Chapter 9: Morphological Image Processingit.nrru.ac.th/krit/411304/Chapter09.pdfExample: Application...

Digital Image ProcessingChapter 9:

Digital Image ProcessingChapter 9:Chapter 9:

Morphological Image ProcessingChapter 9:

Morphological Image ProcessingMorphological Image ProcessingMorphological Image Processing

What are Morphological Operations? What are Morphological Operations?

Morphological operations come from the word “morphing”in Biology which means “changing a shape”.

MorphingMorphing

Image morphological operations are used to manipulateImage morphological operations are used to manipulateobject shapes such as thinning, thickening, and filling.

Binary morphological operations are derived fromset operationsset operations.

Basic Set Operations Basic Set Operations

C f i bi i h lConcept of a set in binary image morphology:Each set may represent one object. Each pixel (x,y) has

i b l b lits status: belong to a set or not belong to a set.

(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

Translation and Reflection Operations Translation and Reflection Operations Translation ReflectionTranslation Reflection

BbbwwB for ,ˆ AazaccA z for ,

AB

A

z = (z1,z2)

(A) B̂(A)z B

Logical Operations* Logical Operations*

*F bi i l(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

*For binary images only

Dilation Operations Dilation Operations

ˆ ABzBA z

= Empty setDilate means “extend”

A = Object to be dilatedB St t i l tB = Structuring element


Dilation Operations (cont.) Dilation Operations (cont.)

ˆR fl ti BReflection

StructuringStructuringElement (B)

Original image (A) Intersect pixel Center pixel

Dilation Operations (cont.) Dilation Operations (cont.)

Result of Dilation Boundary of the “center pixels” where intersects A zB̂

Example: Application of DilationExample: Application of Dilation

“Repair” broken characters(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

Repair broken characters

Erosion Operation Erosion Operation

AA ABzBA z

Erosion means “trim”

A = Object to be erodedi lB = Structuring element


Erosion Operations (cont.) Erosion Operations (cont.)

StructuringElement (B)Element (B)

Original image (A) Intersect pixel Center pixel

Erosion Operations (cont.) Erosion Operations (cont.)

Result of ErosionB d f th “ t i l ”Boundary of the “center pixels”where B is inside A

Example: Application of Dilation and ErosionExample: Application of Dilation and Erosion

Remove small objects such as noiseRemove small objects such as noise


Duality Between Dilation and ErosionDuality Between Dilation and Erosion

BABA cc ˆ) (

Proof:where c = complement

Proof:

ABzBA cc)( ABz

ABzBAcc

z) (

ABz

ABzc

z

z

BAc ˆ

Opening Operation Opening Operation

BBABA )( BBABA ) (

ABBBAor

ABBBA zz

= Combination of all parts of A that can completely contain B p p y


Opening eliminates narrow and small details and corners.

Example of Opening Example of Opening

(Images from Rafael C.Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

Closing Operation Closing Operation

BBBA )A( BBBA )A(

Closing fills narrow gaps and notchesClosing fills narrow gaps and notches


Example of Closing Example of Closing


Duality Between Opening and ClosingDuality Between Opening and Closing

ˆ BABA cc ˆ

Properties OpeningProperties OpeningABA 1

BDBCDC

ABA

then If 2. .1

BABBA .3Properties ClosingProperties Closing

BAA .1Properties ClosingProperties Closing

BABBABDBCDC

3 then If 2.

BABBA .3

Idem potent property: can’t change any more

Example: Application of Morphological OperationsExample: Application of Morphological Operations

Finger print enhancement


HitHit--oror--Miss Transformation Miss Transformation

)( XWAXAXA c )( XWAXAXA c *

h X h b d dwhere X = shape to be detectedW = window that can contain X


HitHit--oror--Miss Transformation (cont.) Miss Transformation (cont.)

)( XWABABA c )( XWABABA c *


Boundary Extraction Boundary Extraction

BAAβ(A) BAAβ(A)

Original B dOriginal image

Boundary


Region Filling Region Filling

cABXX kk ABXX 1

h X d i lwhere X0 = seed pixel p

Original Results of region fillingOriginal image

Results of region filling


Extraction of Connected Components Extraction of Connected Components

ABXX kk 1 where X0 = seed pixel p


Example: Extraction of Connected Components Example: Extraction of Connected Components

X-ray imagef bof bones

ThresholdedThresholdedimage

C t dConnectedcomponents


Convex Hull Convex Hull Convex hull has no concave partConvex hull has no concave part.

Convex hull

i

iDAC

4

1)( i

convi XD Algorithm: where

i1

4,3,2,1 , 1 iABXX ik

ik * 1kk


Example: Convex Hull Example: Convex Hull


Thinning Thinning

cBAABAABA

)() ( *cBAA ) ( *

))...))((...(( 21 nBBBABA


Example: Thinning Example: Thinning

Make an object thinner.


