Docteur de l'université Automatic Segmentation and Shape Analysis ...

60 Chapter 3 Hippocampal segmentation using multiple atlases
such that each of its column sj · Ij ◦ Tj(Ω) is a |Ω| dimensional vector representing
the signed atlas image sk · Ik ◦ Tk of |Ω| voxels. With |A | ≥ 2, the LAR algorithm
for atlas selection is listed in Algorithm 4.
Algorithm 4 Atlas selection by LAR (Efron et al., 2004)
1: while |A | ≤ the number of atlases to be selected do
2: for all k, update the correlation ĉk ← C(Ik ◦ Tk, I − ÎA )
3: Ĉ ← maxk{ĉk}
4: for all k do
5: sk ← sign(ĉk)
6: end for
7: XA ← (sk · Ik ◦ Tk) , k ∈ A
8: GA ← X T
9:
A XA
AA ← (
1T A G −1
A 1A
) 1
− 2
, where 1A is a one-vector of length |A |
10: compute the least-angle image UA
Tk
such that C(Ik ◦ Tk, UA ) = C(Ik ′ ◦
′, UA ), ∀k, k ′ ∈ A
11: for all k do
12: ak ← C(Ik ◦ Tk, UA )
13: end for
14: ˆγ ← min +
{
Ĉ−ĉk
k /∈A AA −ak ,
only positive components
15: select the atlas ˆ k ← arg min +
{
Ĉ−ĉk
k /∈A AA −ak ,
16: A ← A ∪ { ˆ k}
17: update ÎA ← ÎA + ˆγUA
18: end while
}
Ĉ+ĉk , where min AA +ak
+ indicates the minimum takes
}
Ĉ+ĉk
AA +ak
Analysis of computational complexity shows that LAR is efficient. When n < |Ω|,
the computational complexity of entire LAR sequence will be O(n 3 +|Ω|·n 2 ) which
is linear to the number of voxels |Ω| (Efron et al., 2004).
3.4 Results and discussion
In the experiments, we constructed an population specific set of atlases from the
elderly population enrolled in the Australian Imaging, Biomarker & Lifestyle Flag-
ship Study of Ageing (AIBL) study, using our proposed supervised method, ini-
tialized with the generic IBSR atlases. In total 40 atlases of elderly subjects are
produced and evaluated in terms of their agreement propagated on the larger
elderly population.