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Orientation algorithm (1)
1. An algorithm for segmentation of
images containing non-overlapping
fibrilar domains
Nils Persson
Dalar Nazarian
2. Determination of Fiber Orientation
Low-confidence (amorphous) regions show as -180°
Fiber angles range from -90° to +90°
3. Determination of Fiber Orientation
Notice how fibers of the same orientation tend to come in clumps…
I think this is due to the entanglement of the tie-chains between fibers.
4. How?
Threshold: 0.4 0.6
θ
For every threshold,
Two matrices are constructed:
Orientation…
0.4
θ
θ
θ θ
θ
θ θ
θ θ
φ
0.6
θ
θ
θ
φ φ
φ φ
5. How?
Threshold: 0.4 0.6
0.4 0.6
And Confidence
where conf ~ Mi / mi
(major / minor axis)
2
2
2 2
2
2 2
2 2
1.5
1.5
1
3 3
3 3
M1
m1
6. How?
0.4 0.6
2
2
2 2
2
2 2
2 2
1.5
1.5
1
3 3
3 3
Now we find the maximum
confidence across all
thresholds…
θ
θ
θ θ
θ
θ θ
θ θ
θ
θ
θ
φ φ
φ φ
Orient.
Conf.
7. How?
0.4 0.6
2
2
2 2
2
2 2
2 2
1.5
1.5
1
3 3
3 3
Now we find the maximum
confidence across all
thresholds…
And take their corresponding
angles.
θ
θ
θ θ
θ
θ θ
θ θ
θ
θ
θ
φ φ
φ φ
2
2
2 2
2
3 3
3 3
Orient.
Conf.
8. How?
0.4 0.6
2
2
2 2
2
2 2
2 2
1.5
1.5
1
3 3
3 3
Now we find the maximum
confidence across all
thresholds…
And take their corresponding
angles.
θ
θ
θ θ
θ
θ θ
θ θ
θ
θ
θ
φ φ
φ φ
2
2
2 2
2
3 3
3 3
Orient.
Conf.
10. Minor complications
Threshold: 0.4 0.6
Since the borders of the lower segment got “thresholded out” when it split from
the main, their highest confidence was back when the two were connected.
This is rare and should not significantly affect spatial stats.
11. But it works on noisy images with gradients in intensity across fibers…