Digital Image Analysis and ProcessingCPE 0907544CPE 0907544

Morphological Image Processing

Chapter 9Sections : 9 1 – 9 5

D I d J f

Sections : 9.1 – 9.5

Dr. Iyad Jafar

Outline

Introduction

Erosion and Dilation

Opening and Closing

B d EBoundary Extraction

Hole FillingHole Filling

Hit-or-Miss Transformation

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IntroductionMorphology as word describes a branch of biologythat deals with animal and plant structurethat deals with animal and plant structure

In the context of image processing , it refers to aIn the context of image processing , it refers to aset of mathematical tools that can be used to

extract useful description and representation of regionsextract useful description and representation of regionsin images (boundaries, skeletons, convex hull)remove imperfections introduced during segmentationp g g(thinning, regions filling)

Morphological operators can be formulated in anyn-dimensional Euclidean space (binary, gray scale,color)

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Introduction

Image after segmentation Image after segmentation g g g gand morphological

processing

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IntroductionA binary image can be considered as a setb id i “bl k” i l ( ith iby considering “black” pixels (with imagevalue “0”) as elements in the set and “white”pixels (with value “1”) as outside the set, orvice versa.

Morphological filters are essentially set operationsMorphological filters are essentially set operations5

Basic Set OperationsLet x, y, z, … represent locations of 2D pixels, e.g. x= (x1, x2), S denotes the complete set of all pixels inan image, let A, B, … represent subsets of SUnion (OR)( )

Intersection (AND)

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Basic Set OperationsComplement

Translation

ReflectionReflection

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Structuring ElementsAll morphological operations are based on usingstructuring elements (similar to filter masks)

1 1 1

1 1 1

0 1 0

1 1 1

M h l i l i b d i h

1 1 1

1 1 1

1 1 1

0 1 0

Morphological operations are based moving thestructuring element over the image pixels to check for aHIT or FITHIT or FIT

FIT - all ON pixels in the structuring element cover ONpixels in the imagepixels in the image

HIT - any ON pixel in the structuring element covers anON pixel in the imageON pixel in the image

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Structuring Elements

B

Structuring Element

AA Fit AC

A – Fit B – Hit C MiC – Miss

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Structuring ElementsStructuring elements can be of any size and shapeRectangular shapes are usually used with the origin beingat the center pixel

0 0 1 0 01 1 1

1 1 1

1 1 1

0 1 0

1 1 1

0 1 0

0 1 1 1 0

1 1 1 1 1

0 1 1 1 0

Fundamentally morphological image processing is very like

0 0 1 0 0

Fundamentally morphological image processing is very likespatial filteringThe structuring element is moved across every pixel in theg y poriginal image to give a pixel in a new processed imageThe value of this new pixel depends on the operationperformed

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Structuring Elements0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0 0 0 1 1 10 0 1 1 1 1 1 0 0 0 0 0

0 1 1 1 1 1 1 1 0 0 0 0B

C

1 1 1

1 1 1

1 1 1

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

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

Structuring Element 1

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

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

0 0 0 0 0 1 1 1 1 1 1 0A

0 1 01 1 10 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 0Structuring Element 2

Location Structuring Element 1 Structuring Element 2

A FIT FIT

B HIT FIT

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B HIT FIT

C HIT HIT

ErosionErosion of image A by structuringl t B i i b A B h th telement B is given by A B such that

A B =f

{ | ( ) }zz B AA BThe structuring element B is

{ | ( ) }z

positioned with its origin at (x, y) andthe new pixel value is determined usingthe new pixel value is determined usingthe rule:

1 , if fits ( , )

0 other iseB A

g x y ⎧⎨⎩

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0 , otherwise⎩

ErosionExample 9.1Original Image Processed Image

* ** **

* Keep pixels at which the structuring element scores a FIT

Removed Pixels

Structuring Element

structuring element scores a FIT* Erosion shrinks objects Kept Pixels

ErosionExample 9.2

Original image Erosion by 3*3 square structuring

Erosion by 5*5 square structuring

element element

W h I h l 1 f bl k l!Watch out: In these examples a 1 refers to a black pixel!

ErosionExample 9.3

After erosionOriginal image

After erosion with a disc of radius 10

After erosion with a disc of

After erosion with a disc of

radius 20radius 5

What Is Erosion For?

