## 计算机代写|计算机视觉代写Computer Vision代考|CS518

2022年12月24日

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

Images cannot exist without light. To produce an image, the scene must be illuminated with one or more light sources. (Certain modalities such as fluorescence microscopy and X-ray tomography do not fit this model, but we do not deal with them in this book.) Light sources can generally be divided into point and area light sources.

A point light source originates at a single location in space (e.g., a small light bulb), potentially at infinity (e.g., the Sun). (Note that for some applications such as modeling soft shadows (penumbras), the Sun may have to be treated as an area light source.) In addition to its location, a point light source has an intensity and a color spectrum, i.e., a distribution over wavelengths $L(\lambda)$. The intensity of a light source falls off with the square of the distance between the source and the object being lit, because the same light is being spread over a larger (spherical) area. A light source may also have a directional falloff (dependence), but we ignore this in our simplified model.

Area light sources are more complicated. A simple area light source such as a fluorescent ceiling light fixture with a diffuser can be modeled as a finite rectangular area emitting light equally in all directions (Cohen and Wallace 1993; Sillion and Puech 1994; Glassner 1995). When the distribution is strongly directional, a four-dimensional lightfield can be used instead (Ashdown 1993).

A more complex light distribution that approximates, say, the incident illumination on an object

sitting in an outdoor courtyard, can often be represented using an environment map (Greene 1986) (originally called a reflection map (Blinn and Newell 1976)). This representation maps incident light directions $\hat{\mathbf{v}}$ to color values (or wavelengths, $\lambda$ ),
$$L(\hat{\mathbf{v}} ; \lambda),$$
and is equivalent to assuming that all light sources are at infinity. Environment maps can be represented as a collection of cubical faces (Greene 1986), as a single longitude-latitude map (Blinn and Newell 1976), or as the image of a reflecting sphere (Watt 1995). A convenient way to get a rough model of a real-world environment map is to take an image of a reflective mirrored sphere (sometimes accompanied by a darker sphere to capture highlights) and to unwrap this image onto the desired environment map (Debevec 1998). Watt (1995) gives a nice discussion of environment mapping, including the formulas needed to map directions to pixels for the three most commonly used representations.

The most general model of light scattering is the bidirectional reflectance distribution function (BRDF). ${ }^8$ Relative to some local coordinate frame on the surface, the BRDF is a four-dimensional function that describes how much of each wavelength arriving at an incident direction $\hat{\mathbf{v}}_i$ is emitted in a reflected direction $\hat{\mathbf{v}}_r$ (Figure 2.15b). The function can be written in terms of the angles of the incident and reflected directions relative to the surface frame as
$$f_r\left(\theta_i, \phi_i, \theta_r, \phi_r ; \lambda\right)$$

The BRDF is reciprocal, i.e., because of the physics of light transport, you can interchange the roles of $\hat{\mathbf{v}}_i$ and $\hat{\mathbf{v}}_r$ and still get the same answer (this is sometimes called Helmholtz reciprocity).

Most surfaces are isotropic, i.e., there are no preferred directions on the surface as far as light transport is concerned. (The exceptions are anisotropic surfaces such as brushed (scratched) aluminum, where the reflectance depends on the light orientation relative to the direction of the scratches.) For an isotropic material, we can simplify the BRDF to
$$f_r\left(\theta_i, \theta_r,\left|\phi_r-\phi_i\right| ; \lambda\right) \quad \text { or } \quad f_r\left(\hat{\mathbf{v}}_i, \hat{\mathbf{v}}_r, \hat{\mathbf{n}} ; \lambda\right),$$
as the quantities $\theta_i, \theta_r$, and $\phi_r-\phi_i$ can be computed from the directions $\hat{\mathbf{v}}_i, \hat{\mathbf{v}}_r$, and $\hat{\mathbf{n}}$.
To calculate the amount of light exiting a surface point $\mathbf{p}$ in a direction $\hat{\mathbf{v}}_r$ under a given lighting condition, we integrate the product of the incoming light $L_i\left(\hat{\mathbf{v}}_i ; \lambda\right)$ with the BRDF (some authors call this step a convolution). Taking into account the foreshortening factor $\cos ^{+} \theta_i$, we obtain
$$L_r\left(\hat{\mathbf{v}}_r ; \lambda\right)=\int L_i\left(\hat{\mathbf{v}}_i ; \lambda\right) f_r\left(\hat{\mathbf{v}}_i, \hat{\mathbf{v}}_r, \hat{\mathbf{n}} ; \lambda\right) \cos ^{+} \theta_i d \hat{\mathbf{v}}_i,$$
where
$$\cos ^{+} \theta_i=\max \left(0, \cos \theta_i\right) .$$
If the light sources are discrete (a finite number of point light sources), we can replace the integral with a summation,
$$L_r\left(\hat{\mathbf{v}}_r ; \lambda\right)=\sum_i L_i(\lambda) f_r\left(\hat{\mathbf{v}}_i, \hat{\mathbf{v}}_r, \hat{\mathbf{n}} ; \lambda\right) \cos ^{+} \theta_i .$$
BRDFs for a given surface can be obtained through physical modeling (Torrance and Sparrow 1967; Cook and Torrance 1982; Glassner 1995), heuristic modeling (Phong 1975; Lafortune, Foo et al. 1997), or through empirical observation (Ward 1992; Westin, Arvo, and Torrance 1992; Dana, van Ginneken et al. 1999; Marschner, Westin et al. 2000; Matusik, Pfister et al. 2003; Dorsey, Rushmeier, and Sillion 2007; Weyrich, Lawrence et al. 2009; Shi, Mo et al. 2019). ${ }^9$ Typical BRDFs can often be split into their diffuse and specular components, as described below.

# 计算机视觉代考

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

L(v^;λ),

$$f_r\left(\theta_i, \phi_i, \theta_r, \phi_r ; \lambda\right)$$
BRDF 是互惠的，即，由于光传输的物理学，您可以互换角色 $\hat{\mathbf{v}}_i$ 和 $\hat{\mathbf{v}}_r$ 并且仍然得到相同的答案 (这有时称为亥姆霍兹互惠）。

$$f_r\left(\theta_i, \theta_r,\left|\phi_r-\phi_i\right| ; \lambda\right) \quad \text { or } \quad f_r\left(\hat{\mathbf{v}}_i, \hat{\mathbf{v}}_r, \hat{\mathbf{n}} ; \lambda\right)$$

$$L_r\left(\hat{\mathbf{v}}_r ; \lambda\right)=\int L_i\left(\hat{\mathbf{v}}_i ; \lambda\right) f_r\left(\hat{\mathbf{v}}_i, \hat{\mathbf{v}}_r, \hat{\mathbf{n}} ; \lambda\right) \cos ^{+} \theta_i d \hat{\mathbf{v}}_i$$

$$\cos ^{+} \theta_i=\max \left(0, \cos \theta_i\right)$$

$$L_r\left(\hat{\mathbf{v}}_r ; \lambda\right)=\sum_i L_i(\lambda) f_r\left(\hat{\mathbf{v}}_i, \hat{\mathbf{v}}_r, \hat{\mathbf{n}} ; \lambda\right) \cos ^{+} \theta_i .$$

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。