EECE253_17_BinaryMorphology

EECE253_17_BinaryMorphology - 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 on Mathematical Morphology: Binary Images 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. December 6, 2011 2 December 6, 2011 2 1999-2007 by Richard Alan Peters What is Mathematical Morphology? nonlinear, built on Minkowski set theory, part of the theory of finite lattices, for image analysis based on shape, extremely useful, yet not often used. It is: December 6, 2011 3 December 6, 2011 3 1999-2007 by Richard Alan Peters Uses of Mathematical Morphology image enhancement image segmentation image restoration edge detection texture analysis particle analysis feature generation skeletonization shape analysis image compression component analysis curve filling general thinning feature detection noise reduction space-time filtering December 6, 2011 4 December 6, 2011 4 1999-2007 by Richard Alan Peters Notation and Image Def initions An image is a mapping, I, from a set, S P , of pixel coordinates to a set, G , of values such that for every coordinate vector, p = ( r , c ) in S P , there is a value I( p ) drawn from G . S P is also called the image plane . A binary image has only 2 values. That is, G = { v fg , v bg }, where v fg , is called the foreground value and v bg is called the background value. Often, the foreground value is v fg = 0, and the background is v bg = . Other possibilities are { v fg , v bg } = {0, }, {0,1}, {1,0}, {0,255}, and {255,0}. In this lecture we assume that { v fg , v bg } = { 2 5 5 , 0 }, although the fg is often displayed in different colors for contrast. December 6, 2011 5 December 6, 2011 5 1999-2007 by Richard Alan Peters Notation and Image Def initions The foreground of binary image I is i.e. the set of locations, p , where I( p ) = v fg . Similarly, the background is Note that and , and that and The background is the complement of the foreground and vice-versa. December 6, 2011 6 December 6, 2011 6 1999-2007 by Richard Alan Peters A Binary Image This represents a digital image. Each square is one pixel. foreground: R = c c where ) ( I p ) I( = p background December 6, 2011 7 December 6, 2011 7 1999-2007 by Richard Alan Peters Support of an Image That is, the support of a binary image is the set of foreground pixel locations within the image plane....
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EECE253_17_BinaryMorphology - EECE\CS 253 Image Processing...

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