1. Some Basic Morphological Algorithm
Chapter 9
Some Basic Morphological Algorithm

2. Some Basic Morphological Algorithm
Boundary Extraction
Region Filling
Extraction of Connected Components
Convex Hull
Thinning
Thickening
Skeletons
Pruning

3. Boundary Extraction The boundary of a set A denoted by
Where B is a suitable structuring element
Its algorithm is following these
Eroding A by B
Performing the set difference between A and its erosion

4. Boundary Extraction

5. Boundary Extraction

6. Region Filling
Beginning with a point p inside the boundary, the objective is to fill the entire region with 1’s
Point p

7. Region Filling
If all nonboundary (background) points are labeled 0, then we assign a value of 1 to p to begin. The following procedure then fill the region with 1’s
Where X0 = p and B is the symmetric structuring element.

8. Region Filling Algorithm
Pick a point inside p given it value 1
Set X0 = p
Start k = 1
Repeat getting Xk by
Terminate process if Xk = Xk-1
The set union of Xk and A is answer

9. Region Filling Algorithm

10. Region Filling Algorithmp

11. Region Filling

12. Connected Components Extraction
To establish if two pixels are connected, it must be determined if they are neighbors and if their gray levels satisfy a specified criterion of similary.
In practice, extraction of connected components in a binary image is central to many automated image analysis applications.

13. Connected Components Extraction
Let Y represent a connected component contained in a set A and assume that a point p of Y is known
Following expression
Where X0 = p and B is the symmetric structuring element.

14. Connected Components Extraction Algorithm
Pick a point of Y set p
Set X0 = p
Start k = 1
Repeat getting Xk by
Terminate process if Xk = Xk-1
The answer set Y is Xk

15. Convex Hull
A set A is said to be convex if the straight line segment joining any two points in A lies entirely with in A
The convex hull H of an arbitrary set S is the smallest convex set containing
The set difference H-S is called the convex deficiency of S.

16. Convex Hull Let Bi, i=1,2,3,4 represent 4 structure
The procedure consists of implementing the equation
Let , where the subscript “conv” (convergence) in the sense that
Then the convex hull of A is

17. Convex Hull Algorithm Set Do with B1
Repeat to apply hit-or-miss transformation to A with B1 until no further change occur Xn.
Union Xn with A, called D1
Do same as B1 with B2, B3, and B4; hence we will get D1, D2, D3 and D4
Union all of D will be the answer of convex hull

18. Convex Hull Algorithm B1 B2 B3 B4 A Don’t care x x x x x Background
Foreground A

19. HIT-or-MISS A with B1 x

20. HIT-or-MISS A with B2 x

21. HIT-or-MISS A with B3 x

22. HIT-or-MISS A with B4 x

23. Convex Hull

24. Thinning
The thinning of a set A by a structuring element B, can be defined
Where Bi is a rotated version of Bi-1
Using this concept, we now define thinning as

25. x x x x x x x x

26. Thickening
The thickening of a set A by a structuring element B, can be defined
Where Bi is a rotated version of Bi-1
Using this concept, we now define thinning as

27. x x x x x x x x x x x x x x x x