chapter 9 erossion

Morphology in image processing Morphology generally concerned with shape and properties of objects.. Digital Image ProcessingErosion and Dilation... Dilation and Erosionan object bounda

Morphology in image processing

Morphology generally concerned with shape

and properties of objects

Used for segmentation and feature extraction

Segmentation = used for cleaning binary

objects.

Two basic operations

 erosion

 dilation

Digital Image Processing

Erosion and Dilation

Dilation and Erosion

an object

boundary of an object

depends on size and shape of structuring element

Morphological operators are used to prepare

recognition

(specifically salt-and-pepper noise)

black pixels in a white region) Can also have

cracks, picket fence occlusions, etc.

morphological operations that can assist with these problems.

Morphology in image processing

Union of A and B: C=A∪B

Intersection of A and B: D=A∩B

Disjoint sets: A∩B= ∅

Complement of A: Ac = {x|x∉A}

Difference of A and B:

A-B = {x|x ∈ A, x ∉ B} = A ∩Bc

Structuring Elements, Hits & Fits

on pixels in the image

Hit: Any on pixel in the structuring element covers

an on pixel in the image

All morphological processing operations are based

on these simple ideas

Structuring Elements

Structuring elements can be any size and

make any shape

However, for simplicity we will use

rectangular structuring elements with their

origin at the middle pixel

Fitting & Hitting

0 1 0

1 1 1

0 1 0

Structuring Element 2

Fundamental Operations

processing is very like spatial filtering

every pixel in the original image to give a pixel in a new processed image

operation performed

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:

fits if

1 )

,

g

Example for Erosion

1 1

0 1

1 1

0 0

0 1

Input image

Structuring Element

x7 x6

x5 x4

x1 x3

x2 x1

Output Image

1 1

1

Erosion Example

Structuring Element Original Image Processed Image With Eroded Pixels

Erosion Example

Structuring Element

Original Image Processed Image

Erosion Example

A

Erosion Example

Erosion Example 2

Original image

After erosion with a disc of radius 10

After erosion with a disc of radius 20

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:

hits if

1 )

,

g

Example for Erosion

1 1

0 1

1 1

0 0

0 1

Input image

Structuring Element

x3 x2

x1

Output Image

1 1

1

Dilation Example

Structuring Element Original Image Processed Image

Dilation Example

Structuring Element Original Image Processed Image With Dilated Pixels

Dilation Example

Main Applications of Dilation

Dilation Example

Main Applications of Dilation

Main Applications of Dilation

Main Applications of Dilation

clear all;

clc

A=imread('Fill_hold.bmp'); B=im2bw(A);

Dilation: expands image

Erosion: shrink image

erosion+dilation = original image ?

Opening= erosion + dilation

B B

A B

A
= ( ) ⊕

Closing

Closing = dilation + erosion

B B

A B

A • = ( ⊕ )

Example of opening and closing

se=strel(‘square', 20);

(A) Original Image (B) Opening

(C) closing (D) Closing of B

(A) Original Image (B) Opening

(C) closing (D) Closing of B

se=strel('disk', 10);

(A) Original Image (B) Opening

(C) closing (D) Closing of B

closing

From A -> B -> C, counting the number of objects, highlight the boundary of

objets (Boundary Extraction)

exercises

The Hit-or-Miss Transformation

Use the hit-or-miss trnsformation to identify the location of the shape

Use the hit-or-miss trnsformation to identify the location of the shape

bwmorph(f, operation, n)

based on combinations of dilations, erosions and look up table operations

bwmorph(f, operation, n)

bwmorph(f, operation, n)

BW2 = bwmorph(BW,'remove');

figure, imshow(BW2)

bwmorph(f, operation, n)

bwmorph(f, operation, n)

Labeling Connected Components

• Label objects in an image

• 4-Neighbors

• 8-Neighbors

4 and 8 Connect

Input Image 8 – Connect 4 - Connect

4-Neighbors