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…