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

Chapter 3 Hippocampal segmentation using multiple atlases 57
the similarity measurement between two atlases
SimNMI(Ai, Aj) = 1 (
2
SimC(Ai, Aj) = 1
2
3.3.1.2 Atlas selection by MMR algorithm
Sim A
NMI(Ai, Ij) + Sim A
NMI(Aj, Ii) )
(3.22)
(
Sim A
C(Ai, Ij) + Sim A
C(Aj, Ii) )
. (3.23)
We initialize the set of selected atlases A to be empty and select one atlas each
iteration. At each iteration, the atlas ˆ k is selected according to MMR, such that
(
ˆk = arg max λSim
k /∈A
A
(·)(Ak, I) − (1 − λ) max
j∈A Sim(·)(Aj,
)
Ak) , (3.24)
until the selected atlas set A reaches a preset threshold. The similarity Sim A
(·) and
Sim(·) are to be substituted in practice by the metrics described previously. The
parameter λ ∈ (0, 1] controls the similarity measurement Sim A
(·)(·, ·). In addition
to similarity, diversity is introduced by penalizing the redundancy
max
j∈A Sim(·)(Aj, Ak) (3.25)
within the selected set A . When λ = 1, MMR is equivalent to the similarity
ranking using Sim A
(·)(·, ·).
The algorithm of atlas selection using MMR is listed in Algorithm 3. The matrix
of atlas similarity (
Sim(·)(Ai, Aj) )
can be pre-computed and stored.
i,j=1,··· ,n
Algorithm 3 Atlas re-ranking by MMR
1: ˆ k ← arg max Sim
k
A
(·)(Ak, I)
2: A ← { ˆ k}
3: while |A | ≤ the ( number of atlases to be selected do
4: kˆ ← arg max λSim
k /∈A
A
5: A ← A ∪ { ˆ k}
6: end while
(·)(Ak, I) − (1 − λ) maxj∈A Sim(·)(Aj, Ak) )