Morphological Image Processing

Dilation and Erosion

1. MORPHOLOGICAL IMAGE
PROCESSING
D.SHUNMUGAKUMARI
ASSITANT PROFESSOR
DEPARTMENT OF INFORMATION TECHNOLOGY

2. INTRODUCTION
Morphology
About the formand structureof animals and
plants
Mathematical morphology
Using set theory
Extract image component
Representation and descriptionof region shape

3. INTRODUCTION
Setsin mathematical morphology represent
objectsin an image
Example
◦Binary image: the elements of a set is the
coordinate (x,y)of the pixels, in Z
2
◦Gray-level image: the element of a set is the
triple, (x, y, gray-value), in Z
3

4. OUTLINE
Preliminaries –set theory
Dilation and erosion
Opening and closing

5. PRELIMINARIES –SET THEORY
A be a set in Z
2
.
a = (a
1, a
2) is an element of A.
a is notan element of A
Null (empty) set: Aa Aa

6. SET OPERATIONS
A is a subsetof B: every element of A is an
element of another set B
Union
Intersection
Mutually exclusiveBA BAC BAC BA 

7. GRAPHICAL EXAMPLES

8. GRAPHICAL EXAMPLES (CONT.) AwwA
c
  BwAwwBA  ,

9. LOGIC OPERATIONS ON BINARY
IMAGES
Functionally complete operations
AND, OR, NOT

10. BA BA AB

11. OUTLINE
Preliminaries
Dilation and erosion
Opening and closing

12. DILATION  )ˆ(  ABzBA
z
B:structuring
element

13. DILATION
Dilation is one of the basic operation in
mathematical morphology.
Dilation adds the pixels to the Boundaries of
an object in an image.
Dilation process in which binary image is
expanded from its original image.
W B

14. DILATION FORMULA,
f(x) h(s)=max{f(x)+h(s-x)}
f(x) original Image
EXOR operation
s Structuring pattern matching.

16. DILATION EXAMPLE
Original Image expanded Dilation

17. EROSION ABzBA
z )(
z: displacement
B:structuring
element

18. EROSION(CONT.)

19. EROSION
•Erosion is the Reverse process of the Dilation.
•Erosion Remove the pixel on object boundaries.
• B W

20. EROSION FORMULA
f(x) h(s)=min{f(s+x)+h(x)}
f(x) original Image
EXNOR operation
s Structuring pattern matching.

22. EROSION EXAMPLE
Original Image EXNOR Erosion

23. STRUCTURING ELEMENT
The number of pixel added or removed from the
object in an image depends on the size and shape
structuring element.
•It’s s matrix 1’s and 0’s.
The center pixel of the structuring element,
called the origin.

26. DILATION AND EROSION ARE DUALS 
c
z
c
ABzBA )( ) (   
cc
zABz )( 
  )( 
c
z
ABz
  )ˆ(  ABzBA
z BA
cˆ


27. APPLICATION: BOUNDARY
EXTRACTION
Extract boundary of a set A:
First erode A (make A smaller)
A –erode(A)) (BAA
=

28. APPLICATION: BOUNDARY EXTRACTION
Using 5x5 structuring elementoriginal image

29. OUTLINE
Preliminaries
Dilation and erosion
Opening and closing

30. OPENING
Dilation: expands image w.r.t structuring
elements
Erosion: shrink image
erosion+dilation = original image
Opening= erosion + dilationBBABA  ) (

31. OPENING (CONT.)

32. OPENING (CONT.)
Smooththe contour of an image, breaks narrow isthmuses,
eliminates thin protrusions
Find contour Fill in contour

33. CLOSING
Closing= dilation + erosionBBABA )(

34. CLOSING (CONT.)
Find contour Fill in contour
Smooththe object contour, fusenarrow breaks and long
thin gulfs, eliminatesmall holes, and fill in gaps

35. Noisy
image
opening
Remove
outer
noise
Remove
inner
noise
closing