KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
1
MORPHOLOGICAL OPERATORS
KOM3212 Image Processing in Industrial
Systems
Some of the contents are adopted from
R. C. Gonzalez, R. E. Woods, Digital Image Processing, 2nd edition, Prentice Hall, 2008
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
2
Introduction
• Morphology: a branch of biology that deals with the form
and structure of animals and plants
• Morphological image processing is used to extract image
components for representation and description of region
shape, such as boundaries, skeletons, and the convex
hull
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
Introduction
mathematical framework used for:
• pre-processing
• noise filtering, shape simplification, ...
• enhancing object structure
• skeletonization, convex hull...
• Segmentation
• watershed,…
• quantitative description
• area, perimeter
3
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
Basic Set Theory
4
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
Reflection and Translation
Bˆ  {w | w  b, for b  B}
( A) z  {c | c  a  z, for a  A}
5
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
6
Structure elements
Small sets or sub-images used to probe an image under
study for properties of interest
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
Basic idea of using SE
• 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
7
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
Morphological Operations
• Erosion
• Dilation
• Combine in the Operations of
• Opening
• Closening
object
background
keep general shape but smooth with
respect to
8
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
9
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
A  B  {z|(B)z  A}
All points z such that B translated by z is contained in A
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
Erosion
10
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
Erosion
11
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
12
Dilation


Does the structuring element hit the set?
Dilation of a set A by structuring element B: all z in A such that B hits A when
origin of B=z
grow the object
A  B  {z|(Bˆ )z  A  Φ}
All displacements z such that 𝐵 and A overlap at least on one element
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
Dilation
13
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
Dilation
14
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
15
Dilation and Erosion is useful for…
• Erosion
• removal of structures of certain shape and size, given by SE
• Dilation
• filling of holes of certain shape and size, given by SE
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
Combining erosion and dilation
• WANTED:
• remove structures / fill holes
• without affecting remaining parts
• SOLUTION:
• combine erosion and dilation
• (using same SE)
16
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
Combining erosion and dilation
structuring element B = 13x13 pixels of gray level 1
17
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
Opening
erosion followed by dilation, denoted ∘
• eliminates protrusions
• breaks necks
• smooth contours
A  B  ( A  B)  B
18
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
Opening
19
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
Closing
dilation followed by erosion, denoted •
• smooth contour
• fuse narrow breaks and long thin gulfs
• eliminate small holes
• fill gaps in the contour
A  B  ( A  B)  B
20
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
Closing
21
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
Opening-closing
22
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
Useful: open & close
23
KOM3212 Image Processing in Industrial Systems | Dr Muharrem Mercimek
Application: filtering
24

Histogram equalization