Mathematical Morphology

1
Mathematical Morphology
2
Morphological Operations
Structural elements
3
Morphological Operations

• Erosion
• Dilatation
• Median Operation
• Open
• Close
• Open-Clos
• Clos-Open

4
Binary Erosion
J2 ERODE(I, B) if J2(i, j) ANDBI(i, j)
ANDI(i-m, j-n) (m, n) ?B
5
Binary Erosion
6
Erosion Effects
7
Erosion Property
8
Binary Dilatation
J1 DILATE(I, B) if J1(i, j) ORBI(i, j)
ORI(i-m, j-n) (m, n) ? B
9
Binary Dilatation
10
Dilatation Effects
11
Dilatation Property
12
Binary Median
J3 MEDIAN(I, B) if J3(i, j) MAJBI(i, j)
MAJI(i-m, j-n) (m, n) ? B
13
Binary Median
14
Median Effects
15
(No Transcript)
16
Open / Close

• OPEN DILATE (ERODE( Im,B))
• CLOSE ERODE (DIALTE (Im,B))

17
Idempotence
18
Open-Clos / Clos-Open
19
Morph. Operation in Gray Levels
J ERODEI, B if J(i, j) MIN BI(i, j)
(local minimum)
J DILATEI, B if J(i, j) MAX BI(i, j)
(local maximum)