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Modulation transfer function
School of Mechanical EngineeringPusan National University
Seungwoo [email protected]
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
2
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
5
Modulation Transfer Function
6
• 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
9
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