EECE253_08_FrequencyFiltering

EECE253_08_Frequency - EECE\CS 253 Image Processing Richard Alan Peters II Department of Electrical Engineering and Computer Science Fall Semester

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: EECE\CS 253 Image Processing Richard Alan Peters II Department of Electrical Engineering and Computer Science Fall Semester 2007 Lecture Notes Lecture Notes: Frequency Filtering This work is licensed under the Creative Commons Attribution-Noncommercial 2.5 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/2.5/ or send a letter to Creative Commons, 543 Howard Street, 5th Floor, San Francisco, California, 94105, USA. 27 April 2008 2 27 April 2008 2 1999-2007 by Richard Alan Peters II Convolution Property of the Fourier Transform . } { Moreover, . } { Then, ). , ( and ) , ( Transforms Fourier have ) , ( and ) , ( functions Let G F g f G F g f v u G v u F c r g c r f ∗ = ⋅ ⋅ = ∗ F F The Fourier Transform of a convolution equals the product of the Fourier Transforms. Similarly, the Fourier Transform of a convolution is the product of the Fourier Transforms The Fourier Transform of a convolution equals the product of the Fourier Transforms. Similarly, the Fourier Transform of a convolution is the product of the Fourier Transforms * = convolution · = multiplication 27 April 2008 3 27 April 2008 3 1999-2007 by Richard Alan Peters II Convolution via Fourier Transform Image & Mask Transforms Pixel-wise Product Inverse Transform 27 April 2008 4 27 April 2008 4 1999-2007 by Richard Alan Peters II 1. Read the image from a file into a variable, say I . 2. Read in or create the convolution mask, h . 3. Compute the sum of the mask: s = sum(sum(h)); 4. If s == 0, set s = 1; 5. Create: H = zeros(size(I)) ; 6. Copy h into the middle of H . 7. Shift H into position: H = ifftshift(H); 8. Take the 2D FT of I and H : FI=fft2(I); FH=fft2(H); 9. Pointwise multiply the FTs: FJ=FI.*FH; 10. Compute the inverse FT: J = real(ifft2(FJ)); 11. Normalize the result: J = J/s; How to Convolve via FT in Matlab For color images you may need to do each step for each band separately. For color images you may need to do each step for each band separately. The mask is usually 1-band The mask is usually 1-band 27 April 2008 5 27 April 2008 5 1999-2007 by Richard Alan Peters II Coordinate Origin of the FFT Center = (floor( R /2)+1, floor( C /2)+1) Center = (floor( R /2)+1, floor( C /2)+1) Even Even Odd Odd Image Origin Weight Matrix Origin Image Origin Weight Matrix Origin After FFT shift After IFFT shift After FFT shift After IFFT shift 27 April 2008 6 27 April 2008 6 1999-2007 by Richard Alan Peters II 7 9 8 1 3 2 4 6 5 3 2 1 9 8 7 6 5 4 Matlab’s fftshift and ifftshift J = fftshift(I): I ( 1 , 1 ) → J ( ⎣ R /2 ⎦ + 1 , ⎣ C /2 ⎦ + 1 ) I = ifftshift(J): J ( ⎣ R /2 ⎦ + 1 , ⎣ C /2 ⎦ + 1 ) → I ( 1 , 1 ) where ⎣ x ⎦ = floor(x) = the largest integer smaller than x ....
View Full Document

This note was uploaded on 12/06/2011 for the course EECE 253 taught by Professor Alanpeters during the Summer '07 term at Vanderbilt.

Page1 / 46

EECE253_08_Frequency - EECE\CS 253 Image Processing Richard Alan Peters II Department of Electrical Engineering and Computer Science Fall Semester

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online