EECE253_11_SamplingAliasing

EECE253_11_SamplingAliasing - EECE\CS 253 Image Processing...

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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: Sampling and Aliasing Richard Alan Peters II Department of Electrical Engineering and Computer Science Fall Semester 2007 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. Tuesday, December 6, 2011 2 Tuesday, December 6, 2011 2 1999-2007 by Richard Alan Peters Image Resampling Can Lead to the Jaggies ! zo o m e d 2 zo o m e d 2 The jaggies! Warning: Tuesday, December 6, 2011 3 Tuesday, December 6, 2011 3 1999-2007 by Richard Alan Peters >> J = I(1:2:R,1:2:C,:); >> J = I(1:2:R,1:2:C,:); Downsampling (Decimation) E.g.: every 2 nd pixel in every 2 nd row This is a bad way to do it. Tuesday, December 6, 2011 4 Tuesday, December 6, 2011 4 1999-2007 by Richard Alan Peters >> J = I(1:2:R,1:2:C,:); >> J = I(1:2:R,1:2:C,:); Downsampling (Decimation) E.g.: every 2 nd pixel in every 2 nd row Bad, bad, very bad. Tuesday, December 6, 2011 5 Tuesday, December 6, 2011 5 1999-2007 by Richard Alan Peters Power Spectrum from Discrete Fourier Transform Recall: DFT Tuesday, December 6, 2011 6 Tuesday, December 6, 2011 6 1999-2007 by Richard Alan Peters Power Spectrum from Discrete Fourier Transform The DFT of an image is the same size as the image. DFT decimated image power spectrum Recall: Tuesday, December 6, 2011 7 Tuesday, December 6, 2011 7 1999-2007 by Richard Alan Peters The Scaling Property of the FT { } ( 29 ( 29 { } ( 29 2 ( ) If , I , , then I , , . I I i uc vr v u r c e dcdr r c ab av bu a b - +- - = F F This im plie s tha t if a n im a g e is re duc e d in s ize , its fe a ture s in the s pa tia l do m a in b e c o m e s m a lle r a nd its fe a ture s in the fre q ue nc y do m a in b e c o m e la rg e r. This im plie s tha t if a n im a g e is re duc e d in s ize , its fe a ture s in the s pa tia l do m a in b e c o m e s m a lle r a nd its fe a ture s in the fre q ue nc y do m a in b e c o m e la rg e r. Recall: Tuesday, December 6, 2011 8 Tuesday, December 6, 2011 8 1999-2007 by Richard Alan Peters The Uncertainty Relation FT FT space frequency FT FT space frequency A s m a ll o b je c t in s pa c e ha s a la rg e fre q ue nc y e xte nt a nd vic e -ve rs a . A s m a ll o b je c t in s pa c e ha s a la rg e fre q ue nc y e xte nt a nd vic e -ve rs a ....
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This note was uploaded on 12/06/2011 for the course EECE 253 taught by Professor Alanpeters during the Summer '07 term at Vanderbilt.

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EECE253_11_SamplingAliasing - EECE\CS 253 Image Processing...

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