Erosion: Erosion is used for shrinking of element A by using element B One of the simplest uses of...

Erosion:

Erosion:

• Erosion is used for shrinking of element A by using element B

• One of the simplest uses of erosion is for eliminating irrelevant details from a binary image.

Erosion

Typical Uses of Erosion

1. Removes isolated noisy pixels.

2. Smoothes object boundary(removes spiky edges).

3. Removes the outer layer of object pixels:

- Object becomes slightly smaller.

- Sets contour pixels of object to background value

Erosion Example

Erosion explained pixel by pixel

•

•

•

•

••••

••

B

A BA

• •••

Structuring Element in Erosion Example

Image Structuring Element Result

How It Works?

During erosion, a pixel is turned on at the image pixel under the structuring element origin only when the pixels of the structuring element match the pixels in the image

Both ON and OFF pixels should match. This example erodes regions horizontally from the

right.

Image Structuring Element Result

Structuring Element in Erosion Structuring Element in Erosion ExampleExample

Mathematical Definition of Erosion

1. Erosion is the morphological dual to dilation.

2. It combines two sets using the vector subtraction of set elements.

3. Let denotes the erosion of A by BBA

){

},,{

BbeveryforAbxxx

baxAaanexistBbeveryforxBA

Erosion explained pixel by pixel

•

•

•

•

••••

••

BA BA

• •••

(1,1) – (0,0)= (1,1)(1,2) – (0,0)= (1,2)(1,3) – (0,0)= (1,3)(1,4) – (0,0)= (1,4)(0,4) – (0,0)= (0,4)(2,4) – (0,0)= (2,4)(3,4) – (0,0)= (3,4)(4,4) – (0,0)= (4,4)

(1,1) – (1,0)= (0,1)(1,2) – (1,0)= (0,2)(1,3) – (1,0)= (0,3)(1,4) – (1,0)= (0,4)(0,4) – (1,0)= (-1,4)(2,4) – (1,0)= (1,4)(3,4) – (1,0)= (2,4)(4,4) – (1,0)= (3,4)

Properties of Erosion

Erosion is not commutative!

Linearity

Decomposition of structuring element

)()()( CBCACBA

)()()( CABACBA

ABBA

Erosion

In MATLAB Codesstrel:This function creates amorphological structuring element.

SE=strel(‘shape’,parameters)

Erosion image:

imerode: This function erosion the image.

I2=imerode(‘image’,SE)

shape parameters

‘disk’ R

‘line’ Len,deg

‘square’ w

‘rectangle’ [m n]

CodesA = imread(‘Image.tif');

figure,imshow(A);

se = strel('disk',3);

A2 = imerode(A, se);

figure,imshow(A2);



figure,imshow(A3);



figure,imshow(A4);

Pablo Picasso, Pass with the Cape, 1960

Structuring

Element

Example of Erosions Example of Erosions with various sizes of with various sizes of structuring elementsstructuring elements

Erosion and Dilation summary

Boundary Extraction

Boundary Extraction

First, erode A by B, then make set difference between A and the erosion

The thickness of the contour depends on the size of constructing object – B

Boundary Extraction

Edge detectionDilate - originaloriginal Dilate

Opening & Closing

Opening and Closing are two important operators from mathematical morphology

They are both derived from the fundamental operations of erosion and dilation

They are normally applied to binary images

OPENINGOPENING•Opening of A by B, is simply erosion of A by B, followed by dilation of the result by B.

•We use opening for: o Smoothes object boundarieso Eliminates noise (isolated pixels) o Maintains object size

BBABA )(

Opening is defined as an erosion followed by a dilation using the same structuring element

The basic effect of an opening is similar to erosion but Less destructive than erosion

Does not significantly change an object’s size

OPENINGOPENING

Opening Example

Original What combination of

erosion and dilation gives:o cleaned binary image

o object is the same size as in original

Opening Example Cont

Erode original image.

Dilate eroded image.

Smoothes object boundaries, eliminates noise (isolated pixels) and maintains object size.

DilateOriginal Erode

•Closing of A by B, is dilation followed by erosion (opposite to opening).

•We use Closing for: oSmoothes object boundaries oEliminates noise (small holes), fills gaps in contours and close up cracks in objects. o Maintains object size.

CLOSINGCLOSING

BBABA )(

Close Dilation followed by erosion Serves to close up cracks in objects and holes

due to pepper noise Does not significantly change object size

More examples of Closing

Original What combination of

erosion and dilation gives:o cleaned binary image

o object is the same size as in original

More examples of Closing cont

Dilate original image.

Erode dilated image.

Smoothes object boundaries, eliminates noise (holes) and maintains object size.

ErodeDilateOriginal

Open and CloseClose = Dilate next ErodeOpen = Erode next Dilate

OpenClose

Original image dilated

eroded

dilated

eroded

Spatial Filtering

Closing o Opening & Opening o Closing

Use of opening and closing for morphological filtering

Open and Close

Original image; opening; opening followed by closing

Codes

f = imread('noisy-fingerprint.tif');

figure,imshow(f);

se = strel('square', 3);

fo = imopen(f,se);

figure,imshow(fo);

foc = imclose(fo,se);

figure,imshow(foc);

Possible problems with Morphological Operators

Erosion and dilation clean image but leave objects either smaller or larger than their original size.

Opening and closing perform same functions as erosion and dilation but object size remains the same.

Erosion: Erosion is used for shrinking of element A by using element B One of the simplest uses of...

Documents

Transcript of Erosion: Erosion is used for shrinking of element A by using element B One of the simplest uses of...