图像处理Chap 3(2) Image Enhancement in the Spatial Domain-local processing

1 f i, j M


n i, j

S：点(x, y)邻域内的
点集
M：S内总点数。

Box filter
例：对图像采用3×3的邻域平均法，对像素(m,n)， 其邻域像素如下：
(m-1,n-1) (m,n-1) (m+1,n-1) (m-1,n) (m,n) (m+1,n) (m-1,n+1) (m,n+1) (m+1,n+1)
median max min
some
filter : R=median{zk | k=1,2,…,nn}
filter : R=max{zk | k=1,2,…,nn} filter : R=min{zk | k=1,2,…,nn}
nn is the size of the mask
bridging noise
reduction can be accomplished by blurring with a linear filter and also by a nonlinear filter.
3.2.1.1 Smoothing Linear filters
output is simply the average of the pixels contained in the neighborhood of the filter mask.
at
R w1 z1 w2 z2 wmn zmn wi zi
i 1 mn
w1, 1

w1, n
wm, 1

wm, n
3.2.1 Smoothing Spatial filters
used for blurring (模糊) and for noise reduction.
3.2.1.2 Smoothing Nonlinear filters
(Order-Statistics Filters)
the
response is based on ordering (ranking) the pixels contained in the image area encompassed (环绕) by the filter. nonlinear filters
3.2.1.2 Smoothing Nonlinear filters

Median Filters: R=median{zk | k=1,2,…,nn}
replaces
the value of a pixel by the median of the gray levels in the neighborhood of that pixel (the original value of the pixel is included in the computation of the median) popular because for certain types of random noise (impulse noise, salt and pepper (椒 盐) noise), they provide excellent noise-reduction capabilities, with considering less blurring than linear smoothing filters of similar size.
blurring
is used in preprocessing steps, such as
removal
of small details from an image prior to object extraction (连接) of small gaps in lines or curves
3.2.1.1 Smoothing Linear filters

Box filter (局部/邻域平均法)
局部平均法的基本假设：


图像由许多灰度恒定的小块组成。
图像上的噪声是加性的、均值为零，且与图像信号互 不相关。
3.2.1.1 Smoothing Linear filters

Box filter (局部/邻域平均法)
值计算中涉及的像素数。
中值滤波的优点：抑制随机噪声的同时不使边缘模糊。
但对于线、尖顶等细节多的图像不宜采用中值滤波。
Example 1 of Median Filter
取33窗口
212 200 198 206 202 201 208 205 207
从小到大排列，取中间值：
212 200 198 206 205 201 208 205 207
We can see that the result after smoothing and thresholding, the remains are the largest and brightest objects in the image.
3.2.1.1 Smoothing Linear filters
198 200 201 202 205 206 207 208 212
Example 2 of Median Filter —— 去除噪声

80
90
200
110
120

200显然是一个噪声点
取：N=3 80 90 110 120 120
滤波后，200被去除。
空域滤波增强：原理和分类 – 最大值滤波
quite
3.2.1.2 Smoothing Nonlinear filters

Median Filters: R=median{zk | k=1,2,…,nn}
中值滤波用一个含有奇数点的滑动窗口，将邻域中的像
素按灰度级排序，取其中间值为输出像素。
中值滤波的效果取决于两个要素：邻域的空间范围和中
空域滤波增强：原理和分类 – 最小值滤波
Example 3 of Median Filter —— 去除噪声
Matlab: demos\toolboxs\image processing
\enhancement\noise reduction filtering
3.2.1.2 Smoothing Nonlinear filters
3.2 图像的空间域平滑 任何一幅原始图像，在其获取和传输等过程中， 会受到各种噪声的干扰，使图像恶化，质量下降， 图像模糊，特征淹没，对图像分析不利。
为了抑制噪声改善图像质量所进行的处理称图 像平滑或去噪。
平滑可以抑制高频成分，但也使图像变得模糊。
3.2 Spatial filter
use
filter (can also be called as mask/kernel (核)/template or window) values in a filter subimage are referred to as (被称为) coefficients, rather than pixel. focus will be on masks of odd sizes, e.g. (举 例来说) 3x3, 5x5,… w1 w 2 w3 w4 w 5 w6
1 1 1 则平滑化后的图像为：g m, n f m i , n j 9 i 1 j 1

Box filter
模板
1 1 1 1 1 1 1 1 1 1 1 1 1 1 9 9 1 1 1 1 1 1

Box filter
sharp
transitions result from
noise in the image
random edges thБайду номын сангаасs,
of objects in the image
smoothing can reduce noises (desirable) and blur edges (undesirable)
the
our
w7 w 8 w9
3.2 Spatial filter
Spatial Filtering Process:
simply
move the filter mask from point to point in an image. each point (x, y), the response of the filter at that point is calculated using a predefined relationship.

Median Filters: R=median{zk | k=1,2,…,nn}
forces
the points with distinct gray levels to be more like their neighbors.
isolated
clusters of pixels that are light or dark with respect to their neighbors, and whose area is less than n2/2 (one-half the filter area), are eliminated by an nn median filter.
3.2.1.1 Smoothing Linear filters
Two 33 smoothing linear filters
For weighted average filter, the center is the most important and other pixels are inversely weighted as a function of their distance from the center of the mask.