Algorithm 1 Branch detection algorithm Sample N directions di∀i ∈ (1, N) uniformly off the sphere 2.

Construct tubes of radius 1 and length R along each of the N directions, originating at the end point under analysis.

Calculate the mean image intensity within each tube as Imean(di).

Threshold the estimated mean intensities with respect to the parent branch intensity Ithres.

Extract the subset of directions di with mean intensities above the threshold.

Apply k-means clustering [64], [65] to the extracted directions di∀i ∈ (1, N) and Imean(di) > = Ithres, with a target of 3 clusters.

if Number of non-empty clusters < 3 then

Declare nonexistence of branching at end point under analysis

else

Compute the centroid of the directions in each cluster, to yield 3 candidate branch directions.

Eliminate the candidate direction that has maximum overlap with the parent branch's volume.

Compute the dot products of the 2 remaining candidate directions with the tangent of the parent branch at the end point.

Extend the parent branch by the candidate direction better aligned with the tangent at the end point.

Create a new branch in the tree structure using the 1 remaining candidate direction.

end if