### 机器视觉代写|图像处理作业代写Image Processing代考|IMAGE HISTOGRAM

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• 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

## 机器视觉代写|图像处理作业代写Image Processing代考|IMAGE HISTOGRAM

The histogram of an image is a statistic showing the distribution of the pixel intensity values. For an image with $L$ possible intensity levels in the range of $[0, L-1]$, the histogram is the number of pixels in the image at each different intensity level, defined as the discrete function:
$$h\left(r_{k}\right)=n_{k}$$
where $r_{k}$ is the $k^{\text {th }}$ intensity level in the interval $[0, L-1]$, and $n_{k}$ is the number of pixels in the image whose intensity level is $r_{k}$. Note that $L=2^{B}$ where $B$ is the bit depth of the image.

For a grayscale image that has $L$ different possible intensities, $L$ numbers will be displayed in its histogram to show the distribution of pixels among those grayscale values. An example of the histogram of an 8-bit grayscale image, which has 256 possible intensity levels, is shown in Figure 2.7. For a color image, three individual histograms of red, green, and blue channels can be taken, as shown in Figure $2.8$.
A histogram is usually normalized by dividing all elements of $h\left(r_{k}\right)$ by the total number of pixels in the image, denoted by $n$ :
\begin{aligned} p\left(r_{k}\right) &=\frac{h\left(r_{k}\right)}{n} \ &=\frac{n_{k}}{M \times N} \end{aligned}
for $k=0,1, \cdots, L-1$. Note also that $n=M \times N$, where $M$ and $N$ are the row and column dimensions of the image. From basic probability, $p\left(r_{k}\right)$ gives the probability of occurrence of intensity level $r_{k}$ in an image.

## 机器视觉代写|图像处理作业代写Image Processing代考|PIXEL NEIGHBORHOODS

The neighborhood of a pixel plays an important role in image processing; it is often required for many operations, such as denoise, interpolation, edge detection, and morphology etc. The 4-neighbors and 8 -neighbors are two common pixel neighborhoods that are used to process an image.

The 4-neighbors of a pixel $p$ located at $(x, y)$ are a set of pixels that connected vertically and horizontally to $p$. As seen in Figure $2.9$ (a), the 4-neighbors of $p$ are

denoted by $N_{4}(p)$, and given by:
$$(x+1, y),(x-1, y),(x, y+1),(x, y-1)$$
in terms of pixel coordinates. Each 4-neighbor of $p$ is a unit distance from $p$.
The four pixels that connected diagonally to $p$ are called diagonal neighbors $(D-$ neighbors). As seen in Figure $2.9$ (b), the diagonal neighbors of $p$, denoted by $N_{D}(p)$, are given by:
$$(x+1, y+1),(x+1, y-1),(x-1, y+1),(x-1, y-1)$$
and each of them is at Euclidean distance of $\sqrt{2}$ from $p$.
The 8-neighbors of a pixel $p$ include its four 4-neighbors and four diagonal neighbors as seen in Figure $2.9(\mathrm{c})$, and they are denoted by $N_{8}(p)$.

Be aware that some of the points in $N_{4}(p), N_{D}(p)$, and $N_{8}(p)$ fall outside the image if $p$ lies on the border of the image.

Let $V$ be a set of intensity values that is used to define adjacency. It specifies a criterion of similarity that the intensity values of adjacent pixels shall satisfy. For example, $V=1$ when the adjacent pixels are 1 -valued for a binary image. $V$ could also be a subset of the 256 intensity values for an 8 -bit grayscale image. Two pixels $p$ and $q$ with the intensity values from $V$ are said to be:
(a) 4-adjacent, if $q \in N_{4}(p)$.
(b) 8 -adjacent, if $q \in N_{8}(p)$.
(c) $m$-adjacent (mixed adjacent), if
(i) $q \in N_{4}(p)$, or
(ii) $q \in N_{D}(p)$ and $N_{4}(p) \cap N_{4}(q)=\varnothing$ (the set $N_{4}(p) \cap N_{4}(q)$ has no pixels whose intensity values are from $V$ ).

Mixed adjacency is a modification of 8 -adjacency. It is used to eliminate the ambiguities that often arise when 8 -adjacency is used (this will be explained in Section 2.3.3).

## 机器视觉代写|图像处理作业代写Image Processing代考|IMAGE HISTOGRAM

H(rķ)=nķ

p(rķ)=H(rķ)n =nķ米×ñ

## 机器视觉代写|图像处理作业代写Image Processing代考|PIXEL NEIGHBORHOODS

(X+1,是),(X−1,是),(X,是+1),(X,是−1)

(X+1,是+1),(X+1,是−1),(X−1,是+1),(X−1,是−1)

(a) 4-相邻，如果q∈ñ4(p).
(b) 8 – 相邻，如果q∈ñ8(p).
(i)q∈ñ4(p), 或
(ii)q∈ñD(p)和ñ4(p)∩ñ4(q)=∅（该集ñ4(p)∩ñ4(q)没有强度值来自的像素在 ).

## 有限元方法代写

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## MATLAB代写

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