Curs - Operatii Morfologice

8/9/2019 Curs - Operatii Morfologice

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39Lecture 11

Digital Image Processing

Morphological Image Processing

Bibliography:

Dublin Institute of Technology, Image Processing – Morphology

Utah University, CS 4640: Image Processing Basics, Lecture 11


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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 followsassumes segmentation has already taken

place and that images are made up of 0s for

background pixels and 1s for object pixels. After this it doesn’t matter if 0 is black, white,

yellow, green…….


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39Pixel Neighborhoods

Remember the two definitions of “neighbors”that we’ve discussed:

4 Neighborhood 8 Neighborhood


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39What Is Morphology?

Morphological image processing (ormorphology ) describes a range of image

processing techniques that deal with the

shape (or morphology) of features in animage.

Morphological operations are typically

applied to remove imperfections introducedduring segmentation, and so typically

operate on bi-level images.


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39Quick Example

I m a g e s t a k e n f r o m G o n z a l e z & W o o d s ,

D i g i t a l I m a

g e P r o c e s s i n g ( 2 0 0 2 )

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 pixels in the

structuring element coveron pixels in the image.

Hit: Any on pixel in the

structuring element coversan on pixel in the image.

All morphological processing operations are based

on these simple ideas.


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39Structuring Element

Definition: A struc tur ing element is simplya binary image (or mask) that allows us to

define arbitrary neighborhood structures.

Example:

This is the structuring element for the 4-

neighborhood.


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39Structuring Elements

Structuring elements can be any size and makeany shape.

However, for simplicity we will use rectangular

structuring elements with their origin at the middle

pixel (left: 8-neighborhood; center: 4-

neighborhood)

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 performed.There are two basic morphological

operations: erosion and dilation


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39Erosion

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 isdetermined using the rule:

otherwise0

fitsif 1

),(

f s

y x g


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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 1

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

Original image Erosion by 3*3

square structuring

element

Erosion by 5*5

square structuring

element


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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

I m

a g e s t a k e n f r o m G o n z a l e z & W o o d s ,

D i g i t a l I m a

g e P r o c e s s i n g ( 2 0 0 2 )


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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 image f by structuring element s isgiven by f s.

The structuring element s is positioned with

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

otherwise0

hitsif 1

),(

f s

y x g


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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

I m

a g e s t a k e n f r o m G o n z a l e z & W o o d s ,

D i g i t a l I m a

g e P r o c e s s i n g ( 2 0 0 2 )


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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 compoundoperations are:

– Opening

– Closing


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39Opening

The opening of image f by structuringelement s, denoted f ○ s is 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 I m a g e s t a k e n f r o m G o n z a l e z & W o o d s ,

D i g i t a l I m a g e P r o c e s s i n g ( 2 0 0 2 )


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39Opening Example

Original

Image

Image

After

Opening

I m

a g e s t a k e n f r o m G o n z a

l e z & W o o d s ,



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39Opening Example

Structuring Element



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39Opening Example

Structuring Element



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39Opening

Conclusions:• Opening operation is an erosion followed

by a dilation

• Stray foreground structures that aresmaller than the structuring element will

disappear.

• Larger structures will remain.


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39Closing

The closing of image f by structuringelement s, denoted f • s is simply a dilation

followed by an erosion

f • s = (f s) s

Original shape After dilation After erosion

(closing)

Note a disc shaped structuring element is used I m a g e s t a k e n f r o m G o n z a

l e z & W o o d s ,



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39Closing Example

Original

Image

Image

After

Closing

I m


l e z & W o o d s ,



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39Closing Example

Structuring Element


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39Closing Example

Structuring Element


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39Closing

Conclusions:• Closing operation is a dilation followed by

an erosion.

• Holes in the foreground that are smallerthan the structuring element will be filled.

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39Opening and Closing Example

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39Morphological Processing Example

I m


l e z & W o o d s ,


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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.

1. The boundary can be given simply as

β (A) = A – (A B)

I m


l e z & W o o d s ,


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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 I m a g e s t a k e n f r o m G o n z a

l e z & W o o d s ,


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39Boundary Extraction (Outline)

2. Another method for boundary extraction

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39Boundary Extraction

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39Boundary Extraction Example

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39Region Filling

Given a pixel inside a boundary, regionfilling attempts to fill that boundary with

object pixels (1s)

I m


l e z & W o o d s ,

D i g i t a l I m

a g e P r o c e s s i n g ( 2 0 0 2 )

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 X0

is simply the starting point inside

the boundary, B is a simple structuring

element and Ac is 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. I m


l e z & W o o d s ,

D i g i t a l I m

a g e P r o c e s s i n g ( 2 0 0 2 )

.....3,2,1 )( 1 k A B X X c

k k

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39Region Filling Step By Step

I m


l e z & W o o d s ,

D i g i t a l I m

a g e P r o c e s s i n g ( 2 0 0 2 )

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39Region Filling Example

I m


l e z & W o o d s ,

D i g i t a l I m

a g e P r o c e s s i n g ( 2 0 0 2 )

Original Image One RegionFilled

All RegionsFilled

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39Skeletonisation

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39Summary

The purpose of morphological processing isprimarily to remove imperfections added during

segmentation.

The basic operations are erosion and dilation.Using the basic operations we can perform

opening and closing.

More advanced morphological operation canthen be implemented using combinations of all

of these.

Curs - Operatii Morfologice

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