1. Lecture 8 Introduction to Binary Morphology
5th Intensive Course on Soil Micromorphology
Naples 2001
12th - 14th September
Image Analysis
Lecture 8
Introduction to Binary Morphology

2. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
Introduction to Binary Morphology Methods
Requires Segmentation of Image into Binary Form
(may require manual editting).
Foreground pixels are coded 1 - background 0
i.e. Particles 1 (white), voids 0 (black)
or Voids 1 (white), particles 0 (black)
Erosion/Dilation
Opening/Closing
Kernel Shapes
Applications in Particle / Void Size Distribution

3. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
Erosion
strips one layer of foreground pixels at edges of particles
criteria
based on number of surrounding background pixels
can be any number
pixel of interest is red
white - foreground
black - background

4. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
a) foreground pixel removed for all criteria.
h) foreground pixel removed only if criteria is set to 1 pixel.
Criteria may also specify that diagonal erosion is (or is not permitted).
Erosion not permitted if diagonals not allowed in (j)

5. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
Connectivity:
4 - point connectivity
allows connection only up/down and side to side
8 - point connectivity
allows connection on diagonals
In 4 - point connectivity, foreground and background are uniquely separated.
In 8 - point connectivity is background or foreground continuous across diagonal? Both are not possible

6. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
Erosion of original by one layer
criterion - a single touching background pixel
8 - point connectivity
4 - point connectivity

7. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
Erosion by 2 and 3 layers
8 - point connectivity
All foreground features will disappear.
Erosion by 2 and 3 layers
4 - point connectivity
Some residual parts of largest particle remain.
Until particles disappear the residues are less rough

8. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
Dilation
- the reverse of erosion
Once again similar criteria apply
4 - point connectivity
Individual features will merge
8 - point connectivity

9. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
8 - point connectivity erosion
Equivalent to passing a 3 x 3 kernel over binary image.
Where central point of kernel hits background, all pixels covered by kernel are set to background

10. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
4 - point connectivity erosion
Equivalent to passing a 3 x 3 kernel over binary image.
Where central point of kernel hits background, all pixels covered by kernel are set to background

11. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
Non-standard Kernels may be used for special effects

12. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
Consider effect of one erosion followed by one dilation.
This is known as an “OPENING”

13. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
Red: Residual after erosion
Yellow: Recovered after dilation
Blue: Complete particles lost
Green: Roughness lost on large
particles
Using careful housekeeping it is
possible to identify proportion of
particles lost completely and
“roughness” lost from large
particles.

14. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
2 cycles of erosion
(8 - point connectivity)
2 cycles of erosion followed by 2 cycles of dilation
(8 - point connectivity)
Components of “opening” - see next slide

15. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
Light Green: Roughness cycle 1
Dark Green: Roughness cycle 2
Red: Residue after 2 cycles
Yellow: Recovery cycle 1
Orange: Recovery cycle 2
Blue: Particles lost cycle 1
Purple: Particles lost cycle 2

16. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
2 cycles of 3 x 3 kernel are equivalent to 1 cycle by a 5 x 5 kernel.
Can be used for efficiency
Alternative kernel for 5 x 5 which approximates more closely to a circle (i.e. corner pixels are omitted)
Kernel for 3 cycles giving a good approximation to a circle / octagon).

17. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
Standard Kernels for 9 x 9 array
These 4 shapes can be propagated to any size

18. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
Procedure for feature size analysis
n = 1
n = n + 1
Yes
Erode n cycles
Dilate n cycles
Determine pixels lost as roughness
Determine pixels lost from particles
which disappear
Are particle residues
left No
Summarise results

19. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
Grey Level Image Binary Version
Schematic Representation of one erosion and one dilation

20. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
BINARY MORPHOLOGY
During successive opening, features tend towards circles.
At each stage, protrusions are lost and this loss is related to the shape and roughness of grains.
Finally, the remaining feature is lost and this is related to the size of the feature.
Careful housekeeping is needed to differentiate between two types of loss, but procedure is well established in some branches of microscopy.
The difficulty in achieving a reliable threshold makes the method generally unsuitable for analysing images of cores.

21. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology

22. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology

23. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
Binary Morphology used to determine Particle size Distribution

24. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
Roundness
Often defined relating to sharpness of asperities on a grain
Sometimes roundness is defined by drawing circles,
but when exactly should on draw a circle?

25. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
Grain is successively “opened” with different radii.
The lighter colours (yellow) show parts lost first.
Ultimately remainder of grain disappears when inscribed circle is as shown in blue.
If octagonal or square “structuring” elements are used, then grain degenerates to these shapes.

26. Image Analysis - Lecture 8: Binary Morphology
5th Intensive Course on Soil Micromorphology - Naples 2001
Image Analysis - Lecture 8: Binary Morphology
Grain is successively subjected to “opening” of different radii.
The edge of the grain are shown in colour where light colours (e.g. yellow represent areas lost first - i.e. sharp), and dark colours (e.g. dark blue are lost last.
Can be used as a more objective measure of roundness.