}$ to have whatever form is convenient, i.e., to sample space using an arbitrary projection. This can come in particularly handy when setting up multi-view stereo reconstruction algorithms, since it allows us to sweep a series of planes (Section 12.1.2) through space with a variable (projective) sampling that best matches the sensed image motions (Collins 1996; Szeliski and Golland 1999; Saito and Kanade 1999).

## 计算机代写|计算机视觉代写Computer Vision代考|Mapping from one camera to another

What happens when we take two images of a 3D scene from different camera positions or orientations (Figure 2.12a)? Using the full rank $4 \times 4$ camera matrix $\tilde{\mathbf{P}}=\tilde{\mathbf{K}} \mathbf{E}$ from (2.64), we can write the projection from world to screen coordinates as
$$\tilde{\mathbf{x}}0 \sim \tilde{\mathbf{K}}_0 \mathbf{E}_0 \mathbf{p}=\tilde{\mathbf{P}}_0 \mathbf{p} .$$ Assuming that we know the z-buffer or disparity value $d_0$ for a pixel in one image, we can compute the 3D point location $\mathbf{p}$ using $$\mathbf{p} \sim \mathbf{E}_0^{-1} \tilde{\mathbf{K}}_0^{-1} \tilde{\mathbf{x}}_0$$ and then project it into another image yielding $$\tilde{\mathbf{x}}_1 \sim \tilde{\mathbf{K}}_1 \mathbf{E}_1 \mathbf{p}=\tilde{\mathbf{K}}_1 \mathbf{E}_1 \mathbf{E}_0^{-1} \tilde{\mathbf{K}}_0^{-1} \tilde{\mathbf{x}}_0=\tilde{\mathbf{P}}_1 \tilde{\mathbf{P}}_0^{-1} \tilde{\mathbf{x}}_0=\mathbf{M}{10} \tilde{\mathbf{x}}0 .$$ Unfortunately, we do not usually have access to the depth coordinates of pixels in a regular photographic image. However, for a planar scene, as discussed above in (2.66), we can replace the last row of $\mathbf{P}_0$ in (2.64) with a general plane equation, $\hat{\mathbf{n}}_0 \cdot \mathbf{p}+c_0$, that maps points on the plane to $d_0=0$ values (Figure 2.12b). Thus, if we set $d_0=0$, we can ignore the last column of $\mathbf{M}{10}$ in (2.70) and also its last row, since we do not care about the final z-buffer depth. The mapping Equation (2.70) thus reduces to
$$\tilde{\mathbf{x}}1 \sim \tilde{\mathbf{H}}{10} \tilde{\mathbf{x}}0,$$ where $\tilde{\mathbf{H}}{10}$ is a general $3 \times 3$ homography matrix and $\tilde{\mathbf{x}}1$ and $\tilde{\mathbf{x}}_0$ are now $2 \mathrm{D}$ homogeneous coordinates (i.e., 3-vectors) (Szeliski 1996). This justifies the use of the 8-parameter homography as a general alignment model for mosaics of planar scenes (Mann and Picard 1994; Szeliski 1996). The other special case where we do not need to know depth to perform inter-camera mapping is when the camera is undergoing pure rotation (Section 8.2.3), i.e., when $\mathbf{t}_0=\mathbf{t}_1$. In this case, we can write $$\tilde{\mathbf{x}}_1 \sim \mathbf{K}_1 \mathbf{R}_1 \mathbf{R}_0^{-1} \mathbf{K}_0^{-1} \tilde{\mathbf{x}}_0=\mathbf{K}_1 \mathbf{R}{10} \mathbf{K}_0^{-1} \tilde{\mathbf{x}}_0,$$ which again can be represented with a $3 \times 3$ homography. If we assume that the calibration matrices have known aspect ratios and centers of projection ( $2.59$ ), this homography can be parameterized by the rotation amount and the two unknown focal lengths. This particular formulation is commonly used in image-stitching applications (Section 8.2.3).

# 计算机视觉代考

## 计算机代写|计算机视觉代写Computer Vision代考|Plane plus parallax (projective depth)

$$d=\frac{s_3}{z}\left(\hat{\mathbf{n}}_0 \cdot \mathbf{p}_w+c_0\right),$$

$$\tilde{\mathbf{p}}_w=\tilde{\mathbf{P}}^{-1} \mathbf{x}_s .$$

## 计算机代写|计算机视觉代写Computer Vision代考|Mapping from one camera to another

$$\tilde{\mathbf{x}} 0 \sim \tilde{\mathbf{K}}0 \mathbf{E}_0 \mathbf{p}=\tilde{\mathbf{P}}_0 \mathbf{p} .$$ 假设我们知道一幅图像中像素的 z 缓冲区或视差值d_0，我们可以使 用 $\backslash m a t h b f{p} \backslash \operatorname{sim} \backslash m a t h b f{E}_0 0{-1} d_0$ 计算 $3 D$ 点位置 $\left.\backslash m a t h b f p\right}$ Itilde{\mathbf ${K}}{-} 0^{\wedge}{-1} \backslash$ tilde{Imathbf{X}}_0然后将它投影到另一 个图像中 $\mathbf{p}$
$$\begin{gathered} \mathbf{p} \sim \mathbf{E}0^{-1} \tilde{\mathbf{K}}_0^{-1} \tilde{\mathbf{x}}_0 \ \tilde{\mathbf{x}}_1 \sim \tilde{\mathbf{K}}_1 \mathbf{E}_1 \mathbf{p}=\tilde{\mathbf{K}}_1 \mathbf{E}_1 \mathbf{E}_0^{-1} \tilde{\mathbf{K}}_0^{-1} \tilde{\mathbf{x}}_0=\tilde{\mathbf{P}}_1 \tilde{\mathbf{P}}_0^{-1} \tilde{\mathbf{x}}_0=\mathbf{M} 10 \tilde{\mathbf{x}} 0 \end{gathered}$$ 不辛的是，我们通常无法访问常规摄影图像中像嫊的深度坐标。然 而，对于平面场景，如上面 (2.66) 中所讨论的，我们可以用一般平面 方程Ihat ${\backslash m a t h b f{n}}{-} 0 \backslash c d o t$ 替换 (2.64) 中的最后一行 $\backslash$ mathbf{P}_0 Imathbf{p}+c_0，将平面上的点映射到d_ $0=0$ 值 (图 2.12b) 。因 此，如果我们设置d_ $0=0$ ，我们可以忽略Imathbf ${M} 10}$ 的最后一列 $\mathbf{P}_0 \hat{\mathbf{n}}_0 \cdot \mathbf{p}+c_0 d_0=0 d_0=0 \mathbf{M} 10$ 在 (2.70) 及其最后一行，因为 我们不关心最终的 z 缓冲区深度。映射方程 (2.70) 因此简化为
$$\tilde{\mathbf{x}} 1 \sim \tilde{\mathbf{H}} 10 \tilde{\mathbf{x}} 0,$$

$$\tilde{\mathbf{x}}_1 \sim \mathbf{K}_1 \mathbf{R}_1 \mathbf{R}_0^{-1} \mathbf{K}_0^{-1} \tilde{\mathbf{x}}_0=\mathbf{K}_1 \mathbf{R} 10 \mathbf{K}_0^{-1} \tilde{\mathbf{x}}_0,$$

## 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。