1. 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:

2. Erosion

3. Typical Uses of Erosion
Removes isolated noisy pixels.
Smoothes object boundary(removes spiky edges).
Removes the outer layer of object pixels:
- Object becomes slightly smaller.
- Sets contour pixels of object to background value

4. Erosion Example

5. Erosion explained pixel by pixel• • • B

6. Structuring Element in Erosion Example

7. 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.

8. Structuring Element in Erosion Example

9. Structuring Element in Erosion Example

10. Structuring Element in Erosion Example

11. Structuring Element in Erosion Example

12. Structuring Element in Erosion Example

13. Structuring Element in Erosion Example

14. Mathematical Definition of Erosion
Erosion is the morphological dual to dilation.
It combines two sets using the vector subtraction of set elements.
Let denotes the erosion of A by B

15. Erosion explained pixel by pixel• • •
(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)

16. Properties of Erosion Erosion is not commutative! Linearity
Decomposition of structuring element
Erosion is not commutative!

17. Erosion

18. In MATLAB Codes Erosion image:
strel: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]

19. Codes A = imread(‘Image.tif'); figure,imshow(A); se = strel('disk',3);
A2 = imerode(A, se);
figure,imshow(A2);
se = strel('disk',5);
A3 = imerode(A, se);
figure,imshow(A3);
se = strel('disk',10);
A4 = imerode(A, se);
figure,imshow(A4);

20. Example of Erosions with various sizes of structuring elements
Pablo Picasso, Pass with the Cape, 1960

21. Erosion and Dilation summary

22. Boundary Extraction

23. 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

24. Boundary Extraction

25. Edge detection
original
Dilate
Dilate - original

26. 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

27. OPENING
Opening of A by B, is simply erosion of A by B, followed by dilation of the result by B.
We use opening for:
Smoothes object boundaries
Eliminates noise (isolated pixels)
Maintains object size

28. OPENING
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

29. Opening Example Original
What combination of erosion and dilation gives:
cleaned binary image
object is the same size as in original
Original

30. Opening Example Cont Original Erode Dilate Erode original image.
Dilate eroded image.
Smoothes object boundaries, eliminates noise (isolated pixels) and maintains object size.
Original
Erode
Dilate

31. CLOSING
Closing of A by B, is dilation followed by erosion (opposite to opening).
We use Closing for:
Smoothes object boundaries
Eliminates noise (small holes), fills gaps in contours and close up cracks in objects.
Maintains object size.

32. Close Dilation followed by erosion
Serves to close up cracks in objects and holes due to pepper noise
Does not significantly change object size

33. More examples of Closing
What combination of erosion and dilation gives:
cleaned binary image
object is the same size as in original
Original

34. More examples of Closing cont
Dilate original image.
Erode dilated image.
Smoothes object boundaries, eliminates noise (holes) and maintains object size.
Original
Dilate
Erode

35. Open and Close Close = Dilate next Erode Open = Erode next Dilate
Original image
eroded
dilated
dilated
eroded
Open
Close

36. Closing o Opening & Opening o Closing
Spatial Filtering
Closing o Opening & Opening o Closing

37. Use of opening and closing for morphological filtering

38. Open and Close
Original image; opening; opening followed by closing

39. 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);

40. 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.