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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 AttributionNoncommercial 2.5 License. To view a copy of this license, visit http://creativecommons.org/licenses/bync/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 19992007 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 19992007 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 ● spacetime filtering December 6, 2011 4 December 6, 2011 4 19992007 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 19992007 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 viceversa. December 6, 2011 6 December 6, 2011 6 19992007 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 19992007 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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 Summer '07
 AlanPeters
 Electrical Engineering, Image processing, Mathematical morphology, Richard Alan Peters

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