Modulation transfer function

School of Mechanical EngineeringPusan National University

Seungwoo Haseungwooha@pusan.ac.kr

051-510-3921통합기계관 120호

Spatial Frequency & Nyquist Frequency• Spatial frequency? (line-pair/mm 1 cycle/mm)

• space domain: mm spatial frequency domain: mm-1

• inverse number of dimension: • low spatial frequency means large and blunt object

• high spatial frequency means small and sharp object

• Nyquist frequency = maximum spatial frequency that the detector can distinguish

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Pixel pitch 0.096 mm detectorNy = (2×0.096)-1 mm = 5.208 mm-1

Spatial Frequency for DR

3

Fourier Transform

• Any periodic function can be expressed as the sum of a series of sines and cosines (of varying amplitudes)

4

dkexfkF ikx2)()( )sin()cos( xixexi Note:

Imaging System Transfer Function

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Modulation Transfer Function

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• Spatial frequency domain analysis for impulsive excitation• How can we provide an impulse input to the imaging system? (edge and slit device)

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Slit method

Edge method

Extracting edge profile

Fine-sampling

Differentiation

1D Fourier transform

Edge spread function (step impulse response)

Line spread function (line impulse response)

)0(MTF

]LSF[)(MTF

FFTf

Extracting slit profile

Fine-sampling

Edge method

Slit method

Noise removing (Hann filter)

Commercial Products MTF

8

Practice

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Digital image processing

• 디지털 화상처리 또는 디지털 영상 처리는 컴퓨터 알고리즘을 사용하여디지털 이미지에 대한 화상처리를 수행하는 것이다. 디지털 신호처리의 하위분야로, 디지털 영상처리는 아날로그 영상처리에 비해 많은 장점이 있다. 입력자료에 더욱 광범위한 알고리즘을 적용 가능하게 되고, 처리 도중 발생하는 잡음과 신호 왜곡과 같은 문제들을 방지할 수 있다.

• 디지털 영상 처리는 영상 처리를 위한 훨씬 더 복잡한 알고리즘 사용을 가능하게 하므로, 단순작업에 더욱 정교한 성능과 아날로그 수단으로는 불가능한 방법의 실행, 양쪽을 가능하게 한다.

Digital image processing

• Foodie

• SNOW

• B612

• …

Digital image

• Color images : 24 bit

• Medical images : 16 bit

1 9 2 3

2 4 8 5

1 2 4 6

3 8 7 1

ImageJ

• http://imagej.nih.gov/ij/• Google -> ImageJ 검색• ImageJ is an open source

processing program designed for scientific multidimensional images

Dicom

• Open ImageJ…• Image-Show info

Window/level

• Image-Adjust-…Brightness/Contrast

Matlab

Matlab - function

Function Definition Input variable

imread Read a image filename, (format)

imwrite Write a image as a file image, filename

imshow Display image image, display range

Matlab – image I/O

• Use ‘imread’ (‘dicomread’)

• Img = imread(‘TestImg.jpg’);

• ImgBw = sum(double(Img),3)/3;

• ImgBw = uint8(ImgBw)

• imwrite(ImgBw , ’TestImgBw.jpg’);

Gamma transform

0.51

1.5

𝛾=𝛾=1.5 𝛾=1 𝛾=0.5

• img = double(dicomread(‘ChestDR.dcm'));• f = img/max(img(:));• g = (f.^1.5)

Histogram equalization

histogram = zeros(max(max(img)),1);

for i=1:size(img,1)

for j=1:size(img,2)

histogram(img(i,j)) = histogram(img(i,j))+1;

end

end

cdf = zeros(numel(histogram),1);

for i=1:numel(histogram)

cdf(i) = sum(histogram(1:i));

end

cdf_norm = cdf/size(img,1)/size(img,2)*max(max(img));

img2 = zeros(size(img));

for i=1:size(img,1)

for j=1:size(img,2)

img2(i,j) = round(cdf_norm(img(i,j)))+1;

end

end

histogram2 = zeros(max(max(img2)),1);

for i=1:size(img2,1)

for j=1:size(img2,2)

histogram2(img2(i,j)) = histogram2(img2(i,j))+1;

end

end

figure, subplot(2,1,1)

bar(histogram,2,’r’)

subplot(2,1,2)

bar(histogram2,2,’b’)

figure, imshow(img,[])

figure, imshow(img2,[])

Fourier transformation

• Use ‘fft2’, ‘fftshift’, ‘ifft2’

fft2 fftshift

ifft2 fftshift

Fourier domain masking

• Low-pass filtering• Low-pass filtering 은 cutoff 주파수보다 높은 주파수 신호를 제거하여

영상을 smoothing하는 효과를 만들 수 있음

• High-pass filtering• High-pass filtering 은 낮은 주파수 신호를 제거하여 영상의 edge를 강

조하는 효과를 만들 수 있음