Segmentation of 3D Tubular Tree Structures in Medical Images ...

68 Chapter 4. Tube Segmentation
obtained from a gradient magnitude image. In this way, the voxels associated with the
centerline of a tubular structure are segmented.
Algorithm 2 Inverse gradient flow tracking tube segmentation for GVF obtained from
gray value image.
input: GVF field V (x) with direction V n (x) and magnitude M(x)
input: centerline points C = {x 1 , x 2 , . . . , x n }
set S ← C
queue Q ← C
while Q ≠ {} do
x ← extract(Q)
for each voxel y ∈ Adj26(x) do
if y /∈ S and M(y) > M(x) and argmin z∈Adj26(y) 〈V n (y), −→ yz〉 = x then
S ← S ∪ {x}
Q ← Q ∪ {y}
end if
end for
end while
output: segmented tube voxels S
Algorithm 3 Inverse gradient flow tracking tube segmentation for GVF obtained from
gradient magnitude image.
input: GVF field V (x) with direction V n (x) and magnitude M(x)
input: centerline points C = {x 1 , x 2 , . . . , x n }
set S ← C
queue Q ← C
while Q ≠ {} do
x ← extract(Q)
for each voxel y ∈ Adj26(x) do
if y /∈ S and argmin z∈Adj26(y) 〈V n (y), −→ yz〉 = x then
S ← S ∪ {x}
Q ← Q ∪ {y}
end if
end for
end while
output: segmented tube voxels S
4.3 Graph Cut Based Tree Segmentation
In this section, we present an approach to accurately delineate the boundary of tree structures
in a globally optimal manner using a graph cut segmentation approach [17]. The