EECE253_07_Convolution

# EECE253_07_Convolution - EECE\CS 253 Image Processing...

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EECE\CS 253 Image Processing Richard Alan Peters II Department of Electrical Engineering and Computer Science Fall Semester 2011 Lecture Notes Lecture Notes: Spatial Convolution 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.

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12/06/11 2 1999-2011 by Richard Alan Peters II Spatial Filtering ( ) [ ]( ) ( ) { } { } { } ( ) , T , , ,..., ,. .. , ,..., ,. .. . r c r c f r s r r s c d c c d r c r c = = - + - + Î Î J I I That is, the value of the transformed image, J , at pixel location ( r,c ) is a function of the values of the original image, I , in a 2 s +1 × 2 d +1 rectangular neighborhood centered on pixel location ( r,c ). Let I and J be images such that J = T [ I ]. T [·] represents a transformation, such that,
12/06/11 3 1999-2011 by Richard Alan Peters II Moving Windows The value, J ( r,c ) = T[ I ]( r,c ), is a function of a rectangular neighborhood centered on pixel location ( r,c ) in I . There is a different neighborhood for each pixel location, but if the dimensions of the neighbor- hood are the same for each location, then trans- form T is sometimes called a moving window transform .

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12/06/11 4 1999-2011 by Richard Alan Peters II Moving-Window Transformations Neutral  Buoyancy  Facility at  NASA  Johnson  Space Center Neutral  Buoyancy  Facility at  NASA  Johnson  Space Center We’ll take a  section of this  image to  demonstrate the  MWT We’ll take a  section of this  image to  demonstrate the  MWT photo: R.A.Peters II, 1999
12/06/11 5 1999-2011 by Richard Alan Peters II Moving-Window Transformations operate on this region operate on this region

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12/06/11 6 1999-2011 by Richard Alan Peters II Moving-Window Transformations apply a pixel grid apply a pixel grid Pixelize the section to better see  the effects.  Pixelize the section to better see  the effects.
12/06/11 7 1999-2011 by Richard Alan Peters II Moving-Window Transformations sample (average in the  squares). sample (average in the  squares). Pixelize the section to better see  the effects.  Pixelize the section to better see  the effects.

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12/06/11 8 1999-2011 by Richard Alan Peters II Moving-Window Transformations lets get some  perspective on  this lets get some  perspective on  this
12/06/11 9 1999-2011 by Richard Alan Peters II Moving-Window Transformations a neighborhood defined by a  weight matrix a neighborhood defined by a  weight matrix

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12/06/11 10 1999-2011 by Richard Alan Peters II Moving-Window Transformations neighborhoods at other pixel locations neighborhoods at other pixel locations
12/06/11 11 1999-2011 by Richard Alan Peters II Linear Moving-Window Transformations ( i.e. convolution) The output of the transform at

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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_07_Convolution - EECE\CS 253 Image Processing...

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