MKM_501E_Sunum_6inciHafta_2D_FT

# MKM_501E_Sunum_6inciHafta_2D_FT - The Fourier Transform...

This preview shows pages 1–8. Sign up to view the full content.

The Fourier Transform Jean Baptiste Joseph Fourier

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
0 50 100 150 200 250 0 500 1000 1500 2000 2500 0 0 3000 3500 Original histogram Image Operations in Different Domains 1) 2) 3) Frequency (Fourier) domain - Histogram stretching, equalization, specification, etc. .. - Average filter, median filter, gradient, laplacian, etc… Original image Gradient magnitude 2 2 y x f f f + = f Blurry Image Laplacian + = Sharpened Image Noisy image (Salt & Pepper noise) 3 X 3 Average 5 X 5 Average 7 X 7 Average Median
= 3 sin(x) A + 1 sin(3x) B A+B + 0.8 sin(5x) C A+B+C + 0.4 sin(7x) D A+B+C+D A sum of sines and cosines sin(x) A

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Higher frequencies due to sharp image variations (e.g., edges, noise, etc.)
The Continuous Fourier Transform = -∞ = + u iux du x f π 2 F(u)e ) ( ) 2 sin( ) 2 cos 2 ux i ux ( iux + = e

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Complex Numbers Real Imaginary Z=(a,b) a b | Z θ ) (conjugate (phase) spectrum) (Fourier vector) unit (a θ i i e Z ib a Z Z a b tg b a Z i e i i - - = - = = = + = + = - = - = * 1 2 2 2 ) / ( sin cos ) 1 ( 1 i e Z ib a Z i Z Z = + = + = ) Im( ) Re(
x ( 29 ux π 2 cos The wavelength is 1/u .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 12/04/2011 for the course TRADE 1056596 taught by Professor Ayladinç during the Spring '11 term at Istanbul Bilgi University.

### Page1 / 23

MKM_501E_Sunum_6inciHafta_2D_FT - The Fourier Transform...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online