2. Agenda
• Introduction
• Different Approaches
• Method 1
• Method 2
• Method 3
• Comparison & Results & Comments
• Nine-Point Circle for Cell Segmentation
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Nine-Point Circle Rule
How to use?
Results
Implementation
• Conclusion and further work
3. Background
• Learn image processing basics
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Fundamentals
Intensity Transforms
Spatial Filtering
Frequency Domain Processing
Image Segmentation
• Implement different methods in MATLAB and compare them
• Based on the results, improve the algorithm
4. 1st and 2nd Method
1st Method
• Thresholding:
• im2bw with graythresh
• Filling with holes
• imfill with holes
• Counting:
• Numobjects of
bwconncomp
2nd Method
• Thresholding:
• im2bw with graythresh
• Filling with holes
• imfill with holes
• Counting:
• Lenght of bwboundaries
8. Comments
• First two approaches uses nearly the same algorithm except their
counting methods.
• The first algorithm underestimate the number of objects.
• The second algorithm overestimate the number of objects.
• 3rd approach :
• Without watershed segmentation has achieved promising results
when the cells in the image are not connected.
• With watershed segmentation over-segments or mis-segments the
figure, so overestimate the number of objects.
• Challenges: connected cells, incomplete cells on the borders
• Another solution technique can be useful for the solution of
connected cells problem.
9. Nine-Point Circle
• Also known as the Feuerbach Circle
• In every triangle,
lie on a circle:
• The three midpoints of the sides
• The three base points(feet) of the altitudes
• The midpoints of the three segments from the orthocenter to the
vertices
Reference: Dorrie, H. and Woltermann, M, '100 Great Problems of Elementary Mathematics', reworked in 2010
10. How to use?
• Arbitrarily select three points from cell
• Example: A,B,C
• Find 9 points which are
• 3 midpoints
• Example: D,E,F
• 3 base points(feet) of the altitudes
• Example: G,H,I
• Midpoints of 3 segments
from the orthocenter to the vertices
• Example: K,L,M
• Please note that: J is orthocenter.
• Count the points inside the cell:
• D,E,G,K,L,M => 6 inside / 9 total
• Repeat the procedure until the average is an appropriate result
12. Conclusion
• When useful?
• When cells have circular shapes
• Why?
• The more circular the shape, higher the average algorithm gives
so,When the cells are not connected, the average will be higher.
• Can help to distinguish the cells whether connected or not.
• Why important?
• For cell segmentation, not tried before ( based on subjective(my) research)
• Challanges?
• Defining the standard to understand whether cells are connected
• Clear bordering is necessary to run correctly
• Hard to distinguish if cells are connected circularly
13. Future Study
• For nine-point rule cell segmentation:
• Divide the given image in appropriate divisions
• Try on cell images
• Documentation related to all studies
