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## 数学代写|图像处理代写Digital image processing代考|Quantization

For use with a computer, the measured irradiance at the image plane must be mapped onto a limited number $Q$ of discrete gray values. This process is called quantization. The number of required quantization levels in image processing can be discussed with respect to two criteria.
First, we may argue that no gray value steps should be recognized by our visual system, just as we do not see the individual pixels in digital images. Figure $2.7$ shows images quantized with 2 to 16 levels of gray values. It can be seen clearly that a low number of gray values leads to false edges and makes it very difficult to recognize objects that show slow spatial variation in gray values. In printed images, 16 levels of gray values seem to be sufficient, but on a monitor we would still be able to see the gray value steps.

Generally, image data are quantized into 256 gray values. Then each pixel occupies 8 bits or one byte. This bit size is well adapted to the architecture of standard computers that can address memory bytewise. Furthermore, the resolution is good enough to give us the illusion of a continuous change in the gray values, since the relative intensity resolution of our visual system is no better than about $2 \%$.

The other criterion is related to the imaging task. For a simple application in machine vision, where homogeneously illuminated objects must be detected and measured, only two quantization levels, i. e., a binary image, may be sufficient. Other applications such as imaging spectroscopy or medical diagnosis with $\mathrm{x}$-ray images require the resolution of faint changes in intensity. Then the standard 8-bit resolution would be too coarse.

## 数学代写|图像处理代写Digital image processing代考|Signed Representation of Images

Normally we think of “brightness” (irradiance or radiance) as a positive quantity. Consequently, it appears natural to represent it by unsigned numbers ranging in an 8-bit representation, for example, from 0 to 255 . This representation causes problems, however, as soon as we perform arithmetic operations with images. Subtracting two images is a simple example that can produce negative numbers. Since negative gray values cannot be represented, they wrap around and appear as large positive values. The number $-1$, for example, results in the positive value 255 given that $-1$ modulo $256=255$. Thus we are confronted with the problem of two different representations of gray values, as unsigned and signed 8-bit numbers. Correspondingly, we must have several versions of each algorithm, one for unsigned gray values, one for signed values, and others for mixed cases.
One solution to this problem is to handle gray values always as signed numbers. In an 8-bit representation, we can convert unsigned numbers into signed numbers by subtracting 128 :
$$q^{\prime}=(q-128) \bmod 256, \quad 0 \leq q<256 .$$
Then the mean gray value intensity of 128 becomes the gray value zero and gray values lower than this mean value become negative. Essentially, we regard gray values in this representation as a deviation from a mean value.
This operation converts unsigned gray values to signed gray values which can be stored and processed as such. Only for display must we convert the gray values again to unsigned values by the inverse point operation
$$q=\left(q^{\prime}+128\right) \bmod 256, \quad-128 \leq q^{\prime}<128,$$
which is the same operation as in Eq. (2.7) since all calculations are performed modulo $256 .$

## 数学代写|图像处理代写 数字图像处理代考|图像的有符号表示

$$q^{\prime}=(q-128) \bmod 256, \quad 0 \leq q<256 .$$

$$q=\left(q^{\prime}+128\right) \bmod 256, \quad-128 \leq q^{\prime}<128,$$

## 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。

Posted on Categories:Digital image processing, 图像处理, 数学代写

## avatest™帮您通过考试

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## 数学代写|图像处理代写Digital image processing代考|Neighborhood Relations

An important property of discrete images is their neighborhood relations since they define what we will regard as a connected region and therefore as a digital object. A rectangular grid in two dimensions shows the unfortunate fact, that there are two possible ways to define neighboring pixels (Fig. 2.4a, b). We can regard pixels as neighbors either when they have a joint edge or when they have at least one joint corner. Thus a pixel has four or eight neighbors and we speak of a 4-neighborhood or an 8-neighborhood.

Both types of neighborhood are needed for a proper definition of objects as connected regions. A region or an object is called connected when we can reach any pixel in the region by walking from one neighboring pixel to the next. The black object shown in Fig. 2.4c is one object in the 8-neighborhood, but constitutes two objects in the 4-neighborhood. The white background, however, shows the same property. Thus we have either two connected regions in the 8-neigborhood crossing each other or two separated regions in the 4-neighborhood. This inconsistency can be overcome if we declare the objects as 4-neighboring and the background as 8-neighboring, or vice versa.

These complications occur not only with a rectangular grid. With a triangular grid we can define a 3-neighborhood and a 12-neighborhood where the neighbors have either a common edge or a common corner, respectively (Fig. 2.3a). On a hexagonal grid, however, we can only define a 6-neighborhood because pixels which have a joint corner, but no joint edge, do not exist. Neighboring pixels always have one joint edge and two joint corners. Despite this advantage, hexagonal grids are hardly used in image processing, as the imaging sensors generate pixels on a rectangular grid. The photosensors on the retina in the human eye, however, have a more hexagonal shape [193].

## 数学代写|图像处理代写Digital image processing代考|Discrete Geometry

The discrete nature of digital images makes it necessary to redefine elementary geometrical properties such as distance, slope of a line, and coordinate transforms such as translation, rotation, and scaling. These quantities are required for the definition and measurement of geometric parameters of object in digital images.

In order to discuss the discrete geometry properly, we introduce the grid vector that represents the position of the pixel. The following discussion is restricted to rectangular grids. The grid vector is defined in 2-D, 3-D, and 4-D spatiotemporal images as
$$\boldsymbol{r}{m, n}=\left[\begin{array}{c} n \Delta x \ m \Delta y \end{array}\right], \boldsymbol{r}{l, m, n}=\left[\begin{array}{c} n \Delta x \ m \Delta y \ l \Delta z \end{array}\right], \boldsymbol{r}_{k, l, m, n}=\left[\begin{array}{c} n \Delta x \ m \Delta y \ l \Delta z \ k \Delta t \end{array}\right]$$
To measure distances, it is still possible to transfer the Euclidian distance from continuous space to a discrete grid with the definition
$$d_e\left(\boldsymbol{r}, \boldsymbol{r}^{\prime}\right)=\left|\boldsymbol{r}-\boldsymbol{r}^{\prime}\right|=\left[\left(n-n^{\prime}\right)^2 \Delta x^2+\left(m-m^{\prime}\right)^2 \Delta y^2\right]^{1 / 2} .$$
Equivalent definitions can be given for higher dimensions. In digital images two other metrics have often been used. The city block distance
$$d_b\left(\boldsymbol{r}, \boldsymbol{r}^{\prime}\right)=\left|n-n^{\prime}\right|+\left|m-m^{\prime}\right|$$
gives the length of a path, if we can only walk in horizontal and vertical directions (4-neighborhood). In contrast, the chess board distance is defined as the maximum of the horizontal and vertical distance
$$d_c\left(\boldsymbol{r}, \boldsymbol{r}^{\prime}\right)=\max \left(\left|n-n^{\prime}\right|,\left|m-m^{\prime}\right|\right) .$$

.

## 数学代写|图像处理代写数字图像处理代考|离散几何

$$\boldsymbol{r}{m, n}=\left[\begin{array}{c} n \Delta x \ m \Delta y \end{array}\right], \boldsymbol{r}{l, m, n}=\left[\begin{array}{c} n \Delta x \ m \Delta y \ l \Delta z \end{array}\right], \boldsymbol{r}_{k, l, m, n}=\left[\begin{array}{c} n \Delta x \ m \Delta y \ l \Delta z \ k \Delta t \end{array}\right]$$

$$d_e\left(\boldsymbol{r}, \boldsymbol{r}^{\prime}\right)=\left|\boldsymbol{r}-\boldsymbol{r}^{\prime}\right|=\left[\left(n-n^{\prime}\right)^2 \Delta x^2+\left(m-m^{\prime}\right)^2 \Delta y^2\right]^{1 / 2} .$$

$$d_b\left(\boldsymbol{r}, \boldsymbol{r}^{\prime}\right)=\left|n-n^{\prime}\right|+\left|m-m^{\prime}\right|$$

$$d_c\left(\boldsymbol{r}, \boldsymbol{r}^{\prime}\right)=\max \left(\left|n-n^{\prime}\right|,\left|m-m^{\prime}\right|\right) .$$

## 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。

Posted on Categories:Digital image processing, 图像处理, 数学代写

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## 数学代写|图像处理代写Digital image processing代考|Image Processing and Computer Graphics

For some time now, image processing and computer graphics have been treated as two different areas. Knowledge in both areas has increased considerably and more complex problems can now be treated. Computer graphics is striving to achieve photorealistic computer-generated images of three-dimensional scenes, while image processing is trying to reconstruct one from an image actually taken with a camera. In this sense, image processing performs the inverse procedure to that of computer graphics. In computer graphics we start with knowledge of the shape and features of an object $-$ at the bottom of Fig. $1.13$ – and work upwards until we get a two-dimensional image. To handle image processing or computer graphics, we basically have to work from the same knowlhow a three-dimensional scene is projected onto an image plane, etc.
There are still quite a few differences between an image processing and a graphics workstation. But we can envisage that, when the similarities and interrelations between computer graphics and image processing are better understood and the proper hardware is developed, we will see some kind of general-purpose workstation in the future which can handle computer graphics as well as image processing tasks. The advent of multimedia, i. e., the integration of text, images, sound, and movies, will further accelerate the unification of computer graphics and image processing. The term “visual computing” has been coined in this context [58]

## 数学代写|图像处理代写Digital image processing代考|Cross-disciplinary Nature of Image Processing

By its very nature, the science of image processing is cross-disciplinary in several aspects. First, image processing incorporates concepts from various sciences. Before we can process an image, we need to know how the digital signal is related to the features of the imaged objects. This includes various physical processes from the interaction of radiation with matter to the geometry and radiometry of imaging. An imaging sensor converts the incident irradiance in one or the other way into an electric signal. Next, this signal is converted into digital numbers and processed by a digital computer to extract the relevant data. In this chain of processes (see also Fig. 1.13) many areas from physics, computer science and mathematics are involved including among others, optics, solid state physics, chip design, computer architecture, algebra, analysis, statistics, algorithm theory, graph theory, system theory, and numerical mathematics. From an engineering point of view, contributions from optical engineering, electrical engineering, photonics, and software engineering are required.

Image processing has a partial overlap with other disciplines. Image processing tasks can partly be regarded as a measuring problem, which is part of the science of metrology. Likewise, pattern recognition tasks are incorporated in image processing in a similar way as in speech processing. Other disciplines with similar connections to image processing are the areas of neural networks, artificial intelligence, and visual perception. Common to these areas is their strong link to biological sciences.

When we speak of computer vision, we mean a computer system that performs the same task as a biological vision system to “discover from images what is present in the world, and where it is” [120]. In contrast, the term machine vision is used for a system that performs a vision task such as checking the sizes and completeness of parts in a manufacturing environment. For many years, a vision system has been regarded just as a passive observer. As with biological vision systems, a computer vision system can also actively explore its surroundings by, e.g., moving around and adjusting its angle of view. This, we call active vision.

There are numerous special disciplines that for historical reasons developed partly independently of the main stream in the past. One of the most prominent disciplines is photogrammetry (measurements from photographs; main applications: mapmaking and surveying). Other areas are remote sensing using aerial and satellite images, astronomy, and medical imaging.

## 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。