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Image Enhancement in Frequency Domain. Nana Ramadijanti Laboratorium Computer Vision Politeknik Elekltronika Negeri Surabaya PENS-ITS 2009. Image and Its Fourier Spectrum. Basic Steps Multiply pixel f(x,y) of the input image by (-1) x+y . Compute F(u,v), the DFT G(u,v)=F(u,v)H(u,v) - PowerPoint PPT Presentation
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Image Enhancement in Frequency Domain
Nana RamadijantiLaboratorium Computer Vision
Politeknik Elekltronika Negeri Surabaya PENS-ITS2009
Laboratorium Computer VisionPoliteknik Elektronika Negeri Surabaya PENS-ITS
Image and Its Fourier Spectrum
Laboratorium Computer VisionPoliteknik Elektronika Negeri Surabaya PENS-ITS
Filtering in Frequency Domain: Basic Steps
Basic Steps1. Multiply pixel f(x,y) of the
input image by (-1)x+y. 2. Compute F(u,v), the DFT3. G(u,v)=F(u,v)H(u,v)4. g1(x,y)=F-1{G(u,v)}5. g(x,y) = g1(x,y)*(-1)x+y
Laboratorium Computer VisionPoliteknik Elektronika Negeri Surabaya PENS-ITS
Notch Filter
• The frequency response F(u,v) has a notch at origin (u = v = 0).
• Effect: reduce mean value.
• After post-processing where gray level is scaled, the mean value of the displayed image is no longer 0.
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Laboratorium Computer VisionPoliteknik Elektronika Negeri Surabaya PENS-ITS
Low-pass & High-pass Filtering
Laboratorium Computer VisionPoliteknik Elektronika Negeri Surabaya PENS-ITS
Gaussian Filters
• Fourier Transform pair of Gaussian function
• Depicted in figures are low-pass and high-pass Gaussian filters, and their spatial response, as well as FIR masking filter approximation.
• High pass Gaussian filter can be constructed from the difference of two Gaussian low pass filters.
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Laboratorium Computer VisionPoliteknik Elektronika Negeri Surabaya PENS-ITS
Gaussian Low Pass Filters
D(u,v): distance from the origin of Fourier transform
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vuDvuH
Laboratorium Computer VisionPoliteknik Elektronika Negeri Surabaya PENS-ITS
Ideal Low Pass Filters
• The cut-off frequency Do determines % power are filtered out.
• Image power as a function of distance from the origin of DFT (5, 15, 30, 80, 230)
Laboratorium Computer VisionPoliteknik Elektronika Negeri Surabaya PENS-ITS
Effects of Ideal Low Pass Filters
• Blurring can be modeled as the convolution of a high resolution (original) image with a low pass filter.
Laboratorium Computer VisionPoliteknik Elektronika Negeri Surabaya PENS-ITS
Ringing and Blurring
Laboratorium Computer VisionPoliteknik Elektronika Negeri Surabaya PENS-ITS
Butterworth Low Pass Filters
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Laboratorium Computer VisionPoliteknik Elektronika Negeri Surabaya PENS-ITS
• Ideal high pass filter
• Butterworth high pass filter
• Gaussian high pass filter
High Pass Filters
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Laboratorium Computer VisionPoliteknik Elektronika Negeri Surabaya PENS-ITS
Applications of HPFs
• Ideal HPF– Do = 15, 30, 80
• Butterworth HPF– n = 2,– Do = 15, 30, 80
• Gaussian HPF– Do = 15, 30, 80
Laboratorium Computer VisionPoliteknik Elektronika Negeri Surabaya PENS-ITS
Laplacian HPF
• 3D plots of the Laplacian operator,
• its 2D images, • spatial domain response
with center magnified, and• Compared to the FIR mask
approximation
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Ada beberapa hal yang harus dikuasai sebelum menguasai materi di dalam image processing yaitu: matematika, aljabar, pengolahan sinyal,
statistik dan pemrograman.
BergaBunglah denGan Kami
Laboratorium Computer VisionPoliteknik Elektronika Negeri Surabaya
PENS-ITS 2009
