Algorithm 2:

Segment-wise thinning in orientation scores.

Input: the binarized orientation scores Ubf(x, y, θ).

Output: the 2D skeleton map Sf(x, y).

Initialization: for each point (x, y) ∈ f, set S(x, y) = 0.

1: for i = 1 to Nmc do

2:  extract the binarized morphological component $U_{mc}^i\left(x,y,\theta \right)$ with label i using (15).

3:  calculate the 2D map fi(x, y) of each component $U_{mc}^i\left(x,y,\theta \right)$ via (16).

4:  use morphological thinning operation on fi(x, y) and obtain the thinned component Si(x, y).

5:  update the thinning map S(x, y) ← S(x, y) + Si(x, y).

6:  end for

7:  obtain the final thinning map Sf(x, y) by applying morphological pruning on S(x, y) to remove tiny branches.