Algorithm 1 Path calculation algorithm.

input: cost image C

input: set of start point(s) S

input: local path length parameter lmax

output: map with predecessor points on path pred

function CalculatePaths(C, S)

▷ Initialize

Q ← empty priority queue

for each voxel v in C do

pred[v] ← undefined

end for

for each point v in S do

pred[v] = root

for each neighbor x of v do

Q ← Q ⋃ {(C[x], x, v)}

end for

end for

▷ Extend paths

while Q is not empty do

tuple t ← popmin(Q)

v ← second(t)

if pred[v]= undefined then

pred[v] ← third(t)

for each neighbor x of v do

c ← LocalPathCosts (C, pred, v, x)

Q ← Q ⋃ {(c, x, v)}

end for

end if

end while

return pred

end function