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Image Enhancement in Frequency Domain Nana Ramadijanti Laboratorium Computer Vision Politeknik Elekltronika Negeri Surabaya PENS-ITS 2009

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Laboratorium Computer Vision Politeknik Elektronika Negeri Surabaya PENS-ITS Image and Its Fourier Spectrum

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Laboratorium Computer Vision Politeknik Elektronika Negeri Surabaya PENS-ITS Filtering in Frequency Domain: Basic Steps Basic Steps 1.Multiply pixel f(x,y) of the input image by (-1) x+y. 2.Compute F(u,v), the DFT 3.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

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Laboratorium Computer Vision Politeknik 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 Vision Politeknik Elektronika Negeri Surabaya PENS-ITS Low-pass & High-pass Filtering

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Laboratorium Computer Vision Politeknik 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 Vision Politeknik Elektronika Negeri Surabaya PENS-ITS Gaussian Low Pass Filters D(u,v): distance from the origin of Fourier transform

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Laboratorium Computer Vision Politeknik Elektronika Negeri Surabaya PENS-ITS Ideal Low Pass Filters The cut-off frequency D o determines % power are filtered out. Image power as a function of distance from the origin of DFT (5, 15, 30, 80, 230)

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Laboratorium Computer Vision Politeknik 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.

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Laboratorium Computer Vision Politeknik Elektronika Negeri Surabaya PENS-ITS Ringing and Blurring

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Laboratorium Computer Vision Politeknik Elektronika Negeri Surabaya PENS-ITS Butterworth Low Pass Filters

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Laboratorium Computer Vision Politeknik 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 Vision Politeknik Elektronika Negeri Surabaya PENS-ITS Applications of HPFs Ideal HPF –D o = 15, 30, 80 Butterworth HPF –n = 2, –D o = 15, 30, 80 Gaussian HPF –D o = 15, 30, 80

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Laboratorium Computer Vision Politeknik 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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SekilaS InfO Ada beberapa hal yang harus dikuasai sebelum menguasai materi di dalam image processing yaitu: matematika, aljabar, pengolahan sinyal, statistik dan pemrograman.

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BergaBunglah denGan Kami BergaBunglah denGan Kami Laboratorium Computer Vision Politeknik Elektronika Negeri Surabaya PENS-ITS 2009

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