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# 计算机代写|计算机视觉代写Computer Vision代考|CMSC426 Common Optimization Concepts in Computer Vision

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## 计算机代写|计算机视觉代写Computer Vision代考|Common Optimization Concepts in Computer Vision

Before taking a closer look at the diverse optimization methods, let’s first introduce some concepts which are of relevance to optimization and, additionally, in widespread use in computer vision.

With the help of energy functions, for example, it is possible to evaluate and compare different solutions and thus use this measure to find the optimal solution. The well-known MAP estimator, which finds the best solution by estimating the “most likely” one, given some observed data, can be considered as one form of energy minimization.

Markov Random Fields (MRFs) are a very useful model if the “state” of each pixel (e.g., a label or intensity value) is related to the states of its neighbors, which makes MRFs suitable for restoration (e.g., denoising), segmentation, or stereomatching tasks, just to name a few.

Last but not least, many computer vision tasks rely on establishing correspondences between two entities. Consider, for example, an object which is represented by a set of characteristic points and their relative position. If such an object has to be detected in a query image, a common proceeding is to extract characteristic points for this image as well and, subsequently, try to match them to the model points, i.e., to establish correspondences between model and query image points.

In addition to this brief explanation, the concepts of energy functions, graphs, and Markov Random Fields are described in more detail in the following sections.

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

The concept of so-called energy functions is a widespread approach in computer vision. In order to find the “best” solution, one reasonable way is to quantify how “good” a particular solution is, because such a measure enables us to compare different solutions and select the “best”. Energy functions $E$ are widely used in this context (see, e.g., [6]).

Generally speaking, the “energy” is a measure how plausible a solution is. High energies indicate bad solutions, whereas a low energy signalizes that a particular solution is suitable for explaining some observed data. Some energies are so-called functionals. The term “functional” is used for operators which map a functional relationship to a scalar value (which is the energy here), i.e., take a function as argument (which can, e.g., be discretely represented by a vector of values) and derive a scalar value from this. Functionals are needed in variational optimization, for example.

With the help of such a function, a specific energy can be assigned to each element of the solution space. In this context, optimization amounts to finding the argument which minimizes the function:
$$x^*=\arg \min _{x \in S} E(x)$$
As already mentioned in the previous section, $E$ typically consists of two components:

1. A data-driven or external energy $E_{\text {ext }}$, which measures how “good” a solution explains the observed data. In restoration tasks, for example, $E_{\text {ext }}$ depends on the fidelity of the reconstructed signal $\hat{R}$ to the observed data $I$.
2. An internal energy $E_{\text {int }}$, which exclusively depends on the proposed solution (i.e., is independent on the observed data) and quantifies its plausibility. This is the point where a priori knowledge is considered: based on general considerations, we can consider some solutions to be more likely than others and therefore assign a low internal energy to them. In this context it is often assumed that the solution should be “smooth” in a certain sense. In restoration, for example, the proposed solution should contain large areas with uniform or very smoothly varying intensity, and therefore $E_{\text {int }}$ depends on some norm of the sum of the gradients between adjacent pixels.

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

$$x^*=\arg \min _{x \in S} E(x)$$

1. 数据区动或外部能量 $E_{\mathrm{ext}}$ ，它衡量解决方案解释观察到的数据的”好”程度。例如，在恢夏任务中， $E_{\text {ext }}$ 取决于重建信号的 保真度 $\hat{R}$ 对观财数据 $I$.
2.一种内能 $E_{\text {int }}$ ，它完全取决于建议的解决方穼（即，独立于观䕓到的数据）并量化其合理性。这是考虑先验知识的点: 其 于一般考虑，我们可以认为某些解决方宨比其他解决方客更有可能，因此为它们分配较低的内部能量。在这种情况下，通常 假设解决方案在㭉种意义上应该是“平滑的”。例如，在修孭中，建议的解决方依应该包含具有均匀或非常平滑变化强度的大 区域，因此 $E_{\text {int }}$ 取决于相邻像靑之间的梯度总和的某个范数。

## 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。