dip chapter 3- mathematical morphology- binary

7/29/2019 DIP Chapter 3- Mathematical Morphology- Binary

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Chapter 3 :Mathematical morphologyPart 1 : binary morphology

Dr. Hojeij youssef

Digital image processing

1

Binary imageBasicDilationErosionOpenCloseNeighbor transform Thin and thickGeodesic reconstruction

Morphology in gray level

Outline

Dr. Hojeij youssef 2



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Binary images have 1 bit per pixel :1 =object pixel0 = non-object pixel (background pixel)

Binary images


Data

Image

Object =real world thing

Component =blob of connectedpixels

Objectsaredescribedbyacollectionof points,whicharedenotedbyvectors.

A set A in a binary image consists of the points α that sharea commonproperty(value)

Thebackgroundof A is given by thecomplement,

Binary images


1)( A \ A

CAˆ A \ Ac

c A



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Definition : aregion isaset of pixels, whereeachpixel canbereached fromany other pixel in theregion by a finitenumber of steps, whereeach stepstartsatapixel andendsintheneighborhoodof thepixel.

Twobasicneighborhoods(connectivity)onasquaregrid,denotedby:

N 4

N 8

The paradox of the square


Symmetric around

the origin.

The fundamental operations are :

Complement:

Union:

Intersection:

Translation:

Fundamental operations


Set algebra :ComplementUnion Intersection…

Boolean algebra :NotOrAndXor



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Dilation


Dilation of set A by structuring element B :

g(x,y)=Or[W{ f(x,y)} ]= dilate(f,W)

Dilation


Binary dilation effects : Expands the size of 1-valued objects Smoothes object boundaries Closes holes and gapes

Original imageDilatation with

3×3 structuringelement

Dilatation with

7×7 structuringelement



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Erosion


Erosion of setA by structuring element B :

g(x,y)=And[W { f(x,y)} ]= erode(f,W )

Erosion


Erosion effects: Shrinks the size of 1-valued objects Smoothes object boundaries Remove peninsulas, and small objects

Originalimage

Erosion by

11×11structuringelement

Erosion by


Erosion by




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Properties


Erosion is dilation of the background

Erosion is not the inverse of dilation

Commutative :

Non-commutative :

Associative:

Translation invariance :

Properties


Dilation: distributive over the union

Erosion: distributive over the intersection

Multiple dilations:



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Opening and Closing


Openingconsists of a number of erosions followed by the samenumber of dilations :Applications :

Separationof connectedobjectsRemoving small objects (sizediscrimination)

Closingconsists of a number of dilations followed by the samenumber of erosions :Applications :

Connection of disconnected object partsClosingof holesContour smoothing

Rem: close-open and open closeareduals, but not inverses of each other

Majority filter


Binary majority filter is aspecial case of a gray level median filter :g(x,y)=Maj[W{ f(x,y)} ]= majority(f,W)

Effects : Does not generally shrink or expand objects Smoothes object boundaries Removes small peninsulas, bays, small objects, and small holes Less biased than close-open or open close

Binary imagewith 5%«salt&pepper » noise

Binary imagewith 20%«salt&pepper » noise

3×3 majority filter 3×3 majority filter



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Morphological edge detection


Inner boundary extraction :

Outer boundary extraction :) N A( A) A( IB

) N A( A) A(OBc

Neighbor transform


Neighbor transform: if v is the element :

Thin an thick :

Skeleton :

otherwise0

vv / vvsi1) x(v X

1 x

i

)v X ( X v X

)v X ( X v X

dip chapter 3- mathematical morphology- binary

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