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

数学代写|图像处理代写Digital image processing代考|EE637 Quantization

avatest™

avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

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。