Morphological Operations

1
Morphological Operations

• Ku-Yaw Chang
• canseco_at_mail.dyu.edu.tw
• Assistant Professor, Department of Computer
  Science and Information Engineering
• Da-Yeh University

2
Morphology

• ???
• A branch of biology that deals with the form and
  structure of animals and plants.

3
Morphology Operations

• To simplify the objects by
• Filling in small holes
• Eliminating small protrusions from their
  boundaries
• Boundary pixels
• Object pixels that have background neighbors
• Various definition of neighbor

4
Morphology Operations

• Erosion
• Elimination of boundary pixels from objects in
  binary images
• Making objects smaller, also called shrinking
• Dilation
• Each background pixel that has a neighbor in the
  object is relabeled as an object pixel
• Making object bigger, also called growing

5
Morphology Operations

• Erosion/dilation operators
• Also called structuring elements
• The center is designated as its origin

6
Dilation

• R R ? A

d
d/4
d/4
d
d
d/8
d/8
A
R
R
7
Erosion

• R R ? A

d
d/4
d/4
d
3d/4
d/8
d/8
A
R
R
8
Dilation Erosion
d
R ? A
d/4
d/4
d
R
A
R ? A
9
Dilation

• R R ? A

d/2
d/4
d
d
d
d
d/2
d
d/8
d/8
R
A
R
10
Opening and Closing

• Opening
• A single erosion followed by a single dilation by
  the same operator
• R (R ? A) ? A
• Closing
• A single dilation followed by a single erosion by
  the same operator
• R (R ? A) ? A