Image Enhancement in Frequency Domain Nana Ramadijanti Laboratorium

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

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

Filtering in Frequency Domain: 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. g 1(x, y)=F-1{G(u, v)} 5. g(x, y) = g 1(x, y)*(-1)x+y 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. Laboratorium Computer Vision Politeknik Elektronika Negeri Surabaya PENS-ITS

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

Gaussian Filters • Fourier Transform pair of Gaussian function • Depicted in figures are lowpass 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. • Laboratorium Computer Vision Politeknik Elektronika Negeri Surabaya PENS-ITS

Gaussian Low Pass Filters D(u, v): distance from the origin of Fourier transform Laboratorium Computer Vision Politeknik 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. Laboratorium DFT (5, Computer 15, 30, Vision 80, 230) 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. Laboratorium Computer Vision Politeknik Elektronika Negeri Surabaya PENS-ITS

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

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

High Pass Filters • Ideal high pass filter • Butterworth high pass filter • Gaussian high pass filter Laboratorium Computer Vision Politeknik 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 Vision Politeknik Elektronika Negeri Surabaya PENS-ITS

Laplacian HPF • • 3 D plots of the Laplacian operator, its 2 D images, spatial domain response with center magnified, and Compared to the FIR mask approximation Laboratorium Computer Vision Politeknik Elektronika Negeri Surabaya PENS-ITS

Sekila. S Inf. O Ada beberapa hal yang harus dikuasai sebelum menguasai materi di dalam image processing yaitu: matematika, aljabar, pengolahan sinyal, statistik dan pemrograman.

Berga. Bunglah den. Gan Kami Laboratorium Computer Vision Politeknik Elektronika Negeri Surabaya PENS-ITS 2009