4_14755_CS213_20172018_1__2_1_Lecture_5.ppt

DIP

1. Lecture 5
Morphological Image
Processing
Digital Image Processing

2. Remember
GRAY LEVEL THRESHOLDING
Objects
Set threshold
here

3. BINARY IMAGE
Problem here
How do we fill “missing pixels”?

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

5. Z
2
and Z
3
•set in mathematic morphology represent
objects in an image
–binary image (0 = white, 1 = black) : the element
of the set is the coordinates (x,y) of pixel belong
to the object  Z
2
•gray-scaled image : the element of the set is the
coordinates (x,y) of pixel belong to the object and
the gray levels  Z
3
5

6. Basic Set Theory
6

7. Reflection and Translation
7
} ,|{
ˆ
Bfor bbwwB 
} ,|{)( Afor azaccA
z


8. Example
8

9. Structuring element (SE)
9
 small set to probe the image under study
 for each SE, define origo
 shape and size must be adapted to geometric
properties for the objects

10. Examples: Structuring Elements
10
origin

11. Basic idea
•in parallel for each pixel in binary image:
–check if SE is ”satisfied”
–output pixel is set to 0 or 1 depending on used
operation
11

12. Example
12
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.

13. Basic morphological operations
•Erosion
•Dilation
•combine to
–Opening object
–Closening background
13
keep general shape but
smooth with respect to

14. Erosion
•Does the structuring element fit the set?
erosion of a set A by structuring element B: all z
in A such that B is in A when origin of B=z
shrink the object
14

15. Erosion
15

16. Erosion
16

17. Erosion
17

18. Erosion
18
}{ Az|(B)BA
z


19. Dilation
•Does the structuring element hit the set?
•the dilation of A by B can be understood as the
locus of the points covered by B when the
center of B moves inside A.
•grow the object
19
}
ˆ
{ ΦA)Bz|(BA
z 

20. Dilation
20

21. Dilation
21

22. Dilation
22

23. Dilation
23
}
ˆ
{ ΦA)Bz|(BA
z 
B = structuring element

24. Dilation : Bridging gaps
24

25. 25

26. 26

27. 27

28. 28

29. useful
•erosion
–removal of structures of certain shape and size,
given by SE
•Dilation
–filling of holes of certain shape and size, given by
SE
29

30. Combining erosion and dilation
•WANTED:
–remove structures / fill holes
–without affecting remaining parts
•SOLUTION:
•combine erosion and dilation
•(using same SE)
30

31. Erosion : eliminating irrelevant detail
31
structuring element B = 13x13 pixels of gray level 1

32. Opening
erosion followed by dilation, denoted
∘
•eliminates protrusions
•breaks necks
•smoothes contour
32
BBABA  )(

33. Opening
33

34. Opening
34

35. Opening
35
BBABA  )(
})(|){( ABBBA
zz


36. Opening with a 11 pixel diameter disc:
3x9 and 9x3 Structuring Element
Opening example

37. Closing
dilation followed by erosion, denoted •
•smooth contour
•fuse narrow breaks and long thin gulfs
•eliminate small holes
•fill gaps in the contour
37
BBABA  )(

38. Closing
38

39. Closing
39

40. Closing
40
BBABA  )(

41. Closing operation with a 22 pixel disc, closes small holes in
the foreground.
Another closing example

42. Threshold, closing with disc of size 20.
Note that opening is the dual of closing i.e. opening the
foreground pixels with a particular structuring element is
equivalent to closing the background pixels with the same
element.
And another…

43. Properties
43
Opening
(i) AB is a subset (subimage) of A
(ii) If C is a subset of D, then C B is a subset of D B
(iii) (A B) B = A B
Closing
(i) A is a subset (subimage) of AB
(ii) If C is a subset of D, then C B is a subset of D B
(iii) (A B) B = A B
Note: repeated openings/closings has no effect!

44. 46

45. Useful: open & close
47

46. APPLICATIONS
48

47. Application: filtering
49

48. Used to look for particular patterns of foreground and
background pixels
Very simple object recognition
Example for a Hit-and-miss Structuring Element: Contains
0s, 1s and don’t care’s.
Similar to Pattern Matching:
If foreground and background pixels in the structuring
element exactly match foreground and background pixels
in the image, then the pixel underneath the origin of the
structuring element is set to the foreground colour.
Hit-and-miss transform*

49. Structuring Elements representing four corners.
Apply each Structuring Element.
Use OR operation to combine the four results.
Hit-and-miss example: corner detection

50. Boundary Extraction
52
)()( BAAA 

51. Example
53

52. Region Filling
54
,...3,2,1 )(
1


kABXX
c
kk

53. Region Filling Algorithm
55

54. Example
56

55. Thinning
57
c
BAA
BAABA
)(
)(



56. Thickening
58
)(BAABA 
•The thickening operation is calculated by translating the origin of the structuring element to each possible
pixel position in the image, and at each such position comparing it with the underlying image pixels. If the
foreground and background pixels in the structuring element exactly match foreground and background
pixels in the image, then the image pixel underneath the origin of the structuring element is set to
foreground (one). Otherwise it is left unchanged. Note that the structuring element must always have a zero
or a blank at its origin if it is to have any effect.
Alternativel
y, based on
Thining