Thickening Thickening

* )( BAABA . ** ) ( BAABA . ) )...) ) ((...(( 21 nBBBABA . . . .

*

)) ))(( ((

Make an object thicker


Make an object thicker

Skeletons Skeletons

Dot lines are skeletons of thisstructure


Skeletons (cont.) Skeletons (cont.) K

)()(0

ASAS k

K

k

with BkB)AkB)AAS (()( with BkB)AkB)AASk ( ()(

where ...) ) ) (...( ( BBBAkB)A

k times

and kBAkK max

Skeletons Skeletons


Pruning Pruning

BAX 1

8

= thinning

) ( 1

8

12

k

kBXX

* = finding end points

AHXX )( 23 = dilation at end points

314 XXX = Pruned result


Example: Pruning Example: Pruning

Originalgimage

After Thi i EndThinning3 times

End points

DilationPrunedresult

of end points resultp

Summary of Binary Morphological Operations Summary of Binary Morphological Operations

(Tables from Rafael C.Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

Summary of Binary Morphological Operations (cont.) Summary of Binary Morphological Operations (cont.)

(Tables from Rafael C.Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

Basic Types of Structuring ElementsBasic Types of Structuring Elements

x = don’t care


GrayGray--Scale Dilation Scale Dilation

DDbfbf d)(|)()(1 D Case

DyxDytxsyxbytxsfbf )(;)()(|)()(max

bf DxDxsxbxsfbf and )(|)()(max2-D Case1-D Case

bf DyxDytxsyxbytxsfbf ),(;)(),(|),(),(max


Original image

GrayGray--Scale Dilation (cont.) Scale Dilation (cont.) Reflection

SubimageOriginal image

+

Reflectionof B

+

Moving Max

gwindow

StructuringStructuring element B

Note: B can be any shape and subimage must have

Output imagethe same shape asreflection of B.

GrayGray--Scale ErosionScale Erosion1 D Case DDbfbf d)(|)()(i

DyxDytxsyxbytxsfbf )(;)()(|)()(min2-D Case1-D Case bf DxDxsxbxsfbf and )(|)()(min

bf DyxDytxsyxbytxsfbf ),(;)(),(|),(),(min


Original image

GrayGray--Scale Erosion (cont.) Scale Erosion (cont.)

SubimageOriginal image

B

-

Moving

Min

Moving window

StructuringStructuring element B

Note: B can be any shape and subimage must have

Output imagethe same shape as B.

Example: GrayExample: Gray--Scale Dilation and ErosionScale Dilation and ErosionOriginal image After dilationOriginal image After dilation

Darker Brighter


After erosion

GrayGray--Scale OpeningScale Opening

bbfbf )( bbfbf )(

Opening cuts peaks


GrayGray--Scale ClosingScale Closing

bbfbf )( bbfbf )(

Cl i fill ll(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

Closing fills valleys

Example: GrayExample: Gray--Scale Opening and ClosingScale Opening and Closing

Original image After closingAfter opening

Reduce whitebj

Reduce darkobjects


objects j

GrayGray--scale Morphological Smoothing scale Morphological Smoothing

S hi P f i f ll d b l iSmoothing: Perform opening followed by closing

Original image After smoothingOriginal image After smoothing


Morphological Gradient Morphological Gradient

)()( bfbf )()( bfbfg

Original image Morphological Gradient


TopTop--Hat Transformation Hat Transformation

)( bffh

Original image Results of top-hat transform


Example: Texture Segmentation Application Example: Texture Segmentation Application

Small blob

Original image Segmented result

Algorithm:f l i h i b i i l l

Large blob

1. Perform closing on the image by using successively larger structuring elements until small blobs are vanished.2 Perform opening to join large blobs together


2. Perform opening to join large blobs together3. Perform intensity thresholding

Example: Granulometry Example: Granulometry Objective: to count the number of particles of each sizeObjective: to count the number of particles of each sizeMethod:1. Perform opening using structuring elements of increasing size2. Compute the difference between the original image and the result

after each opening operation3 The differenced image obtained in Step 2 are normalized and used3. The differenced image obtained in Step 2 are normalized and used

to construct the size-distribution graph.


Original imageSize distribution

graph

Morphological Watershads Morphological Watershads


Gradient ImageGradient Image

Surface of POriginalimage

P

at edges looklik t i idP

g

like mountain ridges.

Morphological Watershads Morphological Watershads


Convex Hull Convex Hull


Chapter 9: Morphological Image Processingit.nrru.ac.th/krit/411304/Chapter09.pdfExample: Application...

Documents

Transcript of Chapter 9: Morphological Image Processingit.nrru.ac.th/krit/411304/Chapter09.pdfExample: Application...