### 计算机代写|图像处理代写Image Processing代考|EEE6512

statistics-lab™ 为您的留学生涯保驾护航 在代写图像处理Image Processing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。我们的专家在代写图像处理Image Processing代写方面经验极为丰富，各种代写图像处理Image Processing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

## 计算机代写|图像处理代写Image Processing代考|Advantages and Usefulness of Fuzzy Sets

Fuzzy sets have several advantages as they provide a unified framework for representing and processing both numerical and symbolic information, along with its imprecisions, as in other domains of information processing [70].
Basic definitions on fuzzy sets theory will be recalled in Chap. 2.
First, fuzzy sets are able to represent several types of imprecision in images, as, for instance, imprecision in spatial location of objects, or imprecision in membership of an object to a class. For instance, partial volume effect finds a consistent representation in fuzzy sets (membership degrees of a pixel or voxel to objects directly represent partial membership to the different objects mixed up in this pixel or voxel, leading to a modeling consistent with respect to reality). Secondly, image information can be represented at different levels with fuzzy sets (local, regional, or global), as well as under different forms (numerical, or symbolic). For instance, classification based only on gray levels involves very local information (at the pixel level); introducing spatial coherence in the classification, or relations between features, involves regional information; and introducing relations between objects or regions for scene interpretation involves more global information and is related to the field of spatial reasoning. Thirdly, the fuzzy set framework allows for the representation of very heterogeneous information and is able to deal with information extracted directly from the images, as well as with information derived from some external knowledge, such as expert knowledge. This is exploited in particular in model-based pattern recognition, where fuzzy information extracted from the images is compared and matched to a model representing knowledge expressed in fuzzy terms.

Therefore this theory can support tasks at several levels, from low level (e.g., gray-level based classification) to high level (e.g., model-based structural recognition and scene interpretation). It provides a flexible framework for information fusion as well as powerful tools for reasoning and decision making. From a mathematical point of view, fuzzy sets can be equipped with a complete lattice structure, which is suitable for its association with other theories of information processing based on such structures, such as mathematical morphology or logics. While first applications mainly addressed reasoning at low level for classification, edge detection or filtering, higher level information modeling and processing are now more widely developed and still topics of current research. This includes dealing with spatial information at intermediate or higher level, via mathematical morphology, spatial reasoning, ontologies, graphs, or knowledge-based systems, as well as advances in machine learning, higher level descriptions of image content, handling different levels of granularity, to name but a few.

## 计算机代写|图像处理代写Image Processing代考|Imprecision in Images and Related Knowledge

Imprecision is often inherent to images, and its causes can be found at several levels:

• Observed phenomenon: imprecise limits between structures or objects that exist in reality (for instance, between healthy and pathological tissues when the pathology diffuses inside the normal tissues) will induce similar imprecise limits in observed images;
• Acquisition process (limited resolution, numerical reconstruction methods);
• Image processing steps (imprecision induced by a filtering for instance);

Similarly, imprecision occurs in the descriptions of available knowledge. For instance, when describing the organization of brain structures, textbooks often include linguistic descriptions that are inherently imprecise (e.g., “structure A is anterior to structure B”).

Moreover, the aim of an image understanding process can be expressed in an imprecise way, which is sometimes even preferable to a statement which is precise, but likely not sufficiently accurate.

Several examples illustrating the above considerations will be provided in the different chapters of this book.

Fuzzy sets have several advantages for representing such imprecision, as explained in Chap. 1. In particular, fuzzy set theory is of great interest to provide a rich collection of tools in a consistent mathematical framework, for all the issues described in Chap. 1. It allows representing imprecision of objects, relations, knowledge, and aims, at different levels of representation. It provides an unified framework for representing and processing related numerical and symbolic information, as well as structural information (e.g., spatial relations between objects in an image). Therefore this theory can be employed for tasks at several levels, from low level (e.g., gray-level based classification) to high level (e.g., model-based structural recognition and scene interpretation). At the same time, it provides a flexible framework for information fusion as well as powerful tools for reasoning and decision making.

Let us provide a simple example to illustrate the usefulness of fuzzy models to explicitly represent imprecision in the information provided by the images, as well as possible ambiguity between classes. For instance, the problem of partial volume effect finds a consistent representation in this model. A pixel or voxel suffering from partial volume effect is characterized by the fact that it belongs partially to two (or more) different tissues or classes. Using fuzzy sets, this translates immediately into non-zero membership values to more than one class. Figure $2.1$ shows an example of an MR image of the brain of a patient suffering from adrenoleukodystrophy, and where the slice thickness induces a high partial volume effect. The grey levels on the right figure represent the membership values to the pathology. The pathology is then considered as a fuzzy object, represented by a membership function defined on the spatial domain.

## 计算机代写|图像处理代写Image Processing代考|Imprecision in Images and Related Knowledge

• 观察现象：现实中存在的结构或物体之间的不精确限制（例如，当病理扩散到正常组织内部时，健康组织和病理组织之间的限制）将在观察图像中引起类似的不精确限制；
• 采集过程（有限分辨率、数值重建方法）；
• 图像处理步骤（例如由过滤引起的不精确）；

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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。