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50 Chapter 3 Hippocampal segmentation using multiple atlases
3.1.3 Label fusion
The most simple method of label fusion in multi-atlas based segmentation is ma-
jority vote rule, in which the labeling of each voxel is determined by the consensus
ˆL(x) = arg max |{k ∈ A : Lk ◦ Tk(x) = l}| . (3.12)
l∈L
More sophisticated approach is to use weighted votes
ˆL(x) = arg max
l∈L
∑
k∈A and Lk◦Tk(x)=l
wk(x). (3.13)
In the local weighted voting (LWV, Artaechevarria et al., 2009), the weights are
calculated by a similarity metric on the neighbourhood Nx of the voxel x. Using
the mean squared difference (MSD)
wk(x) = MSD(Ik ◦ Tk(Nx), I(Nx)) p
(3.14)
provides the best performance on the subcortical structures, where p is a negative
integer.
The formulation of MSD permits an efficient implementation to calculate the
weight wk(·). We define the MSD MI,J(·) image between image I and J as
MI,J(x) ≡ MSD(I(Nx), J(Nx)) = 1
|Nx|
∑
(I(y) − J(y)) 2 , (3.15)
y∈Nx
which is equivalent of applying a mean filter (over the same neighborhood defi-
nition as N(·)) to the squared difference image (I − J) 2 . The algorithm for the
computation of the local weight wk(·) is listed in Algorithm 1.
Algorithm 1 Computation of the weight wk(·)
1: Compute the squared difference image SDk ← (Ik ◦ Tk − I) 2
2: Compute the MSD image Mk ← SDk ⋆ Kmean, where Kmean is the kernel of
mean filter
3: Compute the weight wk ← (Mk) p by applying power function to Mk