图像基础15 图像滤波与除噪——邻域平均法

本文学习资源《机器学习实践指南 案例应用解析》

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概述

邻域平均法可有效消除高斯噪声，其数学公式如下：
$g(x,y)+\frac{1}{M}\sum_{(k.I)\in S}{f(x-k,y-l)}$

S为邻域，不包括$(x,y)$本身的像素点，核$h(x,y)$可为：
半径为1：
$\frac{1}{4} \begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{pmatrix}$
半径为2：
$\frac{1}{8} \begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{pmatrix}$

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邻域平均法对椒盐噪声滤波进行处理的操作

# -*- coding: utf-8 -*-
# coding=utf-8
# 线性锐化滤波，拉普拉斯图像变换
import cv2
import numpy as np 

fn = "test.jpg"
myimg = cv2.imread(fn)

img = cv2.cvtColor(myimg , cv2.COLOR_BGR2GRAY)

# 加上椒盐噪声
param = 20
# 灰阶范围
w = img.shape[1]
h = img.shape[0]
newimg = np.array(img)

# 噪声点数量
noisecount = 100000
for k in range(0,noisecount):
    xi = int(np.random.uniform(0,newimg.shape[1]))
    xj = int(np.random.uniform(0,newimg.shape[0]))
    newimg[xj,xi]=255

# 邻域平均法去噪
# 脉冲响应函数，核函数
# 图像四个边的像素处理
lbimg = np.zeros((h+2,w+2),np.float32)
tmpimg = np.zeros((h+2,w+2))
myh = h+2
myw = w+2
tmpimg[1:myh-1,1:myw-1] = newimg[0:myh, 0:myw]

# 用领域平均法的（设半径为2）脉冲响应函数
a = 1/8.0
kernel = a * np.array([[1,1,1],[1,0,1],[1,1,1]])
for y in range(1,myh-1):
    for x in range(1,myw-1):
        lbimg[y,x] = np.sum(kernel*tmpimg[y-1:y+2,x-1:x+2])
    print(".")
resultimg = np.array(lbimg[1:myh-1,1:myw-1],np.uint8)
cv2.imshow('src',newimg)
cv2.imshow('dst',resultimg)
cv2.waitKey()
cv2.destroyAllWindows()

原图：

结果：
[外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-12Fxopqe-1574725866018)(https://img-blog.csdn.net/20171023083833261?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQveHVuZGg=/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/SouthEast)]

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邻域平均法对高斯噪声滤波进行处理的操作

# -*- coding: utf-8 -*-
# coding=utf-8
# 线性锐化滤波，拉普拉斯图像变换
import cv2
import numpy as np 

fn = "test.jpg"
myimg = cv2.imread(fn)

img = cv2.cvtColor(myimg , cv2.COLOR_BGR2GRAY)

# 加上高斯噪声
param = 20
# 灰阶范围
grayscale = 256
w = img.shape[1]
h = img.shape[0]
newimg = np.zeros((h,w),np.uint8)

# 加上高斯噪声
param=20
# 灰阶范围
grayscale=256
w=img.shape[1]
h=img.shape[0]
newimg=np.zeros((h,w),np.uint8)

for x in range(0,h):
    for y in range(0,w,2):
        r1 = np.random.random_sample()
        r2 = np.random.random_sample()
        z1=param*np.cos(2*np.pi*r2)*np.sqrt((-2)*np.log(r1))
        z2=param*np.sin(2*np.pi*r2)*np.sqrt((-2)*np.log(r1))

        fxy=int(img[x,y]+z1)
        fxy1 = int(img[x,y+1]+z2)
        #f(x,y)
        if fxy<0:
            fxy_val=0
        elif fxy>grayscale-1:
            fxy_val=grayscale-1
        else:
            fxy_val=fxy
        #f(x,y+1)
        if fxy1<0:
            fxy1_val=0
        elif fxy1>grayscale-1:
            fxy1_val=grayscale-1
        else:
            fxy1_val=fxy1
        newimg[x,y]=fxy_val
        newimg[x,y+1]=fxy1_val
    print("-")
    
# 邻域平均法去噪
# 脉冲响应函数，核函数
# 图像四个边的像素处理
lbimg = np.zeros((h+2,w+2),np.float32)
tmpimg = np.zeros((h+2,w+2))
myh = h+2
myw = w+2
tmpimg[1:myh-1,1:myw-1] = newimg[0:myh, 0:myw]

# 用领域平均法的（设半径为2）脉冲响应函数
a = 1/8.0
kernel = a * np.array([[1,1,1],[1,0,1],[1,1,1]])
for y in range(1,myh-1):
    for x in range(1,myw-1):
        lbimg[y,x] = np.sum(kernel*tmpimg[y-1:y+2,x-1:x+2])
    print(".")
resultimg = np.array(lbimg[1:myh-1,1:myw-1],np.uint8)
cv2.imshow('src',newimg)
cv2.imshow('dst',resultimg)
cv2.waitKey()
cv2.destroyAllWindows()

原图：

滤波结果：