1. Digital Image Processing CP-7008 Lecture # 09 Morphological Image Processing
Fall 2011

2. Agenda Image Morphology Erosion Dilation Opening Closing
Hit-Miss Transformation
Misc. Morphological Operations

3. Introduction
Morphology: a branch of biology that deals with the form and structure of animals and plants
Morphological image processing is used to extract image components for representation and description of region shape, such as boundaries, skeletons, and the convex hull

4. Mathematic Morphology
mathematical framework used for:
pre-processing
noise filtering, shape simplification, ...
enhancing object structure
skeletonization, convex hull...
quantitative description
area, perimeter, ...

5. Basic Set Theory

6. Preliminaries (1)
Reflection
Translation

7. Example: Reflection and Translation

8. Preliminaries (2) Structure elements (SE)
Small sets or sub-images used to probe an image under study for properties of interest

9. Examples: Structuring Elements (1)
origin

10. Examples: Structuring Elements (2)
Accommodate the entire structuring elements when its origin is on the border of the original set A
Origin of B visits every element of A
At each location of the origin of B, if B is completely contained in A, then the location is a member of the new set, otherwise it is not a member of the new set.

11. Erosion

12. Example of Erosion (1)

13. Erosion Example Structuring Element Original Image
Processed Image With Eroded Pixels
Structuring Element 13

14. Erosion Example
Original Image
Processed Image
Structuring Element 14

15. Erosion Example 2
Original image
Erosion by 3*3 square structuring element
Erosion by 5*5 square structuring element
Watch out: In these examples a 1 refers to a black pixel! 15

16. Erosion Example 3 After erosion with a disc of radius 10
Original image
After erosion with a disc of radius 5
After erosion with a disc of radius 20 16

17. What Is Erosion For? Erosion can split apart joined objects
Erosion can strip away extrusions
Watch out: Erosion shrinks objects 17

18. Dilation

19. Examples of Dilation (1)

20. Dilation Example
Original Image
Processed Image
Structuring Element 20

21. Dilation Example Structuring Element Original Image
Processed Image With Dilated Pixels
Structuring Element 21

22. Dilation Example 2
Dilation by 3*3 square structuring element
Original image
Dilation by 5*5 square structuring element
Watch out: In these examples a 1 refers to a black pixel! 22

23. Examples of Dilation (3)

24. What Is Dilation For? Dilation can repair breaks
Dilation can repair intrusions
Watch out: Dilation enlarges objects 24

25. Duality
Erosion and dilation are duals of each other with respect to set complementation and reflection

26. Duality
Erosion and dilation are duals of each other with respect to set complementation and reflection

27. Duality
Erosion and dilation are duals of each other with respect to set complementation and reflection

29. Opening and Closing
Opening generally smoothes the contour of an object, breaks narrow isthmuses, and eliminates thin protrusions
Closing tends to smooth sections of contours but it generates fuses narrow breaks and long thin gulfs, eliminates small holes, and fills gaps in the contour

30. Opening and Closing

31. Opening

32. Opening Example
Original Image
Image After Opening

33. Closing Example
Original Image
Image After Closing

35. Duality of Opening and Closing
Opening and closing are duals of each other with respect to set complementation and reflection

36. The Properties of Opening and Closing
Properties of Closing

38. The Hit-or-Miss Transformation

39. Some Basic Morphological Algorithms (1)
Boundary Extraction
The boundary of a set A, can be obtained by first eroding A by B and then performing the set difference between A and its erosion.

40. Example 1

41. Example 2

42. Some Basic Morphological Algorithms (2)
Hole Filling
A hole may be defined as a background region surrounded by a connected border of foreground pixels.
Let A denote a set whose elements are 8-connected boundaries, each boundary enclosing a background region (i.e., a hole). Given a point in each hole, the objective is to fill all the holes with 1s.

43. Some Basic Morphological Algorithms (2)
Hole Filling
1. Forming an array X0 of 0s (the same size as the array containing A), except the locations in X0 corresponding to the given point in each hole, which we set to 1.
2. Xk = (Xk-1 + B) Ac k=1,2,3,…
Stop the iteration if Xk = Xk-1

44. Example