mathematical morphology & voting filters 姓名 : 陳慧敏 授課老師 : 張顧耀 教授...

Mathematical Morphology & Voting Filters

姓名 : 陳慧敏授課老師 : 張顧耀 教授日期 :2007/6/12

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outline

What is morphology?– Dilation– Erosion

Mathematical Morphology– Binary Filters– Grayscale Filters

Voting Filter– Binary Median Filter– Hole Filling Filter– Iterative Hole Filling Filter

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What is morphology?

A range of methods that deal with (alter) structure and shape in images.– Dilation

– Erosion

=>

Fig.1. 原圖

Fig.2. 經過 Dilation 處理

=>Fig.3. 原圖

Fig.4. 經過 Erosion 處理

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Structuring element

Structuring element– a small array of pixels, each pixel to 0 or 1.

Example:

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Dilation

Fig.6.Structuring element

Fig.5. 原始影像

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Dilation

Fig.7. 做完 Dilation 結果

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Dilation

Fig.8. 原始影像 Fig.9. 經過 Dilation 處理

Fig.10.Structuring element

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Erosion

Fig.11. 原始影像

Fig.12.Structuring element

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Erosion

Fig.13. 做完 Erosion 結果

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Dilation & Erosion

Dilation:

Fig.14. Original, dilated by 3x3 square, dilated by 5x5 square

Erosion:

Fig.15. Original, dilated by 3x3 square, dilated by 5x5 square

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outline

What is morphology?– Dilation– Erosion

Mathematical Morphology– Binary Filters– Grayscale Filters

Voting Filter– Binary Median Filter– Hole Filling Filter– Iterative Hole Filling Filter

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Mathematical Morphology

Binary Filters– Header

#include "itkBinaryBallStructuringElement.h"

#include "itkBinaryErodeImageFilter.h" #include "itkBinaryDilateImageFilter.h"

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Mathematical Morphology

Structuring element 設定 : structuringElementType structuringElement; structuringElement.SetRadius( 1 ); // 3x3 structuring element structuringElement.CreateStructuringElement(); binaryErode->SetKernel( structuringElement ); binaryDilate->SetKernel( structuringElement );

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Mathematical Morphology

Grayscale Filters– 觀念、寫法與 Binary Filters 大致相同

#include "itkBinaryErodeImageFilter.h" 修改

#include "itkGrayscaleErodeImageFilter.h"

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Input Image (DICOM)

型態轉換 signed short unsigned char

Image type?

BinaryErodeImageFilterBinaryDilateImageFilter

GrayscaleErodeImageFilterGrayscaleDilateImageFilter

binary grayscale

設定 structuringElement

Binary threshold

設定 structuringElement

型態轉換 unsigned char signed short

Output image

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Mathematical Morphology

Fig.16.Effect of erosion and dilation in a binary image.

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Mathematical Morphology

Fig.17.Effect of erosion and dilation in a binary image.

Radius =1

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Mathematical Morphology

Fig.18.Effect of erosion and dilation in a grayscale image.

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Mathematical Morphology

Fig.19.Effect of erosion and dilation in a grayscale image.

Radius =1

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outline

What is morphology?– Dilation– Erosion

Mathematical Morphology– Binary Filters– Grayscale Filters

Voting Filter– Binary Median Filter– Hole Filling Filter– Iterative Hole Filling Filter

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Voting Filter

Counting the number of pixels in its neighborhood by applying a rule.– Binary Median Filter– Hole Filling Filter– Iterative Hole Filling Filter

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Binary Median Filter

Binary Median Filter– robust approach for noise reduction– optimize the execution of the filter

0 0 0 0 0 0 1 1 1

median

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Binary Median Filter

Header– #include "itkBinaryMedianImageFilter.h“

indexRadius[0] = radiusX; // radius along x indexRadius[1] = radiusY; // radius along y filter->SetRadius( indexRadius );

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Binary Median Filter

Fig.21. Effect of the BinaryMedianImageFilter on a slice from a MRI

Radius of 2,2

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Binary Median Filter

Fig.23. Effect of the BinaryMedianImageFilter on a slice from a MRIRadius of 1,1

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Hole Filling Filter

Hole Filling Filter– smoothing contours– filling holes in binary images

Converting a background pixel into a foreground pixel by majority threshold.– if the number of foreground neighbors(pixel value=1) su

rpass the number of background neighbors (pixel value=0) by the majority value.

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Hole Filling Filter

Neighborhood size : 3x3

majority threshold: 2

Example:

If foreground neighbors(=1) (3x3-1)/2+majority = 6

then background pixel converting into a foreground pixel

0 1

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Hole Filling Filter

Header#include "itkVotingBinaryHoleFillingImageFilter.h“

設定 majority threshold– filter->SetMajorityThreshold( 2 );

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Hole Filling Filter

Fig.25.Effect of the VotingBinaryHoleFillingImageFilter on a slice from a MRI, radius1 ,2and 3 respectively, majority threshold=2

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Radius=1

Radius=2 Radius=3

原圖

Fig.26.Effect of the VotingBinaryHoleFillingImageFilter on a slice from a MRI, radius1 ,2and 3 respectively , majority threshold=1

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Iterative Hole Filling Filter

Iterative Hole Filling Filter– smoothing contours– filling holes in binary images

The filter can be used in an iterative way, by applying it repeatedly until no pixel changes.

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Iterative Hole Filling Filter

To decide maximum number of iterations that this filter should be run.

#include "itkVotingBinaryIterativeHoleFillingImageFilter.h“;

filter->SetMaximumNumberOfIterations(numberOfIterations );

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Iterative Hole Filling Filter

Fig.27. Effect of 1, 10 and 20 iterations of the VotingBinaryIterativeHoleFillingImageFilter using a 3x3 window.

majority threshold=2

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原圖 numberOfIterations=1

numberOfIterations=10 numberOfIterations=20

5x5 window

majority = 1

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Input Image (DICOM)

型態轉換 signed short unsigned char

BinaryMedianImageFilter VotingBinaryHoleFillingImageFilter VotingBinaryIterativeHoleFillingImageFilter

indexRadius[0] = radiusX; // radius along xindexRadius[1] = radiusY; // radius along y

Binary threshold

設定 MajorityThreshold 設定重複做的次數

Filter ?Median IterativeHoleFilling

HoleFilling

設定 MajorityThreshold

型態轉換

Output image

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參考文獻

ItkSoftwareGuide

林國祥老師 投影片數位影像處理 繆紹綱 譯

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The end