Mean and median filters
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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

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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

Mean and Median Filters


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


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


Outline

  • Introduction

  • Mean Filter

  • Median Filter

  • Summary

  • Demo

Mean and Median Filters


Mean Filter

The Mean Filter is used to

soften an image by averaging surrounding pixel values.

Mean and Median Filters


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 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


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


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 Filter

Mean

Source

Mean and Median Filters


Mean Filter

Source

Mean

Mean and Median Filters


Outline

  • Introduction

  • Mean Filter

  • Median Filter

  • Summary

  • Demo

Mean and Median Filters


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


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 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 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


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 Filter

3×3 median filtering

Source

Mean and Median Filters


Median Filter

Source

3×3 median filtering

9×9 median filtering

Mean and Median Filters


Outline

  • Introduction

  • Mean Filter

  • Median Filter

  • Summary

  • Demo

Mean and Median Filters


Summary

  • Mean filter and Median filter的比較 - 1

Mean and Median Filters


Summary

  • Mean filter and Median filter的比較 - 2

Mean filter

Median filter

Mean and Median Filters


Summary

  • Mean filter and Median filter的比較 - 3

(c) 平均值濾波輸出

Mean and Median Filters


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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