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39Contents

Once segmentation is complete,morphological operations can be used to

remove imperfections in the segmented

image and provide information on the formand structure of the image

In this lecture we will consider

What is morphology? Simple morphological operations

Compound operations

Morphological algorithms

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391, 0, Black, White?

Throughout all of the following slideswhether 0 and 1 refer to white or black is a

little interchangeable

All of the discussion that follows assumessegmentation has already taken place and

that images are made up of 0s for

background pixels and 1s for object pixelsAfter this it doesnt matter if 0 is black, white,

yellow, green.

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39Quick Example

Image after segmentation Image after segmentation and

morphological processing

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39Structuring Elements, Hits & Fits

B

A

C

Structuring Element

Fit:All on pixelsin the

structuring element coveron pixelsin the image

Hit:Any on pixelin the

structuring element coversan on pixelin the image

All morphological processing operations are based

on these simple ideas

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39Structuring Elements

Structuring elements can be any size andmake any shape

However, for simplicity we will use

rectangular structuring elements with theirorigin at the middle pixel

1 1 11 1 1

1 1 1

0 0 1 0 0

0 1 1 1 0

1 1 1 1 1

0 1 1 1 0

0 0 1 0 0

0 1 01 1 1

0 1 0

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39Fitting & Hitting

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0 0 0

0 0 1 1 1 1 1 0 0 0 0 0

0 1 1 1 1 1 1 1 0 0 0 0

0 1 1 1 1 1 1 1 0 0 0 0

0 0 1 1 1 1 1 1 0 0 0 0

0 0 1 1 1 1 1 1 1 0 0 00 0 1 1 1 1 1 1 1 1 1 0

0 0 0 0 0 1 1 1 1 1 1 0

0 0 0 0 0 0 0 0 0 0 0 0

B C

A

1 1 1

1 1 1

1 1 1

Structuring

Element 1

0 1 0

1 1 1

0 1 0

Structuring

Element 2

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39Fundamental Operations

Fundamentally morphological imageprocessing is very like spatial filtering

The structuring element is moved across

every pixel in the original image to give apixel in a new processed image

The value of this new pixel depends on the

operation performedThere are two basic morphological

operations: erosion and dilation

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39Erosion

Erosion of imagefby structuring elementsis given byf s

The structuring element s is positioned with

its origin at (x, y)and the new pixel value isdetermined using the rule:

otherwise0

fitsif1

),(

fs

yxg

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39Erosion Example

Structuring Element

Original Image Processed Image With Eroded Pixels

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39Erosion Example

Structuring Element

Original Image Processed Image

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39Erosion Example 2

Original

image

After erosion

with a disc of

radius 10

After erosionwith a disc of

radius 20

After erosion

with a disc of

radius 5

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39What Is Erosion For?

Erosion can split apart joined objects

Erosion can strip away extrusions

Watch out:Erosion shrinks objects

Erosion can split apart

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39Dilation

Dilation of imagefby structuring elementsisgiven byf s

The structuring element s is positioned with

its origin at (x, y)and the new pixel value isdetermined using the rule:

otherwise0

hitsif1

),(

fs

yxg

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39Dilation Example

Structuring Element


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39Dilation Example

Structuring Element

Original Image Processed Image With Dilated Pixels

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39Dilation Example 1

Original image Dilation by 3*3

square structuring

element

Dilation by 5*5

square structuring

element

Watch out:In these examples a 1 refers to a black pixel!

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39Dilation Example 2

Structuring element

Original image After dilation

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39What Is Dilation For?

Dilation can repair breaks

Dilation can repair intrusions

Watch out:Dilation enlarges objects

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39Compound Operations

More interesting morphological operationscan be performed by performing

combinations of erosions and dilations

The most widely used of these compoundoperationsare:

Opening

Closing

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39Opening

The opening of imagefby structuringelements,denotedf sis simply an erosion

followed by a dilation

f s = (f s) s

Original shape After erosion After dilation

(opening)

Note a disc shaped structuring element is used

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39Opening Example

Original

Image

Image

After

Opening

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39Opening Example

Structuring Element


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39Opening Example

Structuring Element


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39Closing Example

Original

Image

Image

After

Closing

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39Closing Example

Structuring Element


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39Closing Example

Structuring Element


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39Morphological Processing Example

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39Morphological Algorithms

Using the simple technique we have lookedat so far we can begin to consider some

more interesting morphological algorithms

We will look at: Boundary extraction

Region filling

There are lots of others as well though: Extraction of connected components

Thinning/thickening

Skeletonisation

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39Boundary Extraction

Extracting the boundary (or outline) of anobject is often extremely useful

The boundary can be given simply as

(A) = A (AB)

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39Boundary Extraction Example

A simple image and the result of performingboundary extraction using a square 3*3

structuring element

Original Image Extracted Boundary

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39Region Filling

Given a pixel inside a boundary, regionfillingattempts to fill that boundary with

object pixels (1s)

Given a point inside

here, can we fill thewhole circle?

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39Region Filling (cont)

The key equation for region filling is

Where X0is simply the starting point inside

the boundary, B is a simple structuring

element and Acis the complement of A

This equation is applied repeatedly until Xk

is equal to Xk-1

Finally the result is unioned with the original

boundary

.....3,2,1)( 1 kABXX c

kk

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39Region Filling Step By Step

Im

agestakenfromGonza

lez&Woods,

DigitalImageProcessing(2002)

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39Region Filling Example

Original Image One RegionFilled

All RegionsFilled

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Extraction of connected components

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Example

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39 Convex hull

A setAis

said to be

convex if thestraight line

segment

joining any

two points in

A lies

entirely

within A.

i

i DAC

4

1)(

,...3,2,1and4,3,2,1)( kiABXX ii

k

i

k

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Thinning

cBAA

BAABA

)(

)(

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Thickening

)( BAABA

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SkeletonsK

kk ASAS0

)()(

BkBAkBAASk )()()( })(|max{ kBAkK

))((0

kBASA k

K

k

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5 basic structuring elements

53

S

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39Summary

The purpose of morphological processing isprimarily to remove imperfections added during

segmentation

The basic operations are erosionand dilationUsing the basic operations we can perform

openingand closing

More advanced morphological operation canthen be implemented using combinations of all

of these

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S i El Hi & Fi

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39Structuring Elements, Hits & Fits

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HIT! F

IT!

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E i E l

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39Erosion Example

Structuring Element

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Dil ti E l

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39Dilation Example

Structuring Element

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O i E l

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39Opening Example

Structuring Element


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Cl i E l

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39Closing Example

Structuring Element


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R i Filli St B St

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39Region Filling Step By Step

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