Chapter 9 Some Basic Morphological Algorithm. Boundary Extraction Region Filling Extraction of...
-
Upload
pamela-lucas -
Category
Documents
-
view
280 -
download
3
Transcript of Chapter 9 Some Basic Morphological Algorithm. Boundary Extraction Region Filling Extraction of...
Some Basic Morphological Algorithm
Boundary Extraction Region Filling Extraction of Connected Components Convex Hull Thinning Thickening Skeletons Pruning
Boundary Extraction
The boundary of a set A denoted by
Where B is a suitable structuring element
1. Its algorithm is following these2. Eroding A by B3. Performing the set difference between
A and its erosion
)()( BAAA
Region Filling
Beginning with a point p inside the boundary, the objective is to fill the entire region with 1’s
Point p
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
,...3,2,1)( 1 kwhereABXX ckk
Where X0 = p and B is the symmetric structuring element.
Region Filling Algorithm
1. Pick a point inside p given it value 12. Set X0 = p
3. Start k = 14. Repeat getting Xk by
5. Terminate process if Xk = Xk-1
6. The set union of Xk and A is answer
,...3,2,1)( 1 kwhereABXX ckk
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.
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
,...3,2,1)( 1 kwhereABXX kk
Where X0 = p and B is the symmetric structuring element.
Connected Components Extraction Algorithm
1. Pick a point of Y set p2. Set X0 = p
3. Start k = 14. Repeat getting Xk by
5. Terminate process if Xk = Xk-1
6. The answer set Y is Xk
,...3,2,1)( 1 kwhereABXX kk
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.
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
,...3,2,14,3,2,1)( 1 kandiwhereABXX ik
ik
AXwith i 0iconv
i XD
4
1
)(
i
iDAC
ik
ik XX 1
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
AXXXX 40
30
20
10
Convex Hull Algorithm
x
xxx
x
xxx xx x
xxx
xx x
xx x
B1 B2 B3 B4 x Don’t care
Background
Foreground
A
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
cBAA
BAABA
)*(
)*(
,,...,,, 321 nBBBBB
))...))((...((}{ 21 nBBBABA
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
)*( BAAAOB
,,...,,, 321 nBBBBB
))...))((...((}{ 21 nOBOBAOBBAO