SEMINAR ON :

BY:

RaghukumarD.S.

Introduction Set Theory Concepts Structuring Elements , Hits or fits Dilation And Erosion Opening And Closing Hit-or-Miss Transformation Basic Morphological Algorithms Implementation Conclusion

ABSTRCT

Introduction

Morphological – Shape , form , Structure

►Extracting and Describing image component

regions

►Usually applied to binary images

►Based on set Theory

Set Theory

BASICS:

If A and B are two sets then

UNION = AUB

INTERSECTION = A∩B

COMPLIMENT = (A)c

DIFFERENCE = A-B

A BA AND B

A.B

A OR B

A+B

NOT(A)−

𝑨0 0 0 0 1

0 1 0 1 1

1 0 0 1 0

1 1 1 1 0

BASIC LOGIC OPERATIONS :

LOGIC OPERATIONS REPRESENTATION:

Structuring elements can be any size

Structuring make any shape

Structuring Elements

1 1 1

1 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 0

1 1 1

0 1 0

Rectangular structuring elements with their origin at the middle

pixel

Hits And Fits

Hit: Any on pixel in the structuring element covers an on pixel in the image

B

AC

Structuring Element

Fit: All on pixels in the

structuring element cover

on pixels in the image

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 0

0 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

Hits And Fits

Dilation

Dilation of image f by structuring element s is given

by f s

The structuring element s is positioned with its origin

at (x, y) and the new pixel value is determined using

the rule:

otherwise 0

hits if 1),(

fsyxg

Example

Structuring Element

Original Image

Processed Image

Structuring Element

Original Image Processed Image With Dilated Pixels

Example

Erosion

Erosion of image f by structuring element s is given

by f s

The structuring element s is positioned with its

origin at (x, y) and the new pixel value is determined

using the rule:

otherwise 0

fits if 1),(

fsyxg

Structuring Element

Original Image

Processed Image With Eroded Pixels

Example

Structuring Element

Original Image Processed Image

Example

Erosion v/s Dilation

Erosion

removal of structures of

certain shape and size,

given by SE

Erosion can split apart

joined objects and strip

away extrusions

Dilation

filling of holes of

certain shape and

size, given by SE

can repair breaks

and intrusions

Opening And Closing

Combine to

Opening object

Closing background

keep general shape but

smooth with respect to

can be performed by performing combinations of

erosions and dilations

Opening

Erosion followed by dilation

denoted by ∘

BBABA )(

Structuring Element

Original Image Processed Image

Example

Structuring Element

Original Image Processed Image

Example

Closing

Dilation followed by erosion

denoted by •

f • s = (f s)s

Structuring Element

Original Image Processed Image

Example

Structuring Element

Original Image Processed Image

Example

Opening V/S Closing

Opening

AB is a subset

(subimage) of A

If C is a subset of D,

then C B is a subset

of D B

(A B) B = A B

Closing

A is a subset

(subimage) of AB

If C is a subset of D,

then C B is a subset

of D B

(A B) B = A B

Note: repeated openings/closings has no effect!

Hit or Miss Transformation

Useful to identify specified configuration of pixels,

such as, isolated foreground pixels or pixels at end

of lines (end points)

)2()1(* BABABA

Illustration

Original Image A and B1 A eroded by B1

Complement of OriginalImage and B2

Erosion of A complementAnd B2

Intersection of eroded images

Morphological Algorithms

Using the simple technique we have

looked at so far we can begin to consider

some more interesting morphological

algorithms

We will look at:

Boundary extraction

Extracting the boundary (or outline) of an object

is often extremely useful

The boundary can be given simply as

β(A) = A – (AB)

Boundary Extraction

Illusration

A simple image and the result of

performing boundary extraction using a

square structuring element

Original Image Extracted Boundary

Example

Conclusion

Morphology is powerful set of tools for extracting

features in an image

We implement algorithms like Thinning thickening

Skeletons etc. various purpose of image

processing activities like semantation.

Thank you