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

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我们提供的图像处理Image Processing及其相关学科的代写,服务范围广, 其中包括但不限于:

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

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|EEE6512


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

模糊集理论的基本定义将在第 1 章中回顾。2.


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);

同样,对可用知识的描述也存在不精确性。例如,在描述大脑结构的组织时,教科书通常包含本质上不精确的语言描述(例如,“结构 A 先于结构 B”)。



模糊集在表示这种不精确性方面有几个优点,如第 1 章所述。1. 特别是,模糊集理论对于在一致的数学框架中提供丰富的工具集合非常有意义,适用于第 1 章中描述的所有问题。1. 它允许在不同的表示层次上表示对象、关系、知识和目标的不精确性。它提供了一个统一的框架来表示和处理相关的数字和符号信息,以及结构信息(例如,图像中对象之间的空间关系)。因此,该理论可用于多个级别的任务,从低级别(例如,基于灰度级的分类)到高级(例如,基于模型的结构识别和场景解释)。同时,

让我们提供一个简单的例子来说明模糊模型在显式表示图像提供的信息中的不精确性以及类之间可能存在的歧义方面的用处。例如,部分体积效应问题在该模型中找到了一致的表示。遭受部分体积效应的像素或体素的特征在于它部分地属于两个(或更多)不同的组织或类别。使用模糊集,这会立即转化为多个类的非零成员值。数字2.1显示了患有肾上腺脑白质营养不良症的患者大脑的 MR 图像示例,其中切片厚度会导致高局部体积效应。右图的灰度级表示病理学的隶属度值。然后将病理学视为模糊对象,由在空间域上定义的隶属函数表示。

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术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。



有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。





随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。


多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。


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。



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