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Mean and Median Filters. 指導教授:張顧耀 學生姓名:張志坤 學號: E9406011. Outline. Introduction Mean Filter Median Filter Summary Demo. Introduction. 影像濾波的定義. 主要分成兩種方式: 頻率域 (frequency domain) :由空間域影像透過 轉換 ( 如複利葉 , 小波 ) 而形成的影像表示空間

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Mean and median filters

Mean and Median Filters

指導教授:張顧耀

學生姓名:張志坤

學號:E9406011


Outline
Outline

  • Introduction

  • Mean Filter

  • Median Filter

  • Summary

  • Demo

Mean and Median Filters


Introduction
Introduction

  • 影像濾波的定義

  • 主要分成兩種方式:

  • 頻率域(frequency domain) :由空間域影像透過 轉換 (如複利葉, 小波)

  • 而形成的影像表示空間

  • 空間域(spatial domain) :直接對影像上的 pixel value做處理

空間域的方程式表示

g(x,y) = T[ f(x,y) ]

f(x,y) 是輸入的影像

g(x,y) 是經過處理的影像

T ->影像濾波的方法

Mean and Median Filters


Introduction1
Introduction

  • 影像濾波的定義( 方程式 g(x,y) = T[ f(x,y) ] )

Original

Original

y

y

(x,y)

(x,y)

Image f(x,y)

Image g(x,y)

x

x

g(x,y) = T[ f(x,y) ]

f(x,y) 是輸入的影像

g(x,y) 是經過處理的影像

T ->影像濾波的方法

Mean and Median Filters


Outline1
Outline

  • Introduction

  • Mean Filter

  • Median Filter

  • Summary

  • Demo

Mean and Median Filters


Mean filter
Mean Filter

The Mean Filter is used to

soften an image by averaging surrounding pixel values.

Mean and Median Filters


Mean filter1

Original

Original

y

y

(x,y)

(x,y)

Image f(x,y)

x

Image g(x,y)

x

Mean Filter

Grayscale 3x3 pixel window

(x,y)

Center pixel = ( 22 + 77 + 48 + 150 + 77 + 158 + 0 + 77 + 219 ) / 9= 92

Mean and Median Filters


Mean filter2
Mean Filter

(a) 加入點雜訊的方形影像; (b) 點雜訊方形影像的輪廓圖; (c) 經平均值濾波後的影像; (d) 平均值濾波後的輪廓圖。

Mean and Median Filters


Mean filter3

Original

y

(x,y)

Image f(x,y)

x

Mean Filter

  • 演算法

int x , y ;

int a=(n-1)/2;

int color(i) , color(x,y);

for(int k=x-a ; k<=x+a ; k++)

{

for(int m=y-a ; m<=y+a ; m++)

{

color(x,y)+=color(k,m)

}

}

color(i)=[color(x, y)/n*n);

Mean and Median Filters


Mean filter4

Original

y

(x,y)

Image f(x,y)

x

Mean Filter

  • ITK

Header file included

#include “itkMeanImageFilter.h”

Using

Typedef Itk::MeanImageFilter

< InputImageType, OutputImageType > FilterType;

FilterType::Pointer filter = FilterType::New(();

InputImageType::SizeType indexRadius;

indexRadius[0] = 1; // radius along x 1-> 2D 2-> 3*5

indexRadius[1] = 1; // radius along y

Rx * 2 + 1= 2 * 1 + 1 = 3 Rx 就是 x 方向的半徑, 1 代表中心點

Ry * 2 + 1 = 2 * 1 + 1 = 3Ry 就是y 方向的半徑, 1 代表中心點

Mean and Median Filters


Mean filter5
Mean Filter

Mean

Source

Mean and Median Filters


Mean filter6
Mean Filter

Source

Mean

Mean and Median Filters


Outline2
Outline

  • Introduction

  • Mean Filter

  • Median Filter

  • Summary

  • Demo

Mean and Median Filters


Median filter
Median Filter

The Median filter is used to

remove noise from an image

by replacing pixels with the middle pixel value selected from a certain window size.

Mean and Median Filters


Median filter1

Original

Original

y

y

(x,y)

(x,y)

Image f(x,y)

x

Image g(x,y)

x

Median Filter

Grayscale 3x3 pixel window

(x,y)

0, 22, 48, 77, [ 77 ], 77, 150, 158, 219

Mean and Median Filters


Median filter2
Median Filter

(a) 加入點雜訊的方形影像; (b) 點雜訊方形影像的輪廓圖; (c) 經中間值濾波後的影像; (d) 中間值濾波後的輪廓圖。

Mean and Median Filters


Median filter3
Median Filter

  • 演算法

int x , y ;

int z=0;

int a=(n-1)/2;

int color(i) ;

int array[] = new int [nxn-1];

for(int k=x-a ; k<=x+a ; k++)

{

for(int m=y-a ; m<=y+a ; m++)

{

array [z]=color(k,m)

z++;

}

}

sort(array);

color(i)=median(array []);

Mean and Median Filters


Median filter4

Original

y

(x,y)

Image f(x,y)

x

Median Filter

  • ITK

Header file included

#include “itkMedianImageFilter.h”

Using

Typedef Itk::MedianImageFilter

< InputImageType, OutputImageType > FilterType;

FilterType::Pointer filter = FilterType::New(();

InputImageType::SizeType indexRadius;

indexRadius[0] = 1; // radius along x 1-> 2D 2-> 3*5

indexRadius[1] = 1; // radius along y

Mean and Median Filters


Median filter5
Median Filter

3×3 median filtering

Source

Mean and Median Filters


Median filter6
Median Filter

Source

3×3 median filtering

9×9 median filtering

Mean and Median Filters


Outline3
Outline

  • Introduction

  • Mean Filter

  • Median Filter

  • Summary

  • Demo

Mean and Median Filters


Summary
Summary

  • Mean filter and Median filter的比較 - 1

Mean and Median Filters


Summary1
Summary

  • Mean filter and Median filter的比較 - 2

Mean filter

Median filter

Mean and Median Filters


Summary2
Summary

  • Mean filter and Median filter的比較 - 3

(c) 平均值濾波輸出

Mean and Median Filters


Outline4
Outline

  • Introduction

  • Mean Filter

  • Median Filter

  • Summary

  • Demo

Mean and Median Filters


Demo

Mean and Median Filters


Demo

Mean and Median Filters


參考文獻

  • ItkSoftwareGuide.pdf

  • http://www.cee.hw.ac.uk/hipr/html/mean.html

  • http://www.ntut.edu.tw/~s9598008/homework1.htm

  • http://www.cc.ntut.edu.tw/~s8410010/hw1.htm

  • 連國珍,“數位影像處理”,儒林圖書公司(SIM 949)。

  • http://140.128.102.71/東海大學影像視訊處理實驗室

Mean and Median Filters


報告結束

敬請指教

Mean and Median Filters


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