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 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

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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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

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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.

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BergaBunglah denGan Kami

Laboratorium Computer VisionPoliteknik Elektronika Negeri Surabaya

PENS-ITS 2009