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EECE253_17_BinaryMorphology

EECE253_17_BinaryMorphology - 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 2007 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.
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27 April 2008 2 1999-2007 by Richard Alan Peters II What is Mathematical Morphology? O nonlinear, O built on Minkowski set theory, O part of the theory of finite lattices, O for image analysis based on shape, O extremely useful, yet not often used. It is:
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27 April 2008 3 1999-2007 by Richard Alan Peters II Uses of Mathematical Morphology O image enhancement O image segmentation O image restoration O edge detection O texture analysis O particle analysis O feature generation O skeletonization O shape analysis O image compression O component analysis O curve filling O general thinning O feature detection O noise reduction O space-time filtering
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27 April 2008 4 1999-2007 by Richard Alan Peters II Notation and Image Definitions 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 } = { 255, 0 }, although the fg is often displayed in different colors for contrast.
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27 April 2008 5 1999-2007 by Richard Alan Peters II Notation and Image Definitions The foreground of binary image I is i.e. the set of locations, p , where I( p ) = v fg . Similarly, the background is { } ( ) ( ) { } P fg FG I I , , I( ) , r c S v = = = p p p { } ( ) ( ) { } P bg BG I I , , I( ) . r c S v == = = p p p Note that { } { } I I BG I FG = { } { } = I BG I FG and ∅, and that { } { } { } C I FG I BG = and { } { } { } . I BG I FG C = The background is the complement of the foreground and vice-versa.
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27 April 2008 6 1999-2007 by Richard Alan Peters II A Binary Image This represents a digital image. Each square is one pixel. foreground: R = c c where ) ( I p 0 ) I( = p background
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27 April 2008 7 1999-2007 by Richard Alan Peters II Support of an Image ( ) { } P f supp I ( , ) I( ) . g r c S v = = = p p That is, the support of a binary image is the set of foreground pixel locations within the image plane. The complement of the support is, therefore, the set of background pixel locations within the image plane. The support of a binary image, I, is ( ) { } { } C P b supp I ( , ) I( ) . g r c S v = = = p p
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27 April 2008 8 1999-2007 by Richard Alan Peters II Structuring Element (SE) A structuring element is a small image – used as a moving window – whose support delineates pixel neighborhoods in the image plane.
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