An algorithm for segmentation of images containing non-overlapping fibrilar domains
Nils PerssonDalar Nazarian
Determination of Fiber Orientation
Fiber angles range from -90° to +90°
Low-confidence (amorphous) regions show as -180°
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.
Determination of Fiber Orientation
How?
Threshold: 0.4 0.6
θ
For every threshold,Two matrices are constructed:
Orientation…
θθθ θ
θθ θθθ
0.4φ
0.6
θθ
θφ φφφ
How?
Threshold: 0.4 0.6
And Confidence
where conf ~ Mi / mi
(major / minor axis)
222 2
22 222
0.4 0.6
1.51.5
13 333
M1
m1
How?
222 2
22 222
0.4 0.6
1.51.5
13 333
Now we find the maximum confidence across all thresholds…
θθθ θ
θθ θθθ
θθ
θφ φφφ
Orient.
Conf.
How?
222 2
22 222
0.4 0.6
1.51.5
13 333
Now we find the maximum confidence across all thresholds…
And take their corresponding angles.
θθθ θ
θθ θθθ
θθ
θφ φφφ
222 2
23 333
Orient.
Conf.
How?
222 2
22 222
0.4 0.6
1.51.5
13 333
Now we find the maximum confidence across all thresholds…
And take their corresponding angles.
θθθ θ
θθ θθθ
θθ
θφ φφφ
222 2
23 333
Orient.
Conf.
How?
222 2
22 222
0.4 0.6
1.51.5
13 333
θθθ θ
θθ θθθ
θθ
θφ φφφ
222 2
23 333
θθ
φ φφφ
θθ
θ
Orient.
Conf.
Max
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.
But it works on noisy images with gradients in intensity across fibers…