Erosion can split apart joined objects

Erosion can strip away extrusionsp y

DilationDilation of image A by structuringl t B i i b A B h th telement B is given by A B such that

A B =^

{ | ( ) }zz B AA BThe structuring element B is

{ | ( ) }z

positioned with its origin at (x, y) andthe new pixel value is determined usingthe new pixel value is determined usingthe rule:

1 if hiB A⎧ 1 , if hits ( , )

0 otherwiseB A

g x y ⎧⎨⎩

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0 , otherwise⎩

DilationExample 9.4Original Image Processed Image

* Keep pixels at which the structuring element hits at least

Pixels added to object

Structuring Element

one ON pixel * Dilation enlarges objects

Kept Pixels

DilationExample 9.5

Original image Dilation by 3*3 Dilation by 5*5Original image ysquare structuring

element

Dilation by 5 5 square structuring

element

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

DilationE l 9 6

Original image After dilation

Example 9.6

Structuring element

What Is Dilation For?Dilation can repair breaks

Dilation can repair intrusionsDilation can repair intrusions

OpeningThe opening operation on image A byt t i l t B i d fi dstructuring element B is defined as

A o B = (A B) BA o B (A B) Bin other words, it is erosion followedby dilationGenerally opening is used toGenerally, opening is used toSmooth the contour of an object (inner

)contour)Break narrow paths between large objectsEliminate thin protrusions

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OpeningExample 9.7

0 0 1 0 0

0 1 1 1 0

1 1 1 1 11 1 1 1 1

0 1 1 1 0

0 0 1 0 0

Original shapeAfter erosion

Structuring Element

Aft dil ti23

After dilation(opening)

ClosingThe closing operation on image A bystructuring element B is defined asstructuring element B is defined as

A • B = (A B) Bin other words, it is dilation followed byerosionerosionGenerally, closing is used toS h h f bj (Smooth the contour of an object (outercontour)Fuse narrow paths between large objectsEliminate thin small holes and fill gaps in thecontour

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ClosingExample 9.8

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

Original shapeAfter dilation

Structuring Element

Aft i25

After erosion(Closing)

Example 9.9White noise regions removedBlack regions within theBlack regions within the fingerprint have enlarged

Black regions within the fingerprint shrunken But gaps are introducedintroduced between ridges

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Boundary ExtractionThe boundary of set A denoted by (A) can beobtained by first eroding A by a suitabley g ystructuring element B then perform the setdifference between A and its erosionff

Erosion

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Boundary ExtractionExample 9.10

Boundary Extraction

Original binary image Boundary detected based on morphological operatorsmorphological operators

28 Structuring element

Hole FillingfA hole may be defined as a background region surrounded

by a connected border of foreground pixels

The algorithm presented here assumes that we know onepixel for each hole in the image

Algorithm

Form an array X0 of the same size as A and initialize it withzeros except locations that correspond to pixels inside theregions to be filled

Apply the following equation iteratively on array X until Xk =Xk-1 to form the filled holes

( ) cX X B AThe original image with filled holes is found by

1( )k kX X B A

A X A29

filled kA X A

Hole FillingExample 9.11

Original, Complement, and Structuring Element

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Hole FillingExample 9.12

Original One hole filled All holes filled

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Hit-or-Miss TransformationA basic tool for shape detectionSuppose we have an image A that consists of three objectspp g jC, D, and E and we want to detect the presence of shapeD; assuming we know its shape

Object E50x50

Object C200x100

Obj t DObject D80x80

32Image A

Hit-or-Miss TransformationWe can start by eroding A with a structuring element thathas the same shape as Dhas the same shape as D

One pixel that represents the

center of object D

Structuring element

D

Erosion

objectD

Image A

However, the result may contain parts of larger objects

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Hit-or-Miss TransformationConsider the complement of A and a new structuringelement that is one pixel thicker than the objectelement that is one pixel thicker than the object

One pixel that represents the center

Structuring element 82x82

Erosionp

of object D

W-D

Complement of A

Note how the center of object D was detected again !

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Hit-or-Miss TransformationConsider the intersection of the erosion results from theprevious two slidesprevious two slides

Intersection

Object is s ccessf ll l cated !Object is successfully located !Formally, the hit-or-miss transformation on image A todetect some object X is performed bydetect some object X, is performed by

where W is a the object X thickened by one pixel35

Related Matlab Functionsimerode

imdilate

imopen

I lImclose

strelstrel

bwmorphp

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