{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

EECE253_17_BinaryMorphology

# EECE253_17_BinaryMorphology - EECE\CS 253 Image Processing...

This preview shows pages 1–9. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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:
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern