9 Morphological Image Processing

Angela Chih-Wei Tang

Department of Communication Engineering

National Central University

JhongLi, Taiwan

2009 Fall

Outline

� Preliminaries

� Dilation and erosion

� Opening and closing

� Some basic morphological algorithms

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� Some basic morphological algorithms

� Extensions to gray-scale images

Basic Concepts from Set Theory� Sets: objects in an image

� Set theory: the language of mathematical

morphology

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Translation and Reflection

� They are extended from morphology but not

found in basic texts on set theory

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Outline

� Preliminaries

� Dilation and erosion

� Opening and closing

Some basic morphological algorithms

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� Some basic morphological algorithms

� Extensions to gray-scale images

Reflection

Translation

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Use of Morphological Dilation

for Bridging Gaps

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Use of Morphological Erosion for

Removing Image Components

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Outline

� Preliminaries

� Dilation and erosion

� Opening and closing

Some basic morphological algorithms

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� Some basic morphological algorithms

� Extensions to gray-scale images

Opening and Closing

� Opening: smooth the contour of an object, breaks narrow isthmuses, and eliminates thin protrusions

� Closing: smooth sections of contours, but it

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� Closing: smooth sections of contours, but it generally fuses narrow breaks and long thin gulfs, eliminates small holes, and fills gaps in the contour

Opening

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Closing

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Opening

ClosingC.E., NCU, Taiwan 19Angela Chih-Wei Tang, 2009

Use of Opening and Closing for

Morphological Filtering

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Outline

� Preliminaries

� Dilation and erosion

� Opening and closing

Some basic morphological algorithms

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� Some basic morphological algorithms

� Extensions to gray-scale images

Boundary Extraction

StructureElement

Erosion

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Example –

Boundary Extraction

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Region Filling

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Dilation

Complement

Example – Region Filling

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Extraction of Connected Components

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�Converge!!!

1 If

−==

kkXX

kXY =⇒ Let

Outline

� Preliminaries

� Dilation and erosion

� Opening and closing

Some basic morphological algorithms

C.E., NCU, Taiwan Angela Chih-Wei Tang, 2009 27

� Some basic morphological algorithms

� Extensions to gray-scale images

2-D Dilation

� General effects:

� If all the values of the structuring

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� If all the values of the structuring

element are positive, the output image

tends to be brighter than the input

� Dark details either are reduced or

eliminated, depending on how their

values and shapes relate to the

structuring element used for dilation

1-D Dilation

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2-D Erosion

� General effects

If all the elements of the structuring

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� If all the elements of the structuring

element are positive, the output image

tends to be darker than the input image

� The effect of bright details in the input

image that are smaller in area than the

structuring element is reduced

1-D Erosion

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Dilation and Erosion on

A Gray-Scale Image

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Opening and Closing

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Gray-Scale Opening and Closing